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Maths and people Maths is all about people. People are measured by their height, their
weight, the size of their feet and the size of their clothes.
First, let your child draw around
one of their hands and then let them draw around yours. Next, place 1p coins inside the outline
of the hands and draw around them so you donít leave any spaces.
Add up the value of the coins. How
much is their hand worth? How much is your hand worth? Is it worth twice as much if you do
the same with 2p coins? Try it with other coins too. How much is it worth using 5p coins?
you as long as you are wide?
Stretch your arms out and measure the length from the fingertips on one
of your hands to the fingertips on your other hand. This gives you your
arm span. Then, compare the width of your arm span to the length of your
body. Do it with other members of the family and what do you find?
(It is usually about the same!)
many days old are you?
Before you start to work this out using a calculator, try to guess. Have
a good guess, not a wild one! Here are a few tips to start you off.
Take your age in years and multiply
it by 365 (but remember itís 366 for each leap year).
Count the number of days since your
last birthday. Add them all together. Too easy? If
so, work out how many minutes old you are.
Scaling the weights
your child on the bathroom scales. Weigh them again while they are holding
the family pet. Can they work out how much heavier they are? Can you find
two things heavier than your child and two things lighter than your child
around the house?
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Draw a Story
Age Range: 5 to 11
1) Give each child in your class a copy of the storyboard sheet found here.
2) Ask them to make up a story about anything that they want.
3) Ask them to draw the events of the story in the larger boxes in the sheet. The smaller boxes are for text, but they should not fill these in at the moment.
4) When the children have finished their drawings, collect in the storyboards, mix them up, and give them back (but not to the correct children). Now, each child should be looking at a storyboard which is not their own.
5) They should now look carefully at the pictures, and make up some text to go with them.
6) When this is done, the writer and the artist should get together and look at what each other have done. Does the artist agree with the story that the writer has made? Was this what the artist had in mind at the beginning?
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In this chapter we will learn to speak the language of arithmetic. That will allow us to relate any two numbers. We will learn to say, for example, that 6 is the fourth part, or one quarter, of 24, and that 18 is three quarters of 24. We are not concerned here with "How do you do it?" but, rather, "What does that mean?"
What is more, to really understand Percent, it is necessary to understand parts, because a percent is a part of 100%. 50% means half -- because 50 is half of 100. 25% means a quarter, beause 25 is a quarter of 100. And 20% means a fifth, because 20 is the fifth part of 100.
Finally, fractions (Lesson 20) are parts of number 1.
In this Lesson, we will answer the following:
|1.||What is a natural number?|
|It is a collection composed of units; of the same indivisible ones to which we give a name and a symbol.|
The symbols 1, 2, 3, 4, and so on, are the familiar Arabic numerals for the natural numbers. It has become conventional to call those symbols themselves "numbers." Yet a symbol is not what it symbolizes, what it stands for, which in this case is a number of units.
Cardinal and ordinal
The names of the natural numbers have two forms: cardinal and ordinal. The cardinal forms are
One, two, three, four, etc.
They answer the question How many? The ordinal forms are
First, second, third, fourth, etc.
They answer the question Which one? We will see that the ordinal numbers, as they are called, express division into equal parts. They will name which part -- the third part, the fourth, the fifth, and so on.
By a number in what follows, we will mean a natural number.
|2.||What do we mean by the multiples of a number?|
|They are the numbers produced when that number is repeatedly added.|
Here are the first few multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40.
5 is the first multiple of 5; 10 is the second multiple; 15, the third; and so on.
|3.||What does it mean to say that a smaller number is a part of a larger number?|
|It means that the larger number is a multiple of the smaller. Equivalently, the smaller is contained in the larger an exact number of times.|
5, then, is a part of each one its multiples except itself.
(We do not call 5 a part of 12, because 12 is not a multiple of 5. We are speaking throughout of what is called an aliquot part.)
How do we name the part that a smaller number is
of a larger?
|With an ordinal number. With the exception of "half," an ordinal number will name which part.|
Here again are the first few multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40.
Now, since 15 is the third multiple of 5, we say that 5 is the third part of 15. We use that same ordinal number to name the part.
Since 20 is the fourth multiple of 5, we call 5 the fourth part of 20. 5 is the fifth part of 25, the sixth part of 30; and so on. But, 5 is half of 10. (We do not say the second part.) And 5 is not a part of itself; there is no such thing as the first part.
So with the exception of "half," an ordinal number names into which parts a number has been divided.
15 has been divided into Thirds; that is, into three equal parts.
5 is the third part of 15.
If we divide a number into four equal parts,
then we have divided it into fourths (or quarters); if into five equal parts,
into fifths. But if we divide into two equal parts, then we have divided it in half.
It is important to understand that we are not speaking here of proper fractions -- numbers that are less than 1, and that we need for measuring. We are explaining how the ordinal numbers --- third, fourth, fifth, etc. -- name the equal parts into which a number has been divided. When answering the questions of this Lesson, the student should not write fractions. We will come to those symbols in Lesson 20.
It should be clear that the ordinal names of the parts belong to language itself, and are prior to the names of the proper fractions, because the proper fractions are the parts of 1.
|Why is the number we write as 1 over 3 --||1
"one-third"? Because the numerator 1 is one third
of the denominator 3.
That must be understood first. We can then explain
|that the number we call||1
|is one third of 1.|
Example 1. 3 is which part of 18?
Answer. The sixth part. 3 is contained in 18 six times.
Note that 1 is a part of every number (except itself), because every number is a multiple of 1. Which part is it? The part that says the number's name.
1 is the third part of 3, the fourth part of 4, the fifth part of 5, the hundredth part of 100. 1 is half of 2.
Example 2. What number is the fourth part, or a quarter, of 28?
Answer. 7. Because 28 is made up of four sevens.
Example 3. 2 is the fifth part of what number?
Answer. 10. Because five 2's are 10.
Every number is the fifth part of five times itself
4 is the fifth part of 5 × 4, which is 20.
9 is the fifth part of 5 × 9, which is 45.
20 is the fifth part of 5 × 20, which is 100.
|5.||How can we calculate a part of a number?|
|Divide by the cardinal number whose name corresponds to the part. To take half of a number, divide by 2. To take a third, divide by 3. And so on.|
See Lesson 11, Question 2, and especially Example 5.
Example 4. How much is an eighth of $72?
Answer. 72 ÷ 8 = 9. An eighth of $72 is $9.
Example 5. Tenths, hundredths. How much is a tenth of $275?
How much is a hundredth?
Answer. To find a tenth, divide by 10.
275 ÷ 10 = 27.5
Since this is money, we report the answer as $27.50. (Lesson 3.)
As for a hundredth, we will separate two decimal digits:
$275 ÷ 100 = $2.75
Therefore, 10% of $275 is $27.50. 1% is $2.75.
Note: Whenever we divide by any power of 10 -- the digits do not change.
275 ÷ 100 = 2.75
Conversely, then, if two numbers have the same digits, they differ by a power of 10.
Example 6. $85 is which part of $850?
Answer. Apart from the 0 at the end of $850, those numbers have the same digits. Therefore, they differ by a power of 10. 850 is in fact 10 times 85. (Lesson 4, Question 1.) Therefore, $85 is the tenth part of $850. To say the same thing, $85 is 10% of $850.
Example 7. $.98 is which part of $98?
Answer. They have the same digits. They differ by a power of 10.
$.98 is the hundredth part of $98. It is 1% of it.
We say that a smaller number is a divisor of a larger if the larger number is a multiple of the smaller. 3 is a divisor of 12, because 12 is a multiple of 3. 5 is not a divisor of 12. We say however that a number is a divisor of itself. With the exception of the number itself, the divisors of a number are the only parts that a number has. 3 is the fourth part of 12. 5 is not any part of 12; you cannot divide 12 people into groups of 5.
Example 8. Find all the divisors of 30 in pairs. Each divisor (except 30) is which part of 30?
Answer. Here are all the divisors of 30 in pairs:
1 and 30. (Because 1 × 30 = 30.)
2 and 15. (Because 2 × 15 = 30.)
3 and 10. (Because 3 × 10 = 30.)
5 and 6. (Because 5 × 6 = 30.)
On naming which part of 30, each divisor will say the ordinal name of its partner:
1 is the thirtieth part of 30.
2 is the fifteenth part of 30. 15 is half of 30.
3 is the tenth part of 30. 10 is the third part of 30.
5 is the sixth part of 30. 6 is the fifth part of 30.
Divisors always come in pairs. And that implies the following:
Theorem. For every divisor (except 1) that a number has, it will have a part with the ordinal name of that divisor.
(Euclid, VII. 37.)
Since 18, for example, has a divisor 3, then 18 has a third part. Since 18 has a divisor 6, then 18 has a sixth part. But 18 does not have a fifth part, because 5 is not a divisor of 18.
Here is an illustration that 18 has a divisor 3:
18 = 6 × 3.
But according to the order property of multiplication:
18 = 3 × 6.
This shows that 6 -- the partner of 3 -- is the third part of 18.
In other words, since 18 has a divisor 3, then 18 has a third part.
Example 9. Into which parts could 12 people be divided?
Answer. The divisors of 12 are
1, 2, 3, 4, 6, and 12.
Corresponding to each divisor (except 1), there will be a part with the ordinal name of the divisor. 12 people, therefore, could be divided into
Halves, thirds, fourths, sixths, and twelfths.
You cannot take a fifth of 12 people. 12 does not have a divisor 5.
Percent: Parts of 100%
A percent is another way of expressing a part. Because whatever part the percent is of 100%, that is the part we mean.
Since 50% is half of 100%, then 50% means half. 50% of 12 -- half of 12 -- is 6.
Since 25% is a quarter, or a fourth, of 100% --
-- then 25% is another way of saying a quarter. 25% of 40 -- the fourth part of 40 -- is 10.
In the next Lesson, Question 10, we will see how to take 25% by taking half of half
Since 20% is the fifth part of 100% --
(100 is made up of five 20's) -- then 20% is another way of saying a fifth. 20% of 15 -- the fifth part of 15 -- is 3.
See Problems 13 and 14.
Repeated division in half
Every time we take half of something, we get twice as many parts. Half of a whole -- --
-- results in two equal parts. Each part is Half.
If we divide each Half in half --
-- the whole will be in four equal parts, or Quarters.
If we divide each Quarter in half --
-- the whole will then be in twice as many, that is, eight equal parts, or Eighths.
Half of an Eighth is a Sixteenth. Half of a Sixteenth is a Thirty-second. And so on.
Now, here are the number of equal pieces that result when we repeatedly take half:
2, 4, 8, 16, 32, 64, and so on.
Those numbers are called the powers of 2. Repeated division in half is very common. The student should know the names of the sequence of those parts:
Halves, Quarters, Eighths, Sixteenths, Thirty-seconds, and so on.
When we say "5 is the third part of 15," we do not imply a sequence: the first part, the second part, the third, and so on. When we speak of the third part, that is a different meaning for the word "third." It means each one of three equal parts that together make up the whole.
We say that we have divided 15 into thirds.
Yet "third" still retains its ordinal character. Because to the question, "Which part of 15 is 5?", we answer,
"The third part." We use that ordinal number because 15 is the third multiple of 5.
At this point, please "turn" the page and do some Problems.
Continue on to the next Section: Parts, plural
Please make a donation to keep TheMathPage online.
Even $1 will help.
Copyright © 2013 Lawrence Spector
Questions or comments?
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CA Geometry: Secants and Translations 76-80, secants and graph translations
CA Geometry: Secants and Translations
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- We're on 76.
- In the figure below, line AB is tangent to
- circle O at point A.
- Fair enough.
- Secant BD intersects circle O at points C and D.
- Secant just means that it intersects the
- point at two points.
- It's not tangent.
- A tangent intersects the circle at exactly one point.
- Secant BD intersects the circle at points C and D.
- Measure of arc AC is equal to 70 degrees, and the measure of
- arc CD is equal to 110 degrees.
- So what do they want us to figure out?
- What is the measure of ABC?
- So what is this angle?
- That's what they want us to figure out.
- They want us to figure out this right here.
- That angle.
- Let's see what we can do here.
- So there's a couple of ways to think about it.
- Well, if you look at it, this is 70, this is 110, right?
- So if you add them, this whole arc, going for all the way
- around, that's 180 degrees.
- So it's actually perfectly halfway around the circle.
- So actually from A to D is actually a
- diameter of the circle.
- How do I know that?
- Because it goes all the way around the circle.
- The arc length is 180 degrees.
- So we can draw-- let me draw a diameter line.
- I don't know if this thing is drawn to scale.
- A to D is actually a diameter of the circle.
- We know that, because that's 180 degrees, the combined arc
- length right there.
- And we know, that this line is tangent at point A.
- So that has to be a right angle.
- When you're tangent at point A, that means your tangent to
- the radius at that point.
- Fair enough.
- So now let's see what we can figure out.
- We know that this arc length is 70.
- Is there any way to figure out what this angle right here is?
- Because if we know this angle, we know this is 90, then we
- could figure out that angle.
- And this is something that you should just learn about
- inscribed angles in a circle.
- This is an inscribed angle, because the vertex touches on
- one of the sides of the circle.
- So an inscribed angle-- and this is just something good to
- memorize, and you could play around with it to get a little
- bit more intuition about it-- is equal to half of the arc
- length that it intersects.
- So this inscribed angle intersects an arc
- length of 70 degrees.
- So this is 35 degrees.
- And that's just something good to know.
- That this is going to be half of whatever
- this arc length is.
- Now we can figure out x, because x plus 35 plus 90 is
- equal to 180.
- You get x plus 35 is equal to 90. x is equal to 90 minus 35
- is 55, which is choice C.
- Now there's another way you can do this, and this is
- another interesting thing about lines that
- intersect in circles.
- It's that this angle measure, right here, if it's sitting
- outside of the circle-- I think there might be ones
- sitting inside the circle later on-- but if it's sitting
- outside of the circle, it's equal to 1/2 the difference of
- the arc measures that it intersects.
- So for example, it intersects this arc measure of 70, and it
- also has this arc measure right here.
- When it hits the circle and intersects at 70 degrees and
- when it exits the circle, it has this arc measure.
- This arc measure we already figured out.
- It's 180 degrees, because that's 180 degrees.
- So you know that this angle right here, you could say that
- x is equal to 1/2 the difference of these two arc
- measures, and we can do that because x is
- outside of the circle.
- If x was inside the circle, then x would be 1/2 the sum of
- the two measures.
- So what's the difference?
- It's 180 minus 70.
- So that's equal to 1/2 times 110, so that is equal to 55.
- So it's nice to see that math works correctly no matter how
- you do the problem.
- Problem 77: In the circle shown below, the measure of
- arc PR is 140 degrees.
- Sure enough.
- The measure of angle RPQ is 50 degrees.
- OK, that's 50 degrees.
- What is the measure of arc PQ?
- What is this arc right there?
- So we could use what we learned in the last problem.
- 50 degrees is an inscribed angle.
- So it's going to be half of the arc length measured in
- degrees, or arc angle, I guess you could say, of the arc that
- it intercepts.
- So this is 50, then this arc measure is
- going to be 100 degrees.
- So what we're trying to figure out, this arc measure right
- here, it's whatever you really have left over.
- Let's call this x.
- So we know that x plus 100 plus 140, well, that goes all
- the way around the circle, right?
- That's going to be equal to 360 degrees.
- So you have x plus 240 is equal to 360 degrees.
- Subtract 240 from both sides, and you get x is
- equal to 120 degrees.
- Choice D.
- Problem 78: The vertices of triangle ABC are A is 2 comma
- 1, B is 3 comma 4, and C is 1 comma 3.
- If triangle ABC is translated one unit down-- so one unit
- down means that we're subtracting 1 from the y's--
- and three units to the left-- so that means you're
- subtracting 3 from the x's-- to create triangle DEF, what
- are the coordinates of the vertices of DEF?
- So let's see, we have A is 2 comma 1.
- And that's going to be translated to point D.
- What do they say?
- One unit down.
- One unit down means the y decreases by 1.
- So the y-coordinate's going to be-- decrease that
- by 1, you get 0.
- And three units to the left, that means you decrease the
- x-coordinate by 3.
- So 2 minus 3 is negative one.
- Actually, just looking at the choices, we're already done.
- D is the only choice that had a negative 1 comma 0.
- But let's look at the other ones.
- Maybe somehow they changed the lettering or something.
- Let's see point B was 3 comma 4.
- So what do we do?
- With x, we said three units to the left, so that
- becomes point E.
- So you take this three units to left.
- You're subtracting 3 from there, that becomes 0.
- If you take the y-coordinate one unit down,
- that becomes a 3.
- So E is 0 comma 3.
- So that's still consistent with this.
- And let's just make sure that the F works.
- So C was 1 comma 3.
- If we take 3 away, we shift it to the left by 3, so that's
- taking 3 away from the x-coordinate, so
- that's minus 2.
- And if you're shifting the y-coordinate down one, that's
- taking 1 from it, so that's 3, so F is minus 2 comma 2.
- And so D was definitely the answer.
- Problem 79: If triangle ABC is rotated 180 degrees about the
- origin, what are the coordinates of A prime?
- OK, so we're going to rotate this thing 180 degrees.
- And essentially, we can worry about all the coordinates, but
- they just want to know where A prime is, so wherever A sits
- after we've rotated it.
- So let's think about it a little bit.
- When we've rotated the C, this is going to be the new C.
- It's going to be right there.
- B is going to be, when you rotate it-- I just want to
- make sure I'm doing this right.
- This is almost like a visualization problem.
- If you go four to the right and up three.
- So if you were to rotate it around.
- Let's say this little arrow I drew with the four, if I were
- to rotate that 180 degrees-- I just want to make sure I do it
- right-- then that's going to be four this way.
- So you're going to be at that point.
- And then instead of three up, you're going to go three down.
- So that's where A prime is going to be.
- Right at that point.
- And that's the point minus five comma minus four.
- And that's our answer.
- But let's figure out all of the other points.
- So B, you go up three and to the right two.
- The new B, you'd go three down to the left.
- OK, it would be there.
- So that's the new B.
- And so that looks right.
- That's what the triangle is going to look like.
- This is B prime, this is A prime, this is C prime.
- This is the new triangle when you rotate it 180 degrees.
- That was a challenging visualization problem, but the
- key thing is just to keep visualizing
- going around 180 degrees.
- So minus five comma minus four, that's
- choice A for A prime.
- Problem 80: Trapezoid ABCD below is to be translated to
- trapezoid A prime, B prime, C prime, D prime by the
- following motion rule.
- What will be the coordinates of vertex C prime?
- OK, so that's all we have to worry about.
- We're at C and we're going to translate it to some C prime.
- What of the coordinates of C?
- x is equal to five, and y is equal to 1.
- So what's C prime going to be equal to?
- C prime, we'll just use this mapping rule.
- You add 3 to the x, so it's going to be 8, and you
- subtract 4 from the y.
- 1 minus 4 is minus 3.
- 8 minus 3.
- That's choice D.
- And we're all done.
- We're all done with the entire California Standards geometry
- test. And frankly, I started off grumbling a little bit,
- because I thought they were getting a little bit too
- obsessed with the terminology.
- But overall, I think this was a pretty good test. And if you
- understood every problem on this exam, I think you know
- your geometry pretty well.
- Anyway, see you in the next video, although this is the
- last in this geometry series.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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Working with Squares and Square Roots
Students will need to know how to solve problems that include squares and square roots. Help students become comfortable with the keys they will need to use to perform these functions.
The square key is one of the most frequently used keys. To determine the square of a number, first enter the number, and then press the key.
Above the sign is a square root sign in yellow. To compute a square root, first enter the number, and then press the key followed by the key. This engages the square root function.
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Here's what you'll need:
2 "D" cells
3 pieces of aluminum foil cut into strips 6 inches long by 1/4 inch wide
2 standard flashlight bulbs
A roll of cellophane tape
|Here's what to do:|
|Hook up a single battery to a bulb using the aluminum foil strips:|
|1. Tape one strip of foil to the positive (+) end of the battery and a second strip to the negative (-) end of the battery.|
|2. Touch the free end of the positive (+) strip to the metal side of the bulb right below the glass and the free end of the negative (-) strip to the little silver tip at the bottom of the bulb.|
At this point, the bulb should light! Now you're ready for the challenge.
1. What will happen to the brightness of the bulb when you add the second battery to the circuit? Try it yourself! How must the second battery be turned in order to get the bulb to light?
2. What happens to the brightness of the bulb when you add a second bulb to the circuit? Once you've got your results with the two batteries and the single bulb, use the third foil strip to insert the second bulb in the circuit. What happens to the brightness of the bulb now? Why do you think the change occurred? What happens to the bulbs if any of the connections in the circuit break?
Before you try this Science Lab, predict with your classmates what will happen to the brightness of the bulb when you hook up the second battery. Also, make sure you explain HOW the battery must be inserted into the circuit in order to get the bulb to light up. Then, predict what will happen when you add the second bulb to the circuit.When you've finished the Science Lab, share the results with the rest of your class. Make sure you explain how you got these results. Be sure to answer the challenge questions!
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Rational: For children to read and spell words, they first need to be able to recognize the letters and be able to determine what phoneme they make. Consonant elements are either single consonants, consonant digraphs, or consonant blends. This lesson will help children identify /l/ which is a single consonant. Students will be able to recognize /l/ in spoken words by learning a meaningful representation, a letter symbol, and practice recognizing words, that begin with and contain /l/.
Materials: Primary paper, pencil, lettered squares(pieces of paper or construction paper that has different letters written on them such as "a" "b", etc.), crayons, worksheet( see number 8), and Lonely Lula Cat by Joseph Slate.
Procedures: 1. Introduce the lesson by helping students say the letter "l" by learning how to move their mouth properly. Class, today we are going to move our mouths to say /l/. /l/ is usually an easy letter to say and we are going to practice saying it and see if you can spot it in words we say each day.
2. Do you like to sing songs and chants? Have you ever dreamed of becoming a famous singer? We are going to pretend that we are all famous with Barney and we are preparing our voices before we go on stage. First, take a big breath, then put the tip of your tongue on the roof of your mouth where your teeth meet the skin. After all of that push your tongue down toward your bottom teeth while you breathe out - /l/. Now let's all practice. Once you can do it say /l/ fast, four times. You've got it! Class now let's practice a word using /l/ - lazy ladybug.
3. Let's try a tongue twister (on board). "The little lazy ladybug laid on the leaves." Now, everyone say it together. This time when you hear a word with /l/ stretch the /l/ out. Like this "The llittle lllazybug lllaid on the llleaves." That was great, you are all doing very well.
4. Now let's do some practice recognizing the letter "l." In front of the class the teacher asks for four volunteers. She gives each volunteer a square that has a letter on it. The first child has an "l," the second child has the letter "a," the third child has the letter "m," and the fourth child has the letter "p." Who is holding the letter "l?" Child's name , hold up the letter "l." Class what sound does /l/ make. Repeat this process with all of the letters. After you have pronounced and practiced all letters, say the word together. You can do this exercise with other words too. This will test letter recognition.
5. (Have students take out primary paper and pencil). We can
use the letter "l" to spell /l/. Let's write it. First watch
me. For the capital "L" start in sky, go straight down to the side
walk and walk to your right. Now let's all practice. As you
practice I am going to walk around and look at your "L"'s, after I put
a smile on your paper, put your pencil down. Now that everyone can
make a capital "L" letter, we are going to practice making a lowercase
"l." Start at the sky and come straight down to the sidewalk, and
stop. Now let's all practice. As you practice I am going to walk
around and look at your "l"'s, after I put a smile on your paper, put your
6. Call on students to answer and tell how they knew: Do you hear /l/ in lion or mouse? Little or big? Laugh or cry? Doll or truck? Slow or fast?.
7. Read: Lonely Lula Cat by Joseph Slate, then talk about the story. Read it again and have the students say "la la la" when they hear words with /l/. List the words they say on the board. Then have each student write a story about a friend and tell why that friend is special to them, using inventive spelling. Have each student read their story to the class, then display them.
8. For assessment: I will make a worksheet. At the top of the worksheet it will have two lines like their primary paper. On the lines they are to practice making capital and lowercase "l." Under the lines will be several pictures, some of "l" words along with pictures not of "l" words, such as lion, lamp, ladybug, doll, seal, bat, chair, mouse, snail. The students will then color the pictures of "l" words with a yellow crayon. They can color the other pictures any color that they choose.
Reference: Elderedge, Lloyd J. (1995) Teaching Decoding in Holistic Classrooms. Englewood Cliffs, NJ: Merrill.
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“A” What Did You Say?
A key ingredient to fluency is to learn how to read and spell words. One aspect of words that can be challenging to students is a diagraph. A diagraph is one phoneme or grapheme made up of more than one letter.There are many different diagraphs. This lesson will focus on the ay=/A/ correspondence. After the completion of this lesson, the students should be able to identify words in written and spoken language that contain ay=/A/.
Primary paper, pencil, chart with rhyme, class set of cards with ay on one side and a question mark on the other, book – Ray and the Blue Jay, picture page for assessment containing pictures of a child playing (play), the color gray (gray), someone praying (pray), a person paying for something at a checkout counter (pay), and a building swaying (sway), Elkonin Letter Boxes, alphabet letters for each student, oversized letterbox set to be used for whole class modeling.
1. Today we are going to learn some words that use the letter a and the letter y. Together they form to make a new sound. Sometimes when you put letters together they can make a new sound. How cool is that? Now we are going to learn about the sound a and y make when they are combined.
2. Remember we learned that when we see the a by itself it makes the /a/ sound like a crying baby. For example in the words back and hat you hear the /a/ sound. Today we are going to add y to the a to make the /A/ sound. Have you ever had trouble hearing a question someone asked you? Some people respond by putting their hand up to their ear while at the same time saying /A/. Let’s put our hand behind our ear and practice saying /A/.
3. Now I would like for everyone to look at the chart while I read the tongue twister: Today the hay is far away from Kay. Now let’s say it together and stretch out the /A/ sound. Todaaaaaay the haaaaaay, is far awaaaaay from Kaaaaay. What words did we hear that had the ay=/A/ sound? Very Good! Today, hay, kay, away,
4. Now lets practice reading and spelling words that contain ay=/A/. Teacher will hang up her enlarged size letter boxes on the board and invite the students to take out their letterboxes and letters. The enlarged letter boxes will be used for the purpose of modeling to the students. First, I am going to spell out some letters in my boxes on the board and I want to see if you can read it. Remember, I am going to put one mouth move in each box so our ay letters will be in one box because they make one sound. Our first word is hay. We should use on two letterboxes. H-ay. Now I am going to call out words and I would like for everyone to spell them out in their letterboxes. Some sample ay words for a letterbox lesson along with some review words are as follows: mad, way, wash, sway, cave, slay, same, stray. When you are finished spelling the word, raise your hand so I can come around to see how you did. As the teacher is walking around she will make sure students know when to add boxes. After the students have spelled out all the words in the boxes, the teacher will post the spellings of the words on the board and have the class read them aloud together.
5. Now I will distribute the cards out to the students. On one side of the card is a picture of ay and the other side is a slash mark. If students hear a word with /A/ then they are to show the ay, but if they do not hear the /A / sound they are to show the slash mark. Sample Questions:
Do you hear ay=/A/ in May or March?
Stay or Stop?
Lay or Lie?
Play or Work?
Great Job Class
6. I have a story that I would like for you to read. It is called Ray and the Blue Jay. While you are reading, pay attention to the different ay words. When you are finished, write a story about a bird.
7. For assessment, I will distribute a picture page (see materials). I will help the students name the pictures on the page. After we have named each picture, I would like for everyone to circle the pictures whose names have the ay=/A/ correspondence.
Today is May by Laura Meadows
A? I Can’t Hear You by Emily Barnes
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- draw a circle for a face and tell your child that you are drawing a circle to make a head.
- draw 2 eyes, color them, and point them out and tell your child these are eyes.
- draw 2 ears, nose, mouth, and hair describing as you go.
- ask your child to point to each body part.
- take your child's finger and trace the circle with it.
- have your child point to his own eyes, nose, ears, mouth, and hair.
- let your child color the picture.
Slow and Steady Get Me Ready by June Oberlander
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1st Grade Oral Language Resources
Students will:• Learn about the concept of laughing.
• Access prior knowledge and build background about when people laugh.
• Explore and apply the concept of laughing.
Students will:• Demonstrate an understanding of the concept of laughing.
• Orally use words that describe laughing.
• Extend oral vocabulary by speaking about what makes people laugh.
• Use key concept words [laugh, clown, joke; humorous, amuse].
Explain• Use the slideshow to review the key concept words.
• Explain that children are going to learn about:
• Why people laugh.
• When people laugh.
• What makes people laugh.
Model• After the host introduces the slideshow, point to the photo on screen. Ask children: Do these children look like they are having a good time? (Yes). How can you tell? (They are laughing, smiling, happy).
• Ask children: What might these children be laughing about? (A funny joke or story).
• Say: Laughing is a lot of fun. People laugh when something is funny, or when they are happy or when they are celebrating. Sometimes, when one person starts laughing, others join in as well. How can you cheer up someone if they are sad? (answers will vary).
Guided Practice• Guide children through the next three slides, showing them instances when people laugh. Always have the children describe why the children are laughing.
Apply• Have children play the games that follow. Have them discuss with their partner the different topics that appear during the Talk About It feature.
• After the first game, ask children to make funny laughs. After the second game, have them discuss a funny moment they had with friends.
Close• Ask children: What are some bad things to laugh about?
• Say: Laughing places people in better moods however it is not nice to laugh at someone because you can hurt their feelings. You should also be careful that you don't laugh too loudly because you don't want to disturb others. Think about how you laugh and other laughs that you like.
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AAAAAAAA! Cry LIKE a BABY!
By: Ashley Troha
This lesson will help students recognize the vowel correspondence represented by a, which makes the /a/ sound. By using hand gestures, visual representation, and different reading words involving the phoneme /a/, students will have more help in recognizing that phoneme /a/. The tongue tickler will not only aid in the students being able to think about the movement of mouth, but will also help as well in recognizing the letter a and it's phoneme /a/.
Primary paper and pencil for each student
Picture of a crying baby with phoneme /a/
Chart with the tongue tickler "Allie the alligator acts aggravated."
Individual letterboxes for each student
Individual letter tiles for each student a, s, s, m, h, t, d, r, g, f, l, b, c, c, k
Teacher letterboxes and letter tiles
A = /a/ sound worksheet
Individual copies of A Cat Nap for each student and one for teacher
Word card with take, zap, hot, fat, zag, mud, flip, flap, glass, maze, part, track
Word card with be, ab, great, pat, fly, dog, that, glad, ring, shack
Word cards with RAP, CRASH TRASH, SLAB, MAT
assessment worksheet identifying pictures with a = /a/ (URL below)
1. Say: "Our written language is a secret code. The tricky part is
learning what letters stand for the mouth moves we make as we say words. Today we're going to work on spotting the mouth move /a/. We spell /a/ with letter a and demonstrate it with the sound of a crying baby."
2. Say: "Let's pretend to cry like a baby. "aaaaaa." [Pantomime crying like a baby]. Did you notice that when we make the /a/ sound we open our mouth big and wide? Let's try one more time to make sure our mouth is open big and wide. "aaaaaa." Good job!"
3. Say: "Let me show you how to find the /a/ sound in the word bat. Bb-aa-tt. Hmm, if I say it slower like b-b-b-a-a-a-a-a-t-t-t, I feel my mouth open big and wide in the middle of the word. So the a must be in the middle. Now you try it. Do you hear /a/ in map?"
4. Say: "Do you know what this is a picture of? Yes, you're right! It's a crying baby! Remember the /a/ sound a baby makes, "aaaaaa." Now let's try a fun tongue tickler. [Listed on picture sheet] "Allie the alligator acts aggravated." If you hear the /a/ sound, I want you to pretend that you're crying like a baby. Now lets say it together slowly stretching the /a/ sound at the beginning of the words. "Aaaallie the aaaalligator aaaacts aaaagravated." Remember the /a/ sound makes our mouth open big and wide like a baby's mouth when he or she cries. This time let's break off the words as we say them. Here is an example of how to say the words: /a/ llie. Now let's go. "/a/ llie the /a/ lligator /a/ cts /a/ ggravated."
5. Say: "We are now going to use our letterboxes and our letter tiles to spell some words that have our special sound in them. Remember that all of our words our going to include the a = /a/ sound and that for each word one sound goes in each letterbox. < The word list we are going to use will be: (2) as, am; (3) - hat, mad, rag, dash; (4) flag, grab, crack, grass and the letters needed are: a, s, s, m, h, t, d, r, g, f, l, b, c, c, k > Watch as I spell the word trap in my letterboxes < t-r-a-p> . (I will use the overhead projector to model the use of the letterbox and the spelling of the word, making sure to show the students each specific sound.) Now watch and listen as I read the word black. < b-l-a-ck> (I will use the overhead projector to model how to read a word using the vowel-body-coda method." Then I will pass out individual letterboxes and bags of letters.) "Now all the words I say I would like you all to spell in your letterboxes." (I will remind students that the letterboxes are for the sounds of words, not the letters of the words. I will have a list of students and write the words they missed next to their name so they can read it again later when I come back to them and after the lesson is over. I will walk around and observe as the students make the words and be sure that each student has enough time to make the words. If a student makes a mistake creating the word, I will pronounce it the way they spelled it and then pronounce the word we actually want. Then I will give them one more chance to fix it and then model the spelling never asking questions, because that will confuse them. After everyone has the word correctly in their letterboxes, I will model for the class as I did with trap. I will do this for each word so the students will understand exactly how each word should be spelled. We will now put away our letterboxes. I will also make sure to leave time after the letterbox lesson for reading the words.)
6. Say: "I now have a word list on the overhead and I would like you all to read the words out loud." (I will make sure each student can read the word and if a student has trouble I will help the student use the vowel-body-coda method to help.)
7. Say: "We are now going to read a book titled, A Cat Nap which is full of words that make the /a/ sound. (I will hand out copies of A Cat Nap to each student and then give them a short book talk.) This story is about a cat named Tab. Tab likes to take naps in a baseball bag. Tab's owner Sam takes his baseball bag to his game. To find out what happens next, you will have to read the story. (I will then have the students read the book and during the process I will observe their reading.)
8. (I will have students take out paper and pencil). Say: "We use the letter a to spell /a/. Let's write the lowercase letter a. Begin with your pencil on the fence of your paper and first draw little c. After you draw little c then go back to the fence and draw a line straight down on the right side of little c. After I put a smile on it, I want you to make nine more just like it."
9. Call on students to answer and tell how they know: Say: "Do you hear /a/ in take or zap? hot or fat? zag or mud? flip or flap? glass or maze? part or track? Say: Let's see if you can spot your mouth open big and wide in some /a/ words. Pretend to cry like a baby if you hear the a = /a/ sound: be, ab, great, pat, fly, dog, that, glad, ring, shack"
10. Say: "I have an a = /a/ worksheet want you all to do. You will look at the pictures and draw lines from the astronauts to the pictures that represent a = /a/. You can then color the pictures as well." (I will walk around the room and observe students while they are working on the worksheet.)
11. Show ADD and model how to decide if it is add or odd: Say: "The /a/ tells me to open my mouth big and wide, aaaaa, so this word is aaa-dd, add. You try some: RAP: rap or rip? CRASH: trash or CRUSH? TRAP: trap or trip? SLAB: slab or slob? MAT: mat or met"?
12. For assessment, I will distribute the worksheet. Students are to draw lines from the astronauts to the pictures that represent a = /a/ and then may color the pictures. I will then call students individually to read the phonetic cue words from step #11.
Cushman, Sheila. A Cat Nap. Educational Insights, 1990.
Murray, B.A., & Lesniak, T. (1999). The Letterbox Lesson: A hands-on approach for teaching decoding. The Reading Teacher, 52, 644-650.
Young Emily, Aaaaaa! Cry Like a Baby!
Assessment worksheet: http://www.kidzone.ws/kindergarten/vowels/a-begins1.htm
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Now you can print things with print and you can do math. The next step is
to learn about variables. In programming a variable is nothing more than a
name for something so you can use the name rather than the something as you
code. Programmers use these variable names to make their code read more like
English, and because they have lousy memories. If they didn't use good names
for things in their software, they'd get lost when they tried to read their
If you get stuck with this exercise, remember the tricks you have been taught
so far of finding differences and focusing on details:
- Write a comment above each line explaining to yourself what it does in English.
- Read your .py file backwards.
- Read your .py file out loud saying even the characters.
cars = 100
space_in_a_car = 4.0
drivers = 30
passengers = 90
cars_not_driven = cars - drivers
cars_driven = drivers
carpool_capacity = cars_driven * space_in_a_car
average_passengers_per_car = passengers / cars_driven
print "There are", cars, "cars available."
print "There are only", drivers, "drivers available."
print "There will be", cars_not_driven, "empty cars today."
print "We can transport", carpool_capacity, "people today."
print "We have", passengers, "to carpool today."
print "We need to put about", average_passengers_per_car, "in each car."
The _ in space_in_a_car is called an underscore character. Find out how to type it
if you do not already know. We use this character a lot to put an imaginary space between
words in variable names.
What You Should See
$ python ex4.py
There are 100 cars available.
There are only 30 drivers available.
There will be 70 empty cars today.
We can transport 120.0 people today.
We have 90 to carpool today.
We need to put about 3 in each car.
When I wrote this program the first time I had a mistake, and python told me
about it like this:
Traceback (most recent call last):
File "ex4.py", line 8, in <module>
average_passengers_per_car = car_pool_capacity / passenger
NameError: name 'car_pool_capacity' is not defined
Explain this error in your own words. Make sure you use line numbers and
Here's more extra credit:
- I used 4.0 for space_in_a_car, but is that necessary? What happens if it's
- Remember that 4.0 is a "floating point" number. Find out what that means.
- Write comments above each of the variable assignments.
- Make sure you know what = is called (equals) and that it's making names for things.
- Remember _ is an underscore character.
- Try running python as a calculator like you did before and use variable names
to do your calculations. Popular variable names are also i, x, and j.
Common Student Questions
- What is the difference between = (single-equal) and == (double-equal)?
- The = (single-equal) assigns the value on the right to a variable
on the left. The == (double-equal) tests if two things have the
same value, and you'll learn about this in exercise 27.
- Can we write x=100 instead of x = 100?
- You can, but it's bad form. You should add space around operators like
this so that it's easier to read.
- How can I print without spaces between words in print?
- You do it like this: print "Hey %s there." % "you". You will do more
of this soon.
- What do you mean by "read the file backwards"?
- Very simple. Imagine you have a file with 16 lines of code in it.
Start at line 16, and compare it to my file at line 16. Then do
it again for 15, and so on until you've read the whole file backwards.
- Why did you use 4.0 for space?
- It is mostly so you can then find out what a floating point number
is and ask this questions. See the extra credit.
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Connecting Graphs, Tables, and Equations
In Algebra we do a lot of work with lines and their graphs. Connecting graphs, tables, and equations of lines is an important practice so that we can to help understand lines and how to graph them. When looking at graphs and tables, there are important characteristics that we need to be able to identify including the y-intercept and the slope.
When you guys are studying linear equations, you're going to learn about lots of different ways to graph them. Most times students start by learning how to make a table of values then they plot points on the dot and connect, or plot the dots on the graph and connect them with a ruler. But that can take a really long time especially if you're not good with order of operations it's easy to make mistakes.
So another way that students like to learn about graphing lines is by looking at shortcuts, shortcuts and making connections between the table of values, the graph and how steep the line is and also the equation itself.
So what I'm going to do is I'm about to show you guys what it looks like to use one of these calculators. Your teacher might want to have, might have one of these available for you in class but maybe not. It's not important that you know how to use the calculator, what I really want you guys to focus on is looking at similarities and differences between the table of values, the equations and the graphs. So let's go ahead and look at the computer.
When I turn on the graphing calculator this is the home screen but I'm going to be graphing some lines. It's not important that you guys know exactly what I'm typing in here, what's more important is that you guys are looking for patterns. So first thing I want to talk about is what would happen if I were to compare the lines y=x and y=x+2.
First of all, if you look at the equations, you notice they're really really similar right? They both start with y=x and the only difference is this guy has the +2. Let's look at the graphs of those. First we'll see the graph of y=x and then we'll see the line come up y=x+2. Here we go. This is y=x here, this is y=x+2. Notice first of all that these lines are equally steep. They're like parallel lines if you know what that means. The reason why these are equally steep is because they both start with y equal x or y equals 1x. These guys both have the exact same slope. The only thing that's different was that +2 business and that shows up here with the y intercept. I take the line y=x and then I move it up 2. +2 up 2, that makes sense. Let's look at the table of values and see if that makes sense also.
When I'm looking at the table, this first column here represents my x numbers, this column is my y numbers for y=x and this is my y values for y=x+2. So you'll see each one of these numbers +2, gives me these numbers. +2 +2. That's because this is y=x and this equal y=x+2. So it makes sense, they're all plus two.
Look at these two columns. You'll notice the x's and y's are exactly the same and that's because this represents y=x. They're the same numbers. So you can see what happens in the table. I just take my y values from here and I add 2 to them in order to get the line y=x+2.
What I want to do next is add in a couple more equations just so I can show you guys some really cool patterns and so that you can start to understand what's going on. I'm adding in here two more lines, y=x+4 and y=x take away 3 and we'll look at the graph. So before I hit graph, let me tell you what you're going to see. First you'll see y=x then you'll see y=x+2, then x+4 and then x take away 3. So here we go. This, there's all four of them. This is y=x, x+2, x+4 and then x-3. Look at what's the same. All of these graphs have the same slope or the same steepness because the coefficient in front of x for all of them is 1. The thing that's different is that plusing number. +2, +4 meaning I'm moving the y intercept all the way up to 4 or take away 3. I just used the word y intercept and I hope that makes that makes sense to you. What a y intercept is, is the place where the graph crosses this y axis. In the equation y=mx+b the y intercept is the b value.
Okay. So what we've just looked at is what happens if I change the x, excuse me, change the y intercepts by changing what number I'm adding out here. Let's try something different. What I want to do next, is looking at what happens if I change the slope or what happens if I multiply x by some constant. So I'll start by doing y=x, y=2x and also y=4x. Let's look at these graphs and see what they look like. y=x, y=2x, y=4x. Notice how they get steeper. This line was y=x. There's y=2x and y=4x. What's happening is that my y values are increasing more rapidly for this y=4x business because my x number is being multiplied by 4. It makes sense also if we look at the table. Here I have y=x in this column. This is y=2x. I'm taking this x value and multiplying it by 2 to get these guys. 2 times 2 is 4, 3 times 2 is 6, blah blah blah. So you guys can see that my y values are changing more rapidly. The word change is super important when we're talking about how steep lines are because change has to do with slope. The definition of slope that you guys might already know is change in y divided by change in x.
I'm going to go back in here and do something a little bit differently. Now, instead of multiplying by positive numbers, I'm going to show you what happens if I multiply by negative numbers. I have y=x, y=-x. Let's do -2x and let's do -4x just so we can see a whole bunch of different lines. So I already I'm predicting that these lines here, -2 and -4 are going to be steeper because the absolute value of the number multiplied by x is larger. Let's check them out. y=x, y=-x, y=2x and excuse me, -2x and y=-4x. This is tricky. This is the only line that goes in this positive direction because this line is y equals positive x. This guy here is the y=-x. See how it's decreasing from left to right? That's why we call it a negative slope. A negative slope means the line decreases from left to right.
So the thing I really want you guys to remember about what we're looking at here, is how, if I change the number that x is being multiplied by, it affects what we call the slope. I could also do this with a fraction. I'm going to go in just really briefly and show you guys what happens if instead of multiplying by an integer, I multiply by a fraction. I'm actually going to use the decimal value of 0.5 which represents a half and you'll see that instead of making my line steeper it's going to be actually less steep. See, there's y=x. That's more steep than y equals one half x, because my change in y is half as steep as my change in x. That's all slope business.
Let's look at a table of values so we can see what that means. If I look at my table here, this is y=x, this is y equals one half of x. You'll see that my change in y, each time I'm only changing by 0.5 or half. That relates to the slope.
Okay. The last thing I want to do before I set you guys lose on graphing these equationS using patterns, is show you a line that uses all of this stuff put together. Let's look at the graph of y=3x take away 2.
Before I hit graph, I'm going to try to think about what this means. It's a positive slope, so I know my line is going to be increasing from left to right. It's going to be pretty steep because the absolute value of 3 is larger than 1. But then I have this -2 business, this changes my y intercept. It tells me the graph is going to cross the y axis at -2. So here we go. There it is. My y intercept is down here at 2 and my slope is pretty steep. I could count it by going up 3 over 1. Up 3 over 1. If I were to look at the table of values, I would see that my y intercepts, which happens when x is zero, my y intercept is -2 and each time my y value is plusing 3, because my change in y is a positive 3.
So you guys, these are just some shortcuts things to keep in mind when you're graphing lines. You don't have to memorize any of this stuff, it's really just patterns that will help you connect graphs with tables and their equations.
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This lesson will focus on common Japanese particles as well as vocabulary. Particles are very important to the Japanese language. They appear before many verbs and often after the subject of the sentence.
The particles covered in this lesson are:
で に へ を
で is used to talk about where an event or action takes place. It is like the English work “at.”
For example, if you read at the library, you would say:
わたしはとしょかんでよみます。 (I read at the library.)
Many sentences often use more than one particle. If you wanted to modify the above sentence to say, “I read books at the library,” you would actually use the particle を as well.
I read books at the library. わたしはとしょかんでほんをよみます。
The place where the event takes place usually appears first in the sentence, but Japanese does not have really strict rules about sentence placement.
に and へ are both used to mean “to.” If you want to say you are going somewhere or returning somewhere, you need to use に or へ. Both particles signify movement.
Examples: わたしはうちにかえります。 I will return home. (You can also use e instead of ni here).
わたしはにほんへいきます。 I am going to Japan. (You can also use ni instead of e here).
に can also be used to say “at x time” and “on x day.”
Examples: くじにクラスがあります。. I have a class at nine.
げつようびにうちへかえります。I return home Monday.
In the above sentences, に cannot be replaced by へ.
The particle を is used to indicate the direct object of a sentence. Many verbs use this particle.
Examples: みずをのみます。 (I drink water.)
えいがをみます。 (I am watching a movie.)
おんがくをききます。 (I am listening to music.)
にくをたべます。 (I eat meat.)
The particles for verbs stay the same regardless of what form the verb is in.
Below is a vocabulary list to help you form new sentences in Japanese.
Green tea おちゃ
*Note: For time words such as “tomorrow,” and “today,” you do not need to use a particle with the sentence (に).
Study the sentences below to become familiar with the new vocabulary.
I don’t eat breakfast.
I will eat dinner at a restaurant.
What will you do over the weekend?
I will watch a movie.
I will not go to school on Tuesday.
I will read a magazine at home.
I drink green tea.
What time will you be returning?
What time will you go to bed?
I will go to sleep at 10.
I will watch television at home.
When will you go?
I will come/arrive tomorrow.
I read the newspaper in the morning.
Do you eat lunch at school?
I eat lunch at home.
I will listen to music this weekend.
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Topic: Rounding Numbers
i don't know how to round very well. please help me.
When learning how to round numbers, its important to look at the very last number.
For example, lets start with the number 502.
Whats the very last number?
Its 2 right?
And whats the very last number of 507?
Its 7 right?
This is the most important part of rounding. Once you have decided what the last number is, the next question is do you round up or down?
The rule is this, if the last number is 1,2,3, or 4, then you round down.
If the last number is 5,6,7,8, or 9, then you round up.
So, if we were rounding 502, then we already know that the last number is 2. This means we round down. The number 502 rounded to the nearest tenth would be 500.
If we were rounding the number 507 we already know that the last number is 7. This means we round up. The number 507 rounded to the nearest tenth would be 510.
If you have any more questions, dont be afraid to ask your teacher for extra help. Thats what they are there for and trust me, they wont mind! :-)
Here are some flash card sites that will help you learn:
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important for children to learn the letters of
the alphabet and their sounds to become a successful reader and writer.
letter-sound-relationship is vital because it is the core of learning
knowing how to read and write. The children need to understand what
are and that they are essential in reading and writing. The lesson will
focused on the letter /m/. The children will recognize that the letter
makes an mmmmm sound. They will also learn how to write the letter /m/
choose words that start with that letter.
with pictures of words that
begin with m such as muffin, mouse, money, man, monkey, mop,
Matt Will Not Mop book
with tongue twister Maggie made many merry milkshakes
with pictures of /m/ words and non /m/ words.
the lesson by telling the class that they will be learning about the
Ask if anyone knows what sound the letter /m/ makes. Tell the class
letter /m/ makes an mmmmm sound just like mmmmm that taste good. Let’s
making the sound that /m/ makes while we rub our stomachs.
/m/ in the word mouth or space? Muffin or table?
or rat? moose or deer?
- Now lets try a tongue
twister to help you better understand the sound /m/ makes. I want you
to look at the poster and say the tongue twister together. Ready? Maggie made many merry milkshakes using mud.
Wonderful! Now let’s do it again and when you hear the mmm sound I want
you all to rub your stomach as if you are enjoying something delicious.
- Have the students get out
paper and pencil and try writing the letter /m/. Say Let’s try
writing the letter /m/. We start out at the fence and go straight down
to the dirt, then go back up that straight line and near the top of the
line go out and touch the fence and make a little hill, go down to the
dirt and then make another little hill just like you did before.
Wonderful! Now try writing the /m/ by yourself five times and I will
come around and see how you are doing. If you have done it correctly, I
will give you a check mark but if not you need to try again a couple
more times until you get a check mark.
- Teacher will use the
poster of words. Teacher will call on a student and ask what the word
is. Teacher will model the first word. Can you hear the mmm in
mop? Let's sound it out. mmm-ooo-ppp. mop.
- Call on different students
to choose the word that has the /m/ sound.
- Read Matt Will Not Mop
and ask questions about the story. Next, read it again and have the
students rub their stomachs when they come upon words that begin with
/m/. After reading the story the second time, have students raise their
hand and share some of the words they found that started with the
- For assessment, pass out a
worksheet with pictures that start with the letter /m/ and some that do
not. Have the students carefully evaluate them and put stars next to
the pictures that start with /m/.
Lloyd J (2005). Teaching Decoding Why
and How, 29-30.
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How Does It Grow?
1st Grade Oral Language Resources
Children will:• Learn about the concept of growing.
• Access prior knowledge and build background about what things grow.
• Explore and apply the concept of how things grow.
Children will:• Demonstrate an understanding of the concept of growing.
• Orally use words that describe how things grow.
• Extend oral vocabulary by speaking about what things need to grow.
• Use key concept words [cultivate, nutritious].
Explain• Use the slideshow to review the key concept words.
• Explain that children are going to learn about: • What things need to grow.
• How things grow.
Model• After the host introduces the slide show, point to the photo on screen. Ask children: What is going on in this photo? (This family is picking peaches). How do you think these peaches grew? (from a seed).
• Ask children: How long does it take for plants to grow? (answers will vary).
• Say: In order for plants to grow, they need food and water. How is growing a plant different from raising an animal? (you have to play with animals, take them for walks, clean up after them).
Guided Practice• Guide children through the next three slides, showing them how we use things that grow. Always have the student describe whether an animal would need these same things to grow.
Apply• Have children play the games that follow. Have them discuss with their partner the different topics that appear during the Talk About It feature.
• After the first game, ask children to talk about how long it takes animals to grow. After the second game, have them discuss whether they eat those things.
Close• Ask children: How long does it take for people to grow?
• Say: All living things need food, water, and a clean environment to grow. It is important that we take care of ourselves so that we can grow healthily. What other ways can you stay healthy?
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small pieces of paper, pebbles, or some other form of marker
What to Do
Tell students they are going to play a game of Match Five! that will test their knowledge of state capitals.
Divide students into five teams. Hand out Match Five! cards 1–5, giving one to each team.
Explain to students how the game will work: You will read the names of the state capitals. When your students hear the name of a state capital whose state is on their card, the team can put a marker on that state. When a team has five capitals in a row, across, up and down, or diagonally, they should yell “Match Five!”
Read the names of state capitals in random order from the State Capital Checklist. Make a checkmark next to each capital that you read.
When a team yells “Match Five!,” review the states they have tallied to be sure they got their capitals correct.
Keep score on the chalkboard: Each time a team reaches Match Five! correctly, they receive two points. If they make a mistake, they lose one point.
When students have a good grasp of the capitals, use cards 6–10, which list capitals, and have students match states to cities.
If students are just beginning to learn the state capitals, you can give them the State Capital Checklist for reference.
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How Trees Grow
Kindergarten Oral Language Resources
Children will:• Learn about the concept of trees growing.
• Access prior knowledge and build background about trees.
• Explore and apply the concept of how trees grow.
Children will:• Demonstrate an understanding of the concept of trees growing.
• Orally use words that describe trees.
• Extend oral vocabulary by speaking about what helps trees grow.
• Use key concept words [grow, plant].
Explain• Use the slideshow to review the key concept words.
• Explain that children are going to learn about trees growing:
• The steps in helping a tree grow.
• How to help a tree grow.
Model• After the host introduces the slideshow, point to the photo on screen. Ask children: What do you see in this picture? (a tree, leaves, a trunk, branches).
• Ask children: Is the tree tall or small? (tall).
• Say: Trees are just like people, they start very small and grow to be big. Today we are going to learn how trees grow. What do you think trees need to grow? (food, water, care, etc.)
Guided Practice• Guide children through the next three slides, showing them that trees start as a small seed and grow bigger. Always have the children discuss whether they need the same things to grow.
Apply• Play the games that follow. Have them discuss with their partner the different topics that appear during the Talk About It feature.
• After the first game, ask children to talk about how a tree grows. After the second game, have them point to the top, middle, and bottom of a desk.
Close• Ask children: What do you need to do to help a tree grow? Explain.
• Say: Trees need to be taken care of just like people. Think about how you can help a tree grow.
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Which sundae has more ice cream in it? In this worksheet your child will gain practice determining number values. To complete the activity your child will need to look at the different numbers in the grid and determine if they are greater than, or less than the number next to them. He will then need to circle the numbers that are more than the ones next to them. Can your child draw an example of what "more than" looks like?
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Rationale: Before children learn to read and write, they need to learn first, that letters of the alphabet stand for phonemes, and spelling words map out phonemes in spoken words. Of all of the phonemes, short vowels are the hardest to identify. This lesson will teach children to identify /a/ (short a), and how to recognize /a/ in spoken words. This teaches children a meaningful representation of a letter symbol, and then it will give them practice on finding /a/ in different words.
Materials: primary paper and pencil; chart with pockets on it; class set of cards with a and ? on opposite sides; drawing paper and crayons; fishbowl; cut-out fish to go in bowls; fishing stick with magnet hanging from it; My Cap book; concentration game cards with short /a/ words on them; magazine pictures; worksheet.
1. Introduce lesson and explain to students that our written
is like a secret code. But the tricky part is learning what sound
stands for what letter. Today class, we are going to work on
to spot the /a/ mouth move. At first, /a/ will be kind of hard to
spot in works, but as we keep practicing this, it will get easier to
/a/ in words.
2. Ask students: “Has anyone ever gone fishing? Well, at each group table, I have a fish bowl. In each fish bowl, are little fish and three sharks. But, on each fish are some words with the short /a/ sound and each person is to use your fishing pole and stick the magnet in the bowl to get a fish. If you pull out a shark, everyone puts all of his or her words back in the fish bowl, but you get to keep the shark out. Do this for the two remaining sharks, and the person with the most fish at the end of the game wins.”
3. Have class get out their primary writing tablets and a pencil. Say to students, “Boys and girls, we can use the letter “a” to spell /a/. Let’s try to write it. Start at the middle line, and draw a circle to the left hit the bottom line and circle back up to where you started. Then draw a straight line down to the bottom line. I am going to walk around and look at everyone’s a. So remember, we are practicing the short /a/, and if you see ‘a’ in a word, this is the signal for the short /a/ sound.”
4. Divide class into pairs. Demonstrate with one student, and teach class to play concentration. Have short /a/ words written down on each card. Turn cards face down and each student will take a turn and turn over two cards. If the words on the two cards rhyme, then you put those cards aside and go again. If the next two cards do not rhyme, the next person gets to take a turn.
5. Read My Cap to the class and discuss story. Read it again and have students raise their hands when they hear the /a/ sound in words. List these words on the board, and then have each child draw their favorite cap and write a message of why they like it, using inventive spelling. Each child will then show their work to the class.
6. For assessment, have entire class come back to middle of room, and call on one child at a time and ask the students if /a/ is in the words I say to them. “Do you hear /a/ in bark or beak? Walk or run? Banana or peach? Apple or fruit? Cup or glass? Tangerine or pineapple?” Now, pass out cards to every student. The cards have “a” on one side, and “?” on the other side. Tell the children to hold up the “a” side if they hear /a/ in the word given, or hold “?” if they do not hear the /a/ in the word. Give words one by one, such as ask, after, Auburn, hot, night, tomato, his, up, air, tap, desk.
Reference: Shealey, De
me idea on pocket chart and concentration game).
Murray, Bruce A. (ed.) Haiden Pierce and others. Successful Strategies for Teaching Children to Read. Fall 1996.
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900000 ÷ 300 = ? 30 ÷ 100 = ?
Write 900,000 ÷ 300 as . We are used to seeing the divided often called the numerator - above the fraction line and the divider (or denominator) below the fraction line. We can write 900000 as 9 × 100000 and 300 as 3 × 100. The task then looks like .
Let us first consider , which equals 3. We should have divided something 100000 time bigger than 9, making the result 100000 times bigger. We should also have divided by something 100 times bigger than 3, making the result 100 times smaller. What results from making something 100000 times bigger and then 100 times smaller? You can think of the latter as 10 times smaller and then 10 times smaller again, each time knocking one 0 off the 100000, leaving 1000 as the net 'adjustment' to the 3.
In the same way, is just because there is the same m -fold increase as the m-fold decrease. Note that this does not work with, for example, (Try taking m = 3 which gives which is 2, not 3). In the case of 30 ÷ 100, (i.e. 30 %), again we start with and then make it ten times bigger (because the divided is 30, not 3) and one hundred times smaller (because the divider is 100, not 1). The net adjustment is 10 times smaller than the 3, namely 0.3
Remember: The correct value of a fraction can also always be found by long division.
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The derivative. Lesson 5, Section 2: Problems
Problem 1. Let f(x) = 2x − 5.
a) Write the difference quotient and simplify it.
To see the answer, pass your mouse over the colored area.
b) Evaluate f '(x) at x = 9 and at x = −9.
according to Theorem 4 of Lesson 2.
The rate of change of f(x) is 2 for all values of x. f '(x) is constant. But that should be obvious. y = 2x − 5 is the equation of a straight line whose slope is 2. (Topic 9 of Precalculus.) And the value of the slope of a straight line is the rate of change of y with respect to x. So many units of y for each unit of x.
There is no tangent to a straight line, because a tangent, by definition, touches a curve at one point only.
Example. The equation of a tangent to a curve.
a) Calculate the slope of the line that is tangent to y = x2 at the point
b) What is the equation of that line?
a) The slope of the tangent to the curve at x = 4 is the value of the
b) The equation of a straight line has this form:
y = ax + b,
where a is the slope of the line. Therefore, since a = 8, the equation is
y = 8x + b.
To find the value of b, we can now proceed as in Solution 1 to Problem 1 in Lesson 34 of Algebra. Since x = 4 in the function y = x2, then y = 16. The coördinate pair (4, 16) will solve that equation:
The equation of the tangent line is
y = 8x − 16.
See Problem 2f) below.
Problem 2 .
a) Calculate the derivative of f(x) = x3. Follow the sequence of
a) [Hint: (a + b)3 = a3+ 3a2b + 3ab2 + b3. Topic 25 of Precalculus.]
b) Evaluate the slope of the tangent to y = x3 at x = 4.
The slope at x is 3x2. Therefore, at x = 4, the slope is 3· 16 = 48.
c) Evaluate the slope of the tangent to y = x3 at x = −2.
3· (−2)2 = 3· 4 = 12.
d) What is the rate of change of f(x) = x3 at x = −1.
3· (−1)2 = 3· 1 = 3.
At x = −1, the function is increasing at the rate of 3 units of y per unit of x.
e) What is the rate of change of that function at x = 5.
3· 52 = 3· 25 = 75.
At x = 5, the function is increasing at the rate of 75 units of y per unit of x.
f) What is the equation of the tangent to y = x3 at x = 5.
At x = 5, the slope of the tangent is 75. Therefore the equation of the tangent will be
y = 75x + b.
To find b, proceed as in the Example above.
When x = 5, then y = x3 = 125, so that the pair (5, 125) solve that equation.
125 = 75· 5 + b.
Therefore, b = −250. The equation of the tangent is
y = 75x − 250.
Problem 3. Prove: The straight line that is tangent to y = x² at the point (a, a²), bisects the distance of a from the origin.
Let x be the x-intercept of the tangent line. Then we are to prove that x = a/2.
The vertical leg of that right triangle is a². The horizontal leg is a − x. Therefore the slope of that line is
But the slope of that line is 2a, because the derivative of x² is 2x. Therefore,
To see how the difference quotient was simplified, see Lesson 3 of Precalculus, Problem 11c.
b) What is the rate of change of the function at x = 4?
c) What is the rate of change of the function at x = ¼?
rate of 16 units of y per unit of x.
Look at the graph. The closer to 0, the greater the rate of change. The further away from 0, the smaller the rate of change.
We have the following result, then:
This has the form
In what follows we will be exploiting that form.
Please make a donation to keep TheMathPage online.
Copyright © 2013 Lawrence Spector
Questions or comments?
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Rationale: To help students learn that a digraph stands for one mouth movement. Students need to understand that although there are 2 letters that make up the digraph those letters combine to make one sound. Also this lesson will help the students read and write words with the /sh/ digraph. The goal of this lesson is that the students will growing in their understanding of the /sh/ digraph and will be able to identify /sh/ when seen in print. To help accomplish this goal letterbox lessons will be used.
Materials: Elkonin Boxes and letters (i, f, s, h, c, a, t, p, w, m, e, o) for each student, sentence strips with the phrase Shirley’s shoes and shorts were soaked after the shower on Sunday. Fish Wish by Bob Barner, and a fish with the words: fish, list, cat, ship, wish, met, show, spit written inside.
1. Good Morning! Today we are going to talk about the letters ‘s’ and ‘h’ and the sound that they make when you put them side by side in a word. Does anyone know what ‘s’ and ‘h’ make when there together? Well, What does someone usually say when they ask you to be quiet? Shhh! That is right. Well, that is the sound that ‘s’ and ‘h’ make when you say them together! Everyone say Shhh!
2. Now, can anyone tell me any words that they know have the /sh/ sound in them? (wait for reply) Good, ship, fish,… Now we are going to read the sentence up on the wall, Shirley’s shoes and shorts were soaked after the shower on Sunday. Did you hear /sh/ in any of those words? YOU DID, how many? Four, good listening! Now we are going to say it one more time and this time stretch out /sh/ when you hear it and remember we hear it four times. Shirley’s shoes and shorts were soaked after the shower on Sunday.
3. Now have the students show you they can recognize the /sh/ sound. Say, Now I want you to put your finger over your mouth like this (demonstrate) whenever you hear the /sh/ sound then say fish, list, cat, ship, wish
4. Now we are going to try and spell some /sh/ words. I know you can do it. Model, using an elkonin box velcroed to the blackboard, how to spell the first few words. It is important that the student understand the /sh/ make up one letterbox. Give the example, bask needs 3 letterboxes because /sh/ makes the same sound and goes together in one box. Now open so the you have three boxes. Let us spell ship, wish, fish, cash, shop. Now open up to 5 boxes, spell splash.
5. Great Job!! You spelled 6 words. I will write each of the words we have spelled in out letterbox lesson on the board. We will all read each of the words out loud.
6. Now, I will read Fish Wish by Bob Barner to the students. Then, I will have them tell me the words that have the /sh/ sound. I will call on students to tell me a word and write each word on the blackboard
7. For assessment, I will give the student a fish with the words: fish, list, cat, ship, wish, met, shoe, and spit written inside. Have each student read the words and then circle the ones that have the /sh/ sound in them.
Eldridge, J. Lloyd, Teaching Decoding in Holisitic Classrooms. Upper Saddle River, New Jersey. 1995. P. 104-107
CTRD student Wendy Adams
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ELEMENTARY CURRICULUM READING TEST
Dear Parent, Teacher or Student,
The following is the "reading test" to see if
a student is ready to start Connect The Thoughts Elementary
Curriculum, generally for students ages 7-8, or students who
are developing literacy.
Please have drawing paper, pencils or crayon or other
drawing tools ready. Ask the student to do EXACTLY what it
says to do. Let them know before starting that the drawing
art assignments; we just want the student to show that
he/she understands an idea. These drawings can be stick
figures and blobs of color, so long as the student
understands the materials and that can be more or less
"seen" in their drawing.
Each lesson should take about an hour. If the student
can do this in an hour OR SO (give or take, say, 15 minutes)
per lesson, he/she is probably ready for Elementary
To find out more about our reading tests, please watch
the video found at the top of this page.
Table of Contents
from ELEMENTARY CURRICULUM -- LIVING YOUR LIFE I
LESSON # 3:
WORK, PLAY AND REST
(Before Starting - Have a ball for the student(s) to play with. Have some work the student can do, maybe three math problems in his current math.)
- UNDERSTAND THE WORDS:
- Work- Doing things a person must do to take care of himself, take care of his own needs, and take care of other people and their needs.
- Play- Doing things a person wants to do because they are fun.
- Rest- Time spent without work or play, but just sleeping or doing as little as possible to feel better and be able to do more work or play.
- READ ALOUD TO YOUR TEACHER:
There are three things a person can do with time. He can work, he can play, and he can rest.
Doing work is doing things you need to. These are things you do to take care of what you need. That means that being a student and learning is your work. You are learning what you need to, to take care of yourself in the world. That's why you are a student, and that is what you are supposed to be doing with study time, learning to take care of yourself. You are also learning how to help and take care of other people and things like animals or plants. This, for a student, is work. It can also be fun! But because you MUST study, though it may be fun, it's also work. Even eating can be "work", as you need to do it to take care of yourself. It can also be fun, if you like the food.
There are lots of ways to work, which we'll look at later.
Play is doing things you want to, only because they are fun for you. Play should never be a thing you HAVE to do, because then it becomes work. Remember, it's okay to have work that is fun, though! If you are on a baseball team, and you need to be there for practice and to play games, that is work because you agreed to do it and MUST do it, but it's also fun. Play is stuff you do to only have fun.
There are lots of ways to play, which we'll look at later.
Rest is when you do not work or play. Sleeping is rest. Lying around watching TV you really don't care about is rest. Lying down for a while after working hard is rest, too.
- DO: Draw a person working.
- DO: Draw a person playing.
- DO: Draw a person resting.
- DO: Do some work, get something done you need to do, for about five minutes. (Do math.)
- DO: Play for five minutes. (Play ball.)
- DO: Rest for five minutes.
- DO: Explain to your teacher what is good about doing work.
- DO: Explain to your teacher what is good about play.
- DO: Explain to your teacher what is good about rest.
- DO: Decide which of the below is work, play or rest. (The correct answers will be on the next page. If the student struggles with this, read # 2 in this lesson again.)
- Meeting friends to see a movie.
- Playing a video game you want to play and like.
- Eating a lunch you like so you can study.
- Doing history studies that you like.
- Playing piano because you want to.
- Playing piano because your parents say you have to.
- Pulling weeds you don't care about but that must be pulled.
- Sitting around and playing a video game you don't care about.
- Meeting friends to see a movie. Play
- Playing a video game you want to play and like. Play
- Eating a lunch you like so you can study. Work
- Doing history studies that you like. Work
- Playing piano because you want to. Play
- Playing piano because your parents say you have to. Work
- Pulling weeds you don't care about but that must be pulled. Work
- Sleeping. Rest
- Sitting around and playing a video game you don't care about. Rest
LESSON # 4:
DIFFERENT KINDS OF WORK
- UNDERSTAND THE WORDS:
- Physical- Having to do with bodies and things.
- Thinking- To try to understand something by really looking at it and its parts, and figuring it out.
- Plan- A step-by-step list of little things to do which, when done, will get a big thing done.
- Creative- To be able to "make things up" that do not exist until you make them exist.
- READ ALOUD TO YOUR TEACHER:
There are many kinds of work. Here are some of the kinds of work you'll need to do.
There's physical work. This is work done by making your body and other objects move and do what you want them to, so you can get something done. Moving boxes around, cleaning dishes, pulling weeds, cleaning your room; these are all physical work.
There is "thinking" work. Study and school are mostly thinking work. You're thinking when you're trying to figure something out. You're thinking when you read and use what you read to do something. You're thinking when you are trying to understand people, or the world.
Being creative, and making new stories or music or art of any kind, is a sort of work that can be great fun. It can also be play if you don't have to do it, but want to.
Making a plan is work. This is a very important kind of work that makes other work easier. Making a plan is making up a list of things to do. By doing the things on your list, you will get something big done. Let me give you an example. Let's say you wanted to go to Disneyland, but you had no money. The first thing you might wish to do is figure out ways to make some money. Most ways to make money are work, so you will be working (making a plan) so that you can do work, like cutting someone's grass or taking the trash out, so you can make money. The next part of your plan may be to find a way to get to Disneyland. You would figure it out.
A plan is made of little things that need to be done, so that a big thing is done. These are just a few ways you can work. There are others.
- DO: Do some physical work the teacher needs help with, for five minutes.
- DO: Math problems that need you to think to solve them, for five minutes
- DO: Explain to the teacher what the difference is between physical work and thinking work.
- DO: Do something creative for ten minutes. Make up a song, or draw something, or dance, or act, or sing a song.
- DO: Explain to the teacher the difference between thinking work and creative work. How are they different? How are they the same?
- DO: Explain what you like about physical work to the teacher. Explain what you don't like.
- DO: Explain what you like about thinking work to the teacher. Explain what you don't like.
- DO: Explain what you like about creative work to the teacher. Explain what you don't like.
End Lesson # 4
from ELEMENTARY CURRICULUM -- CREATIVE WRITING I
LESSON # 6:
WORDS USED TO DESCRIBE ACTIONS
(Before Staring -- You'll need a TV or computer which plays DVD or has access to films or TV. You'll need to select a show with lots of interesting actions and emotions in it, and a five minute section of that show.)
- UNDERSTAND THE WORD:
- Adverb- A word used to describe an action, something that has happened, is happening, or that will happen.
- READ ALOUD TO THE TEACHER:
You've learned about NOUNS, which are words used to NAME people, places and things. You've learned about VERBS, which are words used to NAME actions. You've learned about ADJECTIVES, which are words which DESCRIBE THINGS.
An ADVERB is a word used to describe an action (a verb).
If you say that you saw a boy "RUN", the verb is "run". If you say that you saw a boy run VERY QUICKLY, both the words very and quickly are ADVERBS.
There are many verbs. A person or an animal, or even a thing can do many things. The wind can blow, it can howl, it can whisper. These are all verbs.
But HOW did the wind blow, or howl, or whisper? Did it blow LOUDLY? Loudly would be an adverb, a word used to describe the verb "blow". Did the wind whisper "softly?" Did it howl "angrily?" Did the wind blow "quickly", or "calmly" or "happily?" These are all adverbs.
There are words that describe how fast a thing was done, such as "slowly" or "quickly". These are adverbs when used to describe how fast or slow an action was DONE.
There are words that describe an emotion. Some of these words are "angrily"; "happily", "cheerfully", "sadly", "miserably", "joyfully". When used to describe an action, or something that is happening or has happened, these words are adverbs. If you said "The boy ran FEARFULLY", fearfully would be an adverb. If you said "She HAPPILY skipped rope", happily would be an adverb. If you said "Betty will UNHAPPILY do her homework tonight", unhappily would be the adverb.
There are words to describe how well an action was done. Some of these are "well", "poorly", "brilliantly", and "badly". Used to describe an action, these words are adverbs. If you said "The house was built WELL", well would be an adverb. If you said "The boy BRILLIANTLY played baseball", brilliantly would be an adverb.
You use adverbs all the time. Everyone uses adverbs to describe HOW things were done, or are being done, or how they will be done.
- DO: Have your partner do an action. Name it (a verb). Have the partner invent ways to do the action. He can do the action any of these ways, or pick some of his own:
Let the partner do the action in ONE way, using the adverb he picked, while you pick an adverb to describe the way the action is being done. Tell the partner the adverb you picked. Get at least three right. (You should get three guesses each time!)
When you get three right, switch places. You do an action, using one way to do it. Let your partner guess which adverb describes the way you're doing the action. Get at least three right. (You should also get three guesses each time.)
- DO: Repeat exercise # 3 with new actions and ways to do them.
- DO: Repeat exercise # 3 with more new actions and ways to do them.
- DO: WATCH a show selected by the teacher for five minutes. As you watch, every time you see an action, use a VERB to say what the action was, and an ADVERB to describe the action. (The teacher should pause the show each time you spot an action.)
- DO: WATCH the same five minutes of the show. Every time you see an action, name it as a verb. Then try to describe the action without using any adverbs. Do this for about 10 minutes.
- DO: Explain to the teacher how using adverbs makes describing actions much easier.
End Lesson # 6
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Pre-K Math: More, Less, Same
Here are some activities for teaching More, Less, and Same in Pre-K and Preschool.
Find more math ideas on the Math Resource Page
We make several floor graphs during the year by placing real objects on the graph and counting them to see which has the most, least, or same amount. A few of the object graphs we have made:
- Gingerbread Man: Children take one bite from a gingerbread man cookie and graph it into a column according to which part they bit: arm, leg, or head.
- People: Children choose a people figure from the block center, and we graph how many boys and girls are in our class.
- Mittens/Gloves: Children bring their mittens or gloves from home and we graph them.
- Leaves: Children collect one leaf and we graph them by color or type.
Pocket Chart Graph
We make several pocket chart graphs during the year. Sometimes we make a graph where children choose their favorite thing (for example, their favorite ice cream flavor). Sometimes we make a graph where children are asked a question with a yes or no answer (for example, “Do you like pizza?”). We often graph to see how many people did or did not like the book we read that day.
This is a game played with a small group of children. The group is divided into two teams. Each team has a giant game die. One child on each team tosses their dice and says the amount. The group decides which die has the most dots.
Print and make your own Giant Dice at this link.
Spray paint lima beans with two colors so that they have one color on each side. Place ten beans in a cup. Children dump the beans onto a mat (I used a sheet of craft foam for the mat). They count each color to see how many beans landed on the red side and how many landed on the blue side. They compare to see which colors have the most, least, or same amount.
Regular playing cards can be used for this game or they can be made with stickers or stamps. Children play this game with one partner. Each child should have a set of cards that represent numbers 1-10, and each child’s cards should be different in some way (e.g. a different color or different picture). To play the game, each child takes the first card from their stack and places it on the table. The children determine which card has the most or same amount. The child whose card has the most wins that round and gets to keep both cards. If the cards are the same, they tie and each child keeps their own card. I have the children place the cards they win in a plastic basket so they won’t get mixed up with their other cards. At the end, the children can count to see how many cards they won, but my students seem to enjoy the game more if we don’t determine who won or lost at the end.
Ice Cube Tray Graph
We use an ice cube tray for a hands-on graph. I place several kinds of counters into a sorting tray. You can use counters of different types or all one type but different colors. Children roll a game die, determine the amount, and count out that amount of counters to place in the graph. I teach them to start at the bottom of the graph and go up the column when they place the counters. They roll the die a second time, determine the amount and place a different type of counters in the second column of the graph. Children look at the graph to determine which has the most, least, or same amount.
Block Building Game
Children roll a game die, determine the amount, and count out that many wooden cubes to stack into a tower. The die is rolled again to make a second tower. The children compare the towers to see which has the most, least, or same amount.
To read about this activity and print the materials, go to the blog post: More, Less Unifix Cubes Lesson.
To read about this activity and print the materials, go to the blog post: More, Less Bear Counters Lesson.
Don’t miss the math resource page!
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What's for Dinner?
Kindergarten Oral Language Resources
Children will:• Learn about the concept of special meals.
• Access prior knowledge and build background about feasts.
• Explore and apply the concept of feasts.
Children will:• Demonstrate an understanding of the concept of special meals.
• Orally use words that describe feasts.
• Extend oral vocabulary by speaking about feasts.
• Use key concept words [special, feasts].
Explain• Use the slideshow to review the key concept words.
• Explain that children are going to learn about special meals:
• What makes a meal a feast.
• How we celebrate special days.
Model• After the host introduces the slideshow, point to the photo on screen. Ask children: What do you see in this picture? (food, a table)
• Ask children: What is your favorite special meal? (Answers will vary)
• Say: A feast is a special meal. What are some times we have feasts? (birthday, holidays)
Guided Practice• Guide children through the next three slides, showing them that food is part of many celebrations. Always have the children describe the food in each celebration.
Apply• Play the games that follow. Have them discuss with their partner the different topics that appear during the Talk About It feature.
• After the first game, ask children to talk about how they knew the food was ready to be placed on the table. After the second game, have them discuss the difference between winter and summer.
Close• Ask children: What is your favorite food to eat on a special day? Explain.
• Say: There are special days in both the winter and in the summer. Think about which days are in the winter and which days are in the summer.
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In order to understand graphing inverse functions, students should review the definition of inverse functions, how to find the inverse algebraically and how to prove inverse functions. The graphs of inverse functions and invertible functions have unique characteristics that involve domain and range. Techniques for graphing inverse functions can make it easier to graph certain functions by hand.
Finding the inverse of a funtion graphically. So for this example we are going to look at the graphic interpretation of what an inverse means. Okay, so behind me I have a function that is defined solely as 2 points to keep our life a little bit simple. Okay?
So what I want to do is plot these points. So we have the point 2, 4. 2, 4. And we also have the point -1, 3. Okay. So rough points right there. Now what I want to do with these is find the inverse. Okay? so remember whenever we find the inverse we just switch our x and our y value. So our inverse then is going to contain the points 4, 2 and the point 3, -1. Okay? Plotting those as well. We now go over 4 up 2 and over 3 down 1. And basically what happens whenever we plot the inverses is we reflect everything over this line y=x, okay? So what that looks like is if you'd sketch in the line y=x, [IB] just the slip of 1 through the origin. Every point is gets reflected or [IB] over that. So this point here just gets flipped over to that. this point here flipped over to that. The easiest way for me to sort of draw these out is to draw perpendicular lines. If you just wanted to find this without finding the actual point, draw perpendicular lines and the distance l is going to be roughly the same distance to that point. Okay? So just draw a perpendicular segment, flip it over and that point should end up reflected over the line y=x.
So finding a graph of an inverse function just by flipping over the line y=x.
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For the positive integers x, a, and b, when x is divided by a, the remainder is b. And, when x is divided by b, the remainder is a – 2. Which of the following statements must be true?
A. a is even. B. x + b is divisible by a. C. x – 1 is divisible by a. D. b = a – 1 E. a + 2 = b + 1
(D) The easiest way to answer this question is by picking numbers. It may take a bit of trial and error to find numbers that satisfy the question stem, but when you do, you can eliminate the wrong answer choices.
Let’s plug in the following values for x and a. Let x = 5 and a = 3. “When x is divided by a, the remainder is b” implies that b is less than a. When we divide 5 by 3, we get 1 with a remainder of 2, so b = 2. We must make sure that these values make the next statement correct as well. When we divide 5 by 2, we get 2 with a remainder of 1, which is what we wanted for a remainder. Therefore, these numbers will help us eliminate answer choices.
Since the question asks which of the choices must be true, we can eliminate any choice that is false for any set of acceptable numbers.
Let’s try the choices with x = 5, a = 3, and b = 2: Choice (A): 3 is even. This is FALSE. Choice (B): 5 + 2 is divisible by 3. This is FALSE. Choice (C): 5 – 1 is divisible by 3. This is FALSE. Choice (D): 2 = 3 – 1. This is TRUE. Choice (E): 3 + 2 = 2 + 1. This is FALSE.
Since Choice (D) is the only choice that survived, it must be the correct answer.
There is an alternative algebraic way of handling it. When x is divided by a, the remainder is b. Therefore, b must be less than a.
When x is divided by b, the remainder is a – 2. Therefore, a - 2 must be less than b.
Thus, a > b > a – 2 ...or, b = a – 1. The correct answer is D. ---------- Would like to know a better way than plugging examples. Because there might be a possibility that the examples I plug in may/may not suit the situation and the answer we are looking at.
Would like to know a better way than plugging examples. Because there might be a possibility that the examples I plug in may/may not suit the situation and the answer we are looking at.
First of all, note that there is the algebraic solution provided in the last part of the explanation.
Secondly, plugging in few easy numbers is a good method that will help to eliminate wrong answers and/or understand a problem better. You may use it if you don't see an algebraic solution. If you eliminate all answer choices except one, then that one is the right answer.
When you plug in numbers, do not pick them all at once, but replace variables one-by-one, trying to fit the new value with the already chosen ones.
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Most study assignments have a collection of important concepts. Part of your work is to get to know and understand these key concepts. One way to take control of these concepts is with recalling cards.
1. Find them. You find key concepts in the headings, introductions, summaries, and questions at the end of the chapter. You also know them by their markings: Bold type and italics. If you used the Explore-a-Chapter Clipit, you may have marked some of them as Wonder Words.
2. Pick the troublemakers: those ideas that you need to know and understand much better than you do when you first meet them.
3. Take names. Use standard note cards. On one side, put the name of the concept. Include any phrase that helps you remember how the text talks about the concept..
4. Get the I.D. On the other side of the card, put reminders of what you may need to recall when you see the concept. These will usually be descriptors. But they don’t have to be words. Try for graphic reminders if you can find them. (Your word processor probably has some clipart you can use).
You will probably need several items here. If there are too many for one card, make a second card.
5. Brain check 1.0. Go through the cards soon after you make them. Look at the concept side and try to recall what is on the back. Them look at the back. Put a green dot by the items you did recall. Put a red dot by the items you did not recall correctly.
6. Brain check 2.0. Go through the cards again a few hours later. Do the same as on check 1. If possible, do this check close to bed time.
7. Brain check 3.0. Do another check the next day. The expression “know it cold” applies if you get all the answers right after leaving the cards alone for at least a day.
8. Brain booster. If you don’t know it cold, carry the cards around with you. When you have a free moment, take out one of the cards and do a brain check with it.
9. Feel good. When you are satisfied with what you can answer, enjoy your satisfaction. One of the main benefits of the recalling cards is that they tell you when you have finished. Keep your cards for later review. But you may want to keep them on your wall. With all those green dots showing. They may not be as impressive as rhino heads. But they’ll take you farther.
Your EngineerStudy Skills Ratem
Copyright (c) D. F. Dansereau & S. H. Evans
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Students will learn about shapes and beginning sounds. This worksheet is for older preschoolers.
First, you will copy the worksheet I have included in this lesson so that each student will have a copy.
Then, you will explain to the students about the different shapes: square, rectangle, circle, oval, and triangle.
You can show the students the actual shapes in the classroom.
After that, you can display the poster with the different shapes and the words on the center of each shape and go over each shape. At this time, you will talk about the beginning sounds of the words.
Then, you will pass out the worksheet and have students write the first letter of the word of that shape.
Example: S = Square. They would write S on the Square.
Finally, you can collect the worksheets so you can see how they did on their sheets.
You can give each student a sticker for completing the worksheet.
- Physical Education
- Reading & Writing
- Social Studies
- Special Education
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|6. Direct Object and Indirect Object|
As mentioned, a sentence has to be clear in its meaning. If I say "I saw", my meaning is not clear to you. You may want to know what I saw. When I say, "I saw a ghost", I named the thing or object that I saw, and my meaning becomes clear. The word "ghost" is the Direct Object of the verb "saw." The object is the part of the sentence that undergoes the action of the verb, which in this case is saw. The direct object generally comes after the verb. (The verb saw is called a Transitive Verb. A transitive verb needs an object to complete a sentence and make its meaning clear.)
EXAMPLE: The dog barks. (subject: dog; verb: barks. No object present.)
EXAMPLE: A cat catches mice.
EXAMPLE: His train departed at ten o'clock. (No object.)
EXAMPLE: He bought her a puppy. (A sentence that contains two/both objects.)
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Discharge Instructions: Taking Your Pulse
Taking your pulse is a way to measure your heart rate. When you take your pulse, you are feeling the force of blood as it's pumped from your heart into other parts of your body. You may need to take your pulse regularly. Or you may just need to take it when you exercise or when you feel something is wrong.
1. Find Your Pulse
With your first 2 fingers (index and middle fingers), press lightly on the inside of your wrist, just below the base of the thumb. You should not be pressing on a bone.
The beats you feel are your pulse. If you can't find your pulse, try moving your fingers slightly to a new spot.
2. Take Your Pulse
Count the beats you feel in your wrist as you watch the second hand on a clock. You may be told to count the beats for 6 seconds and then multiply that number by 10. Or you may be told to count for a full minute.
The number you get is your pulse measurement. It is measured in beats per minute (bpm). A normal pulse is between 60 and 100 beats per minute. The beats should be regular (evenly spaced).
3. Write Down the Results
Write down your pulse each time you take it. You may be asked to bring the results with you each time you visit the doctor.
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Return to Physics Index
Sandi Sorkin Newton Bateman
4220 N. Richmond
Chicago IL 60618
The main objective of this mini-teach is to demonstrate the concept of momentum.
The lesson is designed for grade levels 3, 4, and 5.
3 dynamics carts
block of wood
marked off measurements
4 empty pop cans
small fire cracker
1. Hold the cart in your hand and demonstrate how the cart works by releasing
the spring. Ask the students, "What happens when I release the spring? Why
doesn't it go?"
2. Take the cart and place it next to a wooden block. Ask the students "What do
you think will happen when I release the spring?" Get their responses. Ask,
3. Take 2 carts back to back and place on a wooden board (platform). Ask the
class what will happen? Release the cart and measure the distance. What
4. Compare the results of the equal carts with the cart against the block. Did
they do the same thing?
5. Double the weight of one cart by placing a cart on top of another cart. Ask
class what will happen. Get response and then release the spring.
6. Place a block at each end of a flat board. Place a single cart back to back
with a double cart. Ask the class how the carts should be placed so that they
will hit the blocks at the same time. "What can we say?" Write on the board
that "lighter" is faster and "heavier" is slower.
7. Place 2 single carts on a balance board or teeter totter. What will happen
when the spring is released? Will they stay balanced?
8. Place 2 unequal carts on teeter totter and ask how you should move carts so
they reach end of board at the same time and the board remains balanced.
Explain that when the heavier cart is half as far from pivot the board is always
balanced. This only happens if the speeds are 2:1.
9. Take out the Jensen Bar and ask if you move the heavier weight on one hook
where do you move the lighter weight to balance? Compare this information with
where the carts land on the teeter totter. Ask class if the distance is the
same ratio. Jensen Bar shows 2 mass x 1 distance = 1 mass x 2 distance.
Momentum shows that 2 mass x 1 speed = 1 mass x 2 speeds. When the total
momentum is zero the teeter totter is balanced.
10. Place 3 carts back to back and release the springs. What happens?
11. Have 2 children on skates face to face and ask what is going to happen if
they push off of each other. Have the children push off and observe.
12. Have the skaters facing the same direction. What will happen when the
skater in back pushes from behind? Have skaters do this.
13. Using 4 or 5 skaters lined up - ask what is going to happen when skater at
the end pushes skater in front and then each one every 2 seconds pushes the
other. Have the skaters enact this. For variety have skaters randomly change
their order and see what happens.
14. Take 2 empty pop cans of equal weight and place a fire cracker taped between
them. Ask what will happen. Set off the fire cracker. Now repeat this, but
this time have some melted wax in only one can, so that it is twice the mass of
the other, but do not let the students know.
Do not tell students that the weight in one of the cans is heavier. As an
assessment ask what happened when the 2 cans were set off and explain why.
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Letter How to form the letters Letter name
Draw an angled vertical line facing right: A: /. Draw another angled vertical line facing left: \, both lines should touch at the top: /\. Draw a horizontal line in the middle of the two lines -. This is A.
Draw a vertical line: B: | . On its right side, draw two half-bubbles, going down the line. This is B.
Draw a half-moon, with an opening on the right. C: This is C.
Draw a vertical line: D: |. Then, starting at its top right, draw a backwards C (step 3). This is D.
Draw one vertical line: E: |. Draw three horizontal lines -, on the right side of this, each 1/3rd shorter than the original (but the middle line is shorter than the lines on the top and bottom). One goes on top, one in the middle, one on bottom. This is E.
Draw an E (step 5), but omit the bottom horizontal line. F: This is F.
Draw a C. Then, draw a horizontal line G: -, beginning at the base of the bottom tip, half-way through the C. This is G.
Draw two vertical lines next to each other: H: | |. Then, draw a horizontal line in the middle, connecting them -. This is H.
Draw one vertical line: |. I: This is I.
Draw an I with a hook on it. Like a backward-facing fish hook. J: This is J.
Draw a vertical line: |. Then, draw two lines, starting from the right hand side, each from the middle. One angles up, the other down. K: This is K.
Draw a vertical line: |. Then, draw a shorter, horizontal line: L: _ on the bottom right. This is L.
Draw two vertical lines next to another: | |. Then, starting from the inner, top tips, draw two shorter angled lines that touch 1/2 way in the middle. M: This is M.
Draw two horizontal lines close to each other: | |. Then, draw an angled line: N: \ that starts from the inner top tip of the left line, angled so that it touches the other line, on the inner bottom tip. This is N.
Draw a full circle. O: This is O.
Draw a vertical line: P: |. Then, draw a 1/2 bubble on the right side upper tip, and touching the middle of the vertical line: P. This is P.
Draw a full circle: O. Then, on the near-bottom right, draw a vertical line angling right, partly in the O, and partly out of it. Q: This is Q.
Draw a P. Then, starting from where the bottom 1/2 bubble touches the vertical line, draw a small line angled to the right. R: This is R.
In one stroke, draw a wavy line going left, then right, then left. S: This is S.
Draw a vertical line: T: |. Then, draw a shorter, horizontal line: on top. _ This is T.
Draw a circle, but, leave part of the top open. U: This is U.
Draw two vertical lines next to each other, but, angle the left one to the right and down: V: \, and the right one to the left and down: /. This is V.
Draw two V's next to another: W. W: This is W.
Draw one vertical line headed up and right X: /. Draw another vertical line up and leaning left: \, crossing in the middle. This is X.
Draw a small Y: . Then, where the two lines meet, draw a vertical line v . | This is Y.
In one stroke, draw a horizontal line: Z: _, then a vertical line that angles downward left /, then a horizontal line to the right _. This is Z.
zed in British English
zee in American English
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Group Activity Cards
Use groups of 2.
Draw the diagram shown below on a sheet of paper.
Working together, find the number of paths that can be drawn from the letter S to the letter Y to spell the word strategy. (One path is shown.) Begin by finding all the paths from S to T, from S to R, and from S to A. Do you see a pattern?
Share your work with other pairs.
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Rationale: Children have to recognize phonemes and the letter that corresponds to them. Once children can match these together, they are ready to spell and read. Recognizing short vowels is one of the hardest aspects of learning to read for young children. this lesson will help children identify /a/ short a, one of the short vowels. the children will learn how to recognize it in spoken language and also how to find it in words by learning the symbol.
Materials: Primary paper and pencils, The Cat Nap (Educational Insights), letter A pg from Dr. Suess’ ABC Book, crayons, worksheet with pictures of hat, cat ,bat, bag, drum and bird, memory game with rhyming /a/ words on one side and the other blank, tongue twister rhyme written on board: “Watch the cat act with his hat on the mat”, /a/ straws
1-Introduce the lesson by saying that we are learning another step to being able to break the reading code. Today we are going to learn about /a/. The mouth is open with your tongue laying gently on the floor of your mouth. /a/ is found in many words. As we go through the lesson, listen to what words we have that have /a/ in them and see if you can think of some more.
2-”Don’t you love to have a great big sneeze? When we sneeze we say, ‘achoo’. This is what A says. A says /a/. Let’s say it together, /a/. Once more /a/.”
3-Let’s say our A sentence. I will say it first and you repeat after me. ‘Watch the cat act with his hat on the mat.’ Let’s say it again. Every time you hear the /a/ sound, say the word harder. ‘Watch the cat act with his hat on the mat.’
4-Get the students to take out paper and a pencil. “Let’s practice making short A. Start just below the fence, circle up to the fence, around back to the grass, connect to the starting point and then straight back to the grass. I am going to come around and see everyone’s A. Good now practice writing five more.! Good Job!”
5-(pass out A sticks) “I am going to say some words that may or may not have the /a/ sound in them. If you hear the /a/ sound, hold up your stick. hat, pat, cat, mad, song, knock, fast. Good Job!
6-For a fun review game, tape the memory game to the board with the words face down. Divide the class into two teams and have each team take turns coming up to the board and turning over two cards to see if they match. Pass to teammate if able to get it right or switch teams if get it wrong. The team that makes the most matches wins.
7-Do a book talk and then read A Cat Nap to the class. Talk about the story with the class. Then have the students name the words that have /a/ in them while you write them on the board. You might need to read the story to them again going page by page.
8-For extra activities, pass out the A page from Dr. Suess’ ABC book for them to color. Have the students create an /a/ page for an alphabet book, writing all sorts of /a/ words that they can think of. (use inventive spelling)
9-Pass out the picture page of /a/ words and have the students color the pictures that have /a/ in them.
Cushman. Cat Nap. Educational Insights, Carson, 1990.
Dr. Suess’ ABC Book
Adams, Marilyn. Beginning to Read. University of Ill., 1990.
Click here to return to Insights
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What to do
- Write the letter c on the board; make it at least a foot tall. Alternatively, use a letter card large enough for the whole group to see easily.
- This letter has two sounds; let's review them. Anyone: what are the two sounds? Good: /c/ g(as in cat) and /s/ (as in sat).
- Look for students who are not saying the sounds. Ask them: What are the sounds? Look for students who are making the wrong sounds and model the sounds for them until they have them right. Well done everyone.
- We use the /c/ sound for this letter at the start of words like car, cold, clean and we use the /s/ sound for this letter at the start of words like city, circus, cycle.
- Write 12 letters on the board: 4 of the letters should be c and they should be interspersed with 8 other letters dissimilar in appearance to c, such as T and v.
- When I point to the letter we just learned, say both of its sounds: /c/, /s/. When I point to any other letter, you have to stay quiet. My turn first. Point to a series of letters and either say the sounds or make a performance of saying nothing, as appropriate.
- Your turn. Ready? Point to letters randomly, holding on each one for a few seconds.
- If a student says the sound for one of the other letters (not c), point to c and say: You only need to make a sound for this letter. When I point to any other letter, stay quiet. Ready? Look for individuals who are saying nothing when you point to c. Have those students try letters individually until they have it (but don’t call only on struggling students). Keep going until everyone has it.
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The formula for the volume of pyramids and cones tells you how much space is inside each object.
For these two solid shapes, the volume formula is the same: it's one third of the area of the base times the height.
Why? Here it is in a nutshell. The volume of three pyramids is equal to the volume of one prism with the same base and height. Similarly, the volume of three cones is equal to the volume of one cylinder with the same circular base and height.
The volume of each cone is equal to ⅓Bh = ⅓(28.3 × 10) = 94 ⅓ cm3. All three cones combined equals 283 cm3. The volume of the cylinder is equal to Bh = 28.3 × 10 = 283 cm3, ta da!
The volume of each pyramid is equal to ⅓Bh = ⅓(18 × 8) = 48 cm3. All three pyramids combined equals 144 cm3. The volume of the prism is equal to Bh = 18 × 8 = 144 cm3.
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Fish is Fish
- Grades: PreK–K, 1–2
About this book
Head Off on a Word Hunt!
Send children searching for the action words (verbs) in Fish Is Fish! Note both past and present tense. Some verbs they might find are:
List the words as children name them. Then invite children to choose four verbs from the list and write sentences using these verbs. Depending on the skill levels of the children in your class, you may want to have them use the words to write a brief story.
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Figure It Out With "Ehh?"
Rationale: One of the most important factors in predicting reading success in students is their ability to recognize phonemes. This lesson will teach the letter e and the phoneme /e/ with a gesture, tongue twister, and letterbox lesson.
Picture with an old man trying to hear to represent /e/
Strip with tongue twister written out: "Emmy the Eskimo ate eggs on the elevator."
Letterbox strip for each student
List of words for students to spell: Ed, egg, let, bed, mesh, lend.
Letter tiles for each student: e, d, g, g, l, t, b, m, s, h
Red Gets Fed
List of paired words for evaluation
1. Introduce the lesson. "Class, today we are going to learn a new sound." Write an e on the board. "This is the letter e. It makes the /e/ sound, like in egg. Can every make that sound with me? Good!"
2. Introduce the gesture that goes with "e." "Let's think about the sound we make when we are trying to hear someone better. We say ehhh? Try this sound with me. Great job! Every time we make this sound, lets put our hand to our ear like we're trying to hear someone. Repeat after me. Ehhh? Now you go. Good!"
3. Go over tongue twister. Model the sentence by reading it first and then having the students read it normally. The next time they read it, we will add in the hand gesture and the students will exaggerate the /e/ sound. "Now I am going to show you all a silly tongue twister for us to practice our new sound." Put up strip with "Emmy the Eskimo ate eggs on the elevator." Read strip for students and have them repeat. "Now watch me read the sentence and try to listen with our hand every time I hear the /e/ sound. Eeeemy the Eeeskimo ate eeegs on the eeelevator. Now you all try. Don't forget to use our hand motion!"
4. Have students ready for letterbox when we start the lesson. Have model box and letters written on the board. Model the word "blend" on the board. Have students work their list of words, observing and assisting when needed. "Okay boys and girls, we are going to do a letter box lesson similar to the one we did for the /a/ last week. First, watch me spell the word blend. Bbbblllleeeeennndddd. First, I hear the /b/ sound so I will place a "b" in the first box. Next I hear /l/, then eeeee… oh, /e/, our new sound today! After that, I hear /n/ and /d/ [place letters in box as I am talking]. Now you all are going to try a few words." Before calling out each word, have students change the number of boxes on their letterboxes. After I call out each word, give students time to solve it in their boxes. Check each word before moving on. List of words: 2- [Ed]. 3- [egg, let, bed]. 4- [mesh, lend]. Letters for each student: e, d, g, g, l, t, b, m, s, h.
5. After we finish the LBL, we will read Red Gets Fed. "Okay boys and girls, now that we can spell and read some short e words, we are now going to read a book with our new /e/ sound. This book is about a little puppy who really wants his dinner! He asks everyone in the family- will anyone give him his food? Let's read together to find out. Every time you come across the /e/ sound, use your hand motion with your ear to figure out the sound."
6. Once we finish the book, I will have each student write a message on primary paper. "Now that we have read our book, we are going to write a message! Because we just read about a dog eating dinner, we are going to write about a special dinner you have had with your family." The students should use inventive spelling when they write, and this will help me evaluate if they can make a connection with the story, as well as their phonemic awareness. Once students finish writing, they can draw a picture of their story.
I will have the students come to me individually while they
working on their message. They will listen to some pairs of
words and then tell
me which ones have the /e/ sound. "I have some pairs
of words that I am going to read to you. For example, do you
hear the /e/ sound
in "map" or "wet"? How about "cot" or "Ted"?
"Cake" or "shed"? "Let" or "read"?
Evaluate how well students know the short /e/ sound.
Return to Doorways Index.
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TenMarks teaches you how to solve real life problems on quadratic equations by completing the square.
Read the full transcript »
Learn Applications of Solving Quadratic Equations by Completing the Square Word problems. So the problem it states the Raven wants to create a rectangular garden in her backyard. She wants it to have a total area of 120 feet and it should be 12 feet longer than it is wide. What dimensions should she use for the garden? Round to the nearest hundredth of a foot. All right, so we don’t know the width of the garden. So we’re going to say lets the width be x. So we know that the length of the garden is x+12 feet because it should be 12 feet longer than it is wide. So the length of the garden is 12 feet longer than it is wide. All right, and we also know that the area of the garden is 120 square feet. So to find the area, we know that the formula for an area is L×W. So we’re going to go ahead and make our substitutions. So we know the area is 120 feet and we know that our length is whatever the width is plus 12, so our length is x+12. And then, we multiply that by our width which we said was x. So our width is x. So, now we go ahead and we’re going to multiply. So 120=x×x is x2+x×12 is 12x. So 120=x12+12x or we can rewrite it and say x2+12x=120. All right, now here are the steps to find x. Now we need to solve for x. So our first step is we need to make sure and write the equation in the form x2+bx=c. however, our equation is already written in that form. So we don’t have to worry about changing it into this form, so we’re okay with this. So our second step then is we need to add (b/2)2 to both sides of the equation. So in this equation b is 12, so b=12. So I'm going to take (12÷2)2 which gives me 62 which gives me 36. So that means I'm going to add 36 to both sides of the equation. So that means I get x2+12x+36=120+36, so now I’ve added 36 to both sides of the equation. So I get x2+12x+36 and that would give me 156. Now our third step is we factor and simplify. So, x2+12x+36 is written in the form, so its written in the form x2+bx+(b/2)2, so its written in this form. And we know that x2+bx+(b/2)2 is equal to x+(b/2)2. So we know that there equal to each other. So that means that x+b/2, b is 12. So 12/2 would be 6, so we know that x+62 is equal to 156. So now we need to take the square root of both sides. So I take the square root of both sides, it would be x+6=v156 and -v156. So if I take the approximate, so the approximate square root would be of 156 would be 12.489 and -12.489. So now, we need to write and solve the two equations. So now we’re going to write and solve our two equations. So here, we have x+6=12.489 and we have x+6=-12.489. So that means if I subtract 6 from both sides, I get x=6.489 or x=-18.489. So remember the width cannot be a negative. You can't have a negative width, so it cannot be a negative. So we can only use the positive number and in our word problem if you remember. The word problem said we need to round to the nearest hundredth of a foot. So if I take x=6.489 and I round to the nearest hundredth, I get 6.49. So that means that the width would be x which equals 6.49 and remember that our length of the garden then was our width plus 12. So our length would be x+12, so that would be 6.49+12 which is equal to 18.49 feet. So the dimensions of the garden would be 6.49 feet by 18.49 feet. All right, so things to keep in mind that when a trinomial is a perfect square there is a relationship between the coefficient of the x-term and the constant term. So if x+n2 is equal to x2+2nx+n2 or and (2n/2)2=n2 and the same could be true with (x-n)2, and that would be equal to x2-2nx+n2. And that would be also equal to (-2n÷2)2 which is equal to n2. And then remember to complete the square of x2+bx. You add (b/2)2 to the expression and this will form a perfect square trinomial.
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One to Two Years
How Does Your Child Hear and Talk? | Birth to One Year | Two to Three Years
Three to Four Years | Four to Five Years | Learning Two Languages
What should I do if I think my child has a problem?
What should my child be able to do?
|Hearing and Understanding
- Points to a few body parts when asked.
- Follows simple commands and understands simple questions ("Roll the ball," "Kiss the baby," "Where's your shoe?").
- Listens to simple stories, songs, and rhymes.
- Points to pictures in a book when named.
- Says more words every month.
- Uses some one- or two- word questions ("Where kitty?" "Go bye-bye?" "What's that?").
- Puts two words together ("more cookie," "no juice," "mommy book").
- Uses many different consonant sounds at the beginning of words.
What can I do to help?
- Talk while doing things and going places. When taking a walk in the stroller, for example, point to familiar objects (e.g., cars, trees, and birds) and say their names. "I see a dog. The dog says 'woof.' This is a big dog. This dog is brown."
- Use simple but grammatical speech that is easy for your child to imitate.
- Take a sound walk around your house or in the baby's room. Introduce him/her to Timmy Clock, who says "t-t-t-t." Listen to the clock as it ticks. Find Mad Kitty Cat who bites her lip and says "f-f-f-f" or Vinnie Airplane who bites his lip, turns his voice motor on and says "v-v-v-v." These sounds will be old friends when your child is introduced to phonics in preschool and kindergarten.
- Make bath time "sound playtime" as well. You are eye-level with your child. Play with Peter Tugboat, who says "p-p-p-p." Let your child feel the air of sounds as you make them. Blow bubbles and make the sound "b-b-b-b." Feel the motor in your throat on this sound. Engines on toys can make a wonderful "rrr-rrr-rrr" sound.
- Expand on words. For example, if your child says "car," you respond by saying, "You're right! That is a big red car."
- Continue to find time to read to your child every day. Try to find books with large pictures and one or two words or a simple phrase or sentence on each page. When reading to your child, take time to name and describe the pictures on each page.
- Have your child point to pictures that you name.
- Ask your child to name pictures. He or she may not respond to your naming requests at first. Just name the pictures for him or her. One day, he or she will surprise you by coming out with the picture's name.
Return to Top
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What to do
- Some words try to trick you. You can sound them out, just like you’ve been doing, but then you have to say the word a bit differently. Let’s meet a new trick word.
- Write the irregular word on the board in letters at least a foot high or, for a small group, show students the index card printed word. Let’s sound out this word. My turn first. Touch each letter and say the sound: wwwaaasss. But when we say this word fast, we say was. What’s the word?
- You try it. When I touch each letter, say its sound and keep saying it until I touch the next letter. Students: Wwwaaasss (or whatever the irregular word you are teaching is). What’s the word? Correct any student who blends the sounded-out word, e.g., says wass with a short a, instead of was. We say: was. What's the word? Ask them to sound it out and then say it again.
- Write 6 words on the board (arrange them randomly): 2 of the words should be the irregular word you are teaching, and they should be interspersed with 4 regular words that the students already know how to sound out.
- I'm going to try to trick you. When I point to the word we just learned, say the word. When I point to any other word, you have to stay quiet. My turn first. Point to a series of words and either say the word or make a performance of saying nothing, as appropriate.
- Your turn. Ready? Point to words randomly, holding on each one for a few seconds.
- If a student says one of the other words, point to the irregular word and say: You only need to make a sound for this word. When I point to any other word, stay quiet. Ready? Look for individuals who are saying nothing when you point to the irregular word. Have those students try words individually until they have it (but don’t call only on struggling students). Keep going until everyone has it.
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To learn to read and spell words, children need
to know that letters stand for phonemes and spellings map out the phonemes
in spoken words. Children must learn to recognize phonemes before
they can match them to letters. This lesson will help children identify
/i/ (short i). They will learn to recognize /i/ in spoken words as
well as the letter representing it.
Primary paper and pencil; chart with ãSid,
the Indian, is in his iglooä; drawing paper and crayons; picture page
with bug, pin, kitten, tint, lips, dog, and chin.
1. Introduce the lesson by explaining that writing
is a secret code. Today weâre going to work on spotting the
mouth move /i/. As you get to know /i/ it will be easy to spot in
2. Ask students: Have you ever put your hands
in something gross and said ãthis is ickyä. The beginning
of ãickyä is the mouth move that weâll be looking for
today. Everybody say kitty and stretch it out. See if you hear
the icky sound. Yes, right in the middle.
3. Letâs try a tongue twister. (on chart)
Sid the Indian is in his igloo. Everybody say it together.
Say it again but this time stretch the /i/ at the beginning of the words.
ãSid the iiindian iiis iiin his iiigloo.ä Try it again,
and this time break it off the word: Sid the /i/ ndian /i/ s /i/ n his
/i/ gloo. Good work
4. We can use the letter i to spell /i/.
Letâs write it. Start at the fence line. Draw a line
straight down to the sidewalk. Then right above the fence line, make
a dot. After I check your letter i, I want you to make a whole row
just like that one.
5. Iâm going to ask you some questions
and raise your hand to answer. Do you hear /i/ in pin or bat?
Sit or stand? Kitty or dog? Bit or eat? I am going to
give you a card with the letter i on it. If you hear the /i/ sound,
I want you to raise your card. If you donât here it, keep your
card on your desk.
6. Have students get out their paper and
pencil. "We are going to learn to make the letter i. Begin
at the fence line and draw a straight line down. Then go between
the fence line and the sky line and make a dot. When you get finished,
show me. Then I want you to make a whole row of them.
7. For assessment, hand out picture page and
get students to name each picture. Then get students to circle each
picture whose names have /i/ in them.
Eldredge, J. Loyd. (1995) Teaching Decoding
in Holistic Classrooms
Click here to return to Illuminations
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It was springtime and mother and father bird decided to
build a nest. Who can tell me some of the things they
might have used to make their nest?
(Fold the paper in half and cut a semi circle.)
Mother bird sat on the nest and laid a beautiful egg.
(Open the nest to reveal the egg shape.)
Now, mother bird could not leave the egg. She had
to sit on it and keep it warm and safe. Even when it
rained and the wind blew hard, mother bird had to sit there
and protect her egg. Fortunately, two little bugs who
lived in the tree made friends with mother bird and
kept her company. This is one little bug. His name was _____.
(Use a child’s name in the class.)
(Draw a little dot for the bug.)
This is the other little bug. Her name was _____,
(Use another child’s name in the class.)
(Draw another little dot on the opposite side.)
One day as mother bird was sitting on the egg, she heard
a little cracking sound. She looked down and saw a little
crack in her egg.
(Cut a little slit on the fold slanted toward the eyes.)
Then she heard a great, big cracking sound.
(Cut around the eye and slit as shown stopping before
you get to the end of the egg.)
And guess what mother bird saw coming out of the big
crack in her egg? She saw her baby bird!
(Open the egg and bend up the beak as shown.)
Hint! You can also cut this story out of a paper plate.
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This week, our first graders started with brand new Math Switch groups and a new math unit on Halves and Doubles! We first started out sketching a whole number geometrically on our whiteboard grids. Next, we discussed what it might look like to “double” this number. We concluded that the word double also means 2 groups of something. Knowing this also helped our first graders to write equations to go along with doubles.
Next, we moved to “halves”. Our students were able to create a definition of their own for the quantity of half… To find half of a number, you split the total into two equal groups. And that is just what we practiced! The easiest way to solve doubles and halves is to draw a simple picture such as circles. For some it was easiest to use the “dealing method”. This helped our students to visually practice how to split the number into two equal groups by “dealing” one circle at a time to each of the two groups until they reach the total.
Next week our mathematicians will begin to work with Circle Graphs!
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Rationale: Phonemic awareness is a prerequisite for phonics knowledge, spelling development, and word recognition, and is a predictor of later reading and spelling achievement. (Eldredge, p.27) Through this lesson plan, students will learn /O/ (long o) by tongue twisters, identifying /O/ in spoken language and recognizing /O/ in several words.
1. One large chart with the tongue twister, "Opie knows old boats
2. Each student needs a pencil and a piece of primary paper.
3. Each student needs a dry-erase board and a dry-erase marker and a tissue.
4. Each student needs a sheet of paper and crayons.
5. Bo and Rose book
1. Reading and writing is a very big mystery that we have been learning how to solve little by little throughout this year. Today we are going to learn a very important vowel sound, O (long o).
2. Have you ever been walking around your house with your shoes off and stumped your toe and you automatically grab your toes and jump around groaning "OOhhh"? O is the sound that we are going to look for today in words. Let's all practice the OOhhh sound by pretending that we have just stumped our toe and let's all groan OOhhh!!!! Let's listen for the toes sounds in cone: coo-o-ne. Good job, I could hear everyone make the OOhhh sound.
3. Now we have a tongue twister for the day!!!! Reveal the chart with "Opies knows the old boats go slow." Everybody say it together. Now, we acre going to say it again and we are going to hold out the /O/ sound in the words: O-O-Opie knO-O-O-O-Ows O-O-O-O-Old BO-O-Oats gO-O-O-O slO-O-O-O-Ow. Good job!!! Now, we are going to try and do the tongue twister again, but this time we are going to break-off the /O/ from the word: /O/ pie kn /O/ ws /O/ ld b /O/ ts g /O/ sl /O/ w. Great job!!!
4. Okay, now we are going to take out our special lined paper and we are going to practice making the letter O. To make a lowercase o, we are going to make a little c and then close it up. I am going to walk around and look at all of your little o's and when I see one that looks just right, I am going to make the little o a smiley face and I want you to make a row of o's just like that one.
5. Everyone needs to take out their dry-ease boards, a dry erase marker and a tissue to erase with. I am going to say two words; I want you to listen for the hurt toe sound in the words. If you hear /O/ in the first word, I want you to write the number 1 on your dry-erase board. If you /O/ in the second word, I want you to write the number 2 on your dry-ease board. Then, we are going to share our answers and decide which word had the toe-stomp sound in it. Do you hear /O/ in boat or bat? Home or hide? Load or like? Rope or rake? Bike or bowl? Get or goat? Rat or roam? Everyone make the O shape with your mouth like you are about to say /O/. When I say the next few words, see if you can see my mouth make the /O/ sound. Home, lone, phone, doze, hole, cone road.
6. Read Bo and Rose. To Introduce the students to the book, tell them that this books is about a donkey named Rose who likes to have fun at the beach, but sometimes can get into a little bit of trouble. Let's read the book to find out what kind of trouble Rose gets into. After reading the book have a short class discussion about what the students thought about the book. Read it again and have student make the /O/ sound with their mouth when they hear the /O/ sound. List words on the other side of the tongue twister chart. Have each student write in the journal 3 sentences using different /O/ words. The students will be using inventive spelling. When the students are finished, have them draw pictures on /O/ words on a sheet of paper and label the different words. The student should use their crayons to make the pictures more interesting. Then hang the students work on a bulletin board in the classroom
7. For assessment ask students to identify the other students work on the bulletin boards and pronounce in the /O/ sound in each of the different items.
Reference: Eldredge, J. (1995) . Teaching Decoding in the Holistic Classrooms. Prentice Hall Inc. p.27
(1990) Bo and Rose. Phonics Readers Long Vowels.
Clich here to return to Openings
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Loops are things that keep on repeating and repeating until you tell it to stop. There are two types of loops that we'll be learning: for-loops and regular loops.
For-loops increase the value of an integer i (or anything else) by a given amount (default: 1), until it has reached its upper limit.
for i : 1 .. 10 %Start with 1, end with 10, increase i by 1 (i.e. 1,2,3...10) put i end for
That's all there is to it! Whatever's in the middle will be executed each time the loop is run. This program will print all numbers from 1 to 10.
Now there are a few things you may have noticed. Firstly, we haven't declared i. Actually, you're not supposed to declare for-loop variables. In fact, if you do, then it won't work!
What if we want to print all multiples of 5 between 1 and 103?
for i : 0 .. 103 by 5 put i end for
Excellent! You're now a for-loop guru! Loops are pretty simple, and the syntax is almost the same. So why would you want to use normal loops instead of for-loops? For-loops are used when you know how many times to repeat it. However, sometimes the amount of times you repeat depends on how many lines there are in a text file. More often, you'll want a program to loop until the user tells you to exit. This is what we'll be doing.
var word : string loop put "Enter any word you want, and I'll tell you what it is! (type 'exit' to exit)" get word exit when word = "exit" put "You entered ", word end loop
That's pretty self explanatory. We're getting a string from the user, and if the string is exit, then we exit. Turing is a very easy program to use, and it avoids complicated syntax, which becomes handy in cases like this; 'exit when' means exactly that, you exit when the following case is true.
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A member of our team will call you back within one business day.
If you have asthma, you know how it feels to have a “flare-up.” It’s hard to breathe. You may cough a lot, or hear a whistling sound in your chest (called wheezing). Your chest may feel tight. You may feel tired and not want to play. Why does this happen? Use a paper horn to see how your lungs work. First, blow into the horn. Air goes in and out. That’s what healthy lungs are like. Now squeeze the middle of the horn (like the doctor in the picture). Air can’t get in and out. That’s like your lungs when you have an asthma flare-up.
Of course, lungs aren’t exactly like a paper horn. Inside the lungs, air goes in and out through very small tubes. These tubes are called airways. Asthma makes airways a little bit inflamed all the time. (That means swollen and red, like your nose when you have a cold.) Air can still go in and out. You may not notice a problem. But lots of things can bother inflamed airways. Then they get even more swollen. Pushing the air in and out gets harder. Less air gets into your lungs. That’s a flare-up.
Color the open airways green. Color the narrow airways red.
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IRVINE UNIFIED SCHOOL DISTRICT
FAMILY LITERACY PROJECT
QUESTIONS FOR READING
Below you will find a list of possible questions to help you with conversations about your childs reading. They are not intended to be used all at once or every time you read with your child. Use them at your discretion and where they are appropriate. Happy Reading !!
Questions to ask before you read
- Can you look at the pictures and predict what you think will happen in this book?
- What makes you think that?
- What characters do you think might be in our story?
- Do you think there will be a problem in this story? Why or why not?
- Does the topic/story relate to you or your family? How?
Questions to ask during the reading
- What do you think will happen next?
- What can you tell me about the story so far?
- Can you predict how the story will end?
- Why do you think the character did _______?
- What would you have done if you were the character?
- How would you have felt if you were the character? (use different characters)
- As I read____________, it made me picture________ in my head. What pictures do you see in your head?
- As you read, what are you wondering about?
- Can you put what youve just read in your own words?
Questions to ask after reading
- Can you remember the title?
- In your opinion, was it a good title for this book? Why or why not?
- Were your predictions about the story correct?
- If there was a problem, did it get solved?
- What happened because of the problem?
- Why do you think the author wrote this book?
- What is the most important point the author is trying to make in his writing?
- What was your favorite part of the story?
- If you could change one thing in the story, what would it be?
- Can you retell the story in order?
- If you were __________, how would you have felt?
- What is the most interesting situation in the story?
- Is there a character in the story like you? How are you alike?
- Why did you like this book?
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Free Algebra Worksheet - Pythagorean Theorem Walkthrough and Problems
# of Problems: 14
# of Pages: 2
Answer Key?: Yes
Sample Problems from Worksheet
(Worksheet pictures and diagrams not shown)
1. In a right triangle, the side opposite the right angle is called the _________________.
2. The hypotenuse is the _______________ side. We use the variable c to represent the hypotenuse when we don’t know it’s length.
3. The other two sides of the triangle are called the _______ (these two sides form the right angle). We use the variables a and b to represent the legs.
4. Label the hypotenuse and legs in this right triangle:
5. The ___________________ _______________ describes the relationship of the lengths of the sides of a _____________ triangle.
6. The Pythagorean Thereom is named after ________________, a Greek philospher and mathematician who taught around 530 BC.
1. What is the length of the hypotenuse of the triangle? Using the triangle at the right, find the length of the missing side. 3. a = 6, b = 8, c = ?
6. A pigeon leaves its nest and flies 5 km due east. Then he flies 3 km due north. How far is the pigeon from his nest? (Draw a picture! Round to nearest tenth).
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Got the Giggles?
Rationale: Phoneme awareness is essential to begin the reading process. Therefore, to be successful readers, children need to be able to recognize phonemes in spoken words and the letters they represent. In this lesson, students will learn the correspondence g = /g/ in spoken and written words. They will practice using and identifying the letter g.
Giggle, Giggle, Quack By: Doreen Cronin
Poster with the following:
Tongue Twister- Good girls get the giggles and give them to guys.
Upper- and lowercase drawings of G
Pictures of things: guitar, grape, gum, glue, fish, bear, duck, cat
“G” word wall: bulletin board with upper and lowercase cutouts of the letter and room to put things around
Worksheet with pictures of words with the /g/ sound and some that do not have it: dog, cat, flag, girl, frog, boat, house, tree, pig, car, grape, guitar
1. Explain that every letter makes a sound that we can make with our mouth. “Today we are going to learn about the letter g. It makes the /g/ sound. The /g/ sound can either be at the beginning, middle, or end of a word. With practice today, you will be able to pick out the letter g and the /g/ sound in any word!”
2. Relate the /g/ sound to the students. “Now turn to your friend and give them a gift with your arms stretched out. Can you hear the /g/ sound in both of those words? When you hear the /g/ sound today, put your arms out and give your friend a gift.”
3. Give the students a tongue twister to help them remember the sound. “Now we are going to try a tongue twister to help us remember the /g/ sound. I will say it first and then you can repeat it. Good girls get the giggles and give them to guys. (Let them repeat the saying) Now when we say it together, I want you to stretch out the /g/ sound and give your friend a gift when you hear it. GGGoog gggirls ggget the gggiggggggles and gggive them to ggguys.
4. Point out the letter g on the poster and tell students to get their pencil and paper ready. “We can write the /g/ sound if we use the letter g. First, I am going to show you how to write the lowercase g and then we will move on to the uppercase one. Take your pencil and make an a, then go down to the ditch and make a basket. If the ball drops it goes in the basket. So make your ball and drop it into the basket. Write ten more just like that one. Now we will practice the uppercase g. First, draw an uppercase C, then come up to the fence and give him a tray to hold straight. So uppercase C, up and give him a tray. Great, now practice writing ten more of those.”
5. See if the students can hear the /g/ in spoken words. “Now I’m going to see if you can hear the /g/ sound in some words. The sound may be at the beginning or end of words. When you hear the /g/ sound, reach out and give your friend a gift. Do you hear the /g/ sound in gum or boy? Dog or cat? Hat or get? Log or pot? Grip or drip? Flag or top? Sack or frog? Shoes or pig?”
6. Now see if students can recognize the letter g in words with pictures of the words. “Now I’m going to show you some pictures of some things that begin with the letter g. Raise your hand if you think the word starts with the letter and tell me why you think that. Show pictures: guitar, bear, grape, duck, gum, fish, glue, and cat. When the students have chosen the correct pictures, put the pictures on a “G” word wall and display in the classroom.
7. Read Giggle, Giggle, Quack to the students. This story is about a duck who always gets in trouble when the farmer leaves. When the farmer is away on a weekend, the duck leaves notes that the caretaker thinks is from the farmer himself. The duck asks for food, baths, and movies, but he takes it too far! Will Farmer Brown get back in time to stop the duck? You’ll have to read to find out! Have the students give a gift to their friend whenever they hear the /g/ sound. After reading, ask the children which words they heard with the /g/ sound and make an index card with the word on it to put on the “G” word wall.
8. For assessment: Give students the worksheet with pictures and have them color the words that have the /g/ sound in them. Display on word wall.
Return to the
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Money Comes and Goes
This lesson printed from:
A budget is a plan that shows how much money comes in (income) and how much money goes out (expenses). We use a budget to make sure we have enough money to buy the things we need and really want. A budget also helps us set aside money for things that we can’t afford to buy right now. The money we set aside is called savings.
You will learn the different parts of a budget. You will also create a budget you could use to reach a savings goal.
Read the story Tim’s Turn to Learn and answer the questions on the worksheet. When you are finished, you will discuss the worksheet answers with your class.
Tim and Money Mouse reduced their spending in order to save money for the future. Another way they could have saved more money is by increasing their income. Read the story Heather Learns About Earning to find out how Heather increased her income.
Then, answer these questions about the story:
1. What was Heather’s problem?
2. How did she earn the money she needed?
3. What else might Heather have done to earn the money she needed?
Now that you know what income and expenses are, can you find the income and expenses in this budget?
A budget helps us keep track of our money so that we can use it on things we really need and want. A budget also helps us save for things that we can’t afford to buy right now. A balanced budget has money in (income) equal to money out (spending and saving).
Now it is your turn to create a budget!: www.econedlink.org/interactives/EconEdLink-interactive-tool-player.php?filename=em483_budget2.swf&lid=483
- Read the story, Alexander Who Used to Be Rich Last Sunday. Discuss with your class what happened to Alexander’s money. Also discuss how you can keep from buying things that you don't need.
- Think of something special that you would like to save money for. Use the “Spending Tale” to keep a personal spending diary. Then create a budget that will help you reach your savings goals.
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Grammar page 2
The second page of the grammar lessons.
In Japanese, grammatical parts of the sentence are shown very clearly by "particles." These particles are placed after the word (or phrase) they modify. The best way to learn to use them is to memorize useful examples and say them!
See also Particles page.
wa - overall topic particle
は wa - overall topic particle - shows the main topic of the conversation [NOTE: it is a hiragana ha but pronounced as "wa"]
あなたはやさしいです。 anata wa yasashii desu. You are nice. [Makes "you" the main topic]
ga - the subject particle
が ga - the subject particle - sometimes the difference between wa and ga are hard to tell. Sometimes they can be used interchangeably with only a slight change in meaning. Don't worry about this now!
ねこがへんです。 neko ga hen desu. The cat is strange. [Makes the "cat" the subject]
Comparing は and が
The topic particle は can easily be confused with the subject particle が. That is because は overrides が, in other words in a sentence something can very easily be both the topic and the subject of that sentence. In such cases the が 'disappears' and it looks like the は is acting as a subject marker.
Take this simple sentence.
watashi wa kurei desu.
I am Clay.
["I" (that is the speaker, Clay) is the topic and now this is known, it won't be repeated unless the topic changes]
What is the subject of the sentence? That's right - Clay is. But because Clay is also the topic only the topic marker は is used. Now we'll let Clay continue and say another sentence ...
neko ga suki desu.
(I) like cats.
["cats" is the subject here. "I" is still the topic. He could have said "watashi wa neko ga suki desu." but that is unnecessary because he has already said "watashi wa" establishing the topic in the previous sentence.]
if both are in a sentence, the wa is first
o - The Direct Object particle
を o - The Direct Object particle
hon o yomimashita.
(I) read a book.
[NOTE: it makes "book" the object. If we were to say "I" it would be watashi wa at the beginning.]
ni - usually shows movement (to)
に ni - usually shows movement (to)
nihon ni ikimashou!
Let's go to Japan!
[There is movement going to Japan]
or shows time (at)
roku ji ni ikimashou!
Let's go at 6.
de - Shows location (at, in)
で de - Shows location (at, in)
nihon de asobimashou!
Let's play (have fun) in Japan!
[Notice there is no movement]
も mo means "also" or "too" and like other particles, it is placed after the word it modifies. Let's see some examples:
watashi wa neko ga suki desu.
I like cats.
watashi wa neko ga suki, soshite inu mo suki desu.
I like cats, and I also like dogs.
N.B. The mo after inu replaces ga. You can't say "ga mo"
watashi mo neko to inu ga suki desu.
I also like cats and dogs.
NOTE: 私も watashi mo by itself means "Me too."
STOP and test yourself.
Adjectives (part 1)
There are 2 types of adjectives:
-i adjectives - adjectives that end in 'i', if you like their 'dictionary form' ends in 'i'. -na adjectives - adjectives that add -na when placed before nouns
The -i adjectives change:
|あつい atsui - (It's) hot||i|
|あつくない atsukunai - not hot||-i + kunai|
|あつかった atsukatta - was hot||-i + katta|
|あつくなかった atsukunakatta - wasn't hot||-i + kunakatta|
The -na adjectives don't change! But when placed before nouns they add a -na
げんき genki (healthy, active, fine) げんきな子 genki na ko (healthy child)
The basic definition of adjectives is that they go before a noun to modify or further define it. For example in English "Car." -> "Red car." Japanese does just the same "車 kuruma" -> "赤い車 akai kuruma".
More on what can be done with adjectives in Japanese later.
There are several ways to say "and" (connecting things). Let's look at 2 of them
と to - connecting nouns
watashi wa nihongo to eigo to furansugo ga hanasemasu.
I can speak Japanese and English and French.
そして soshite - connecting phrases
watashi wa nihongo ga hanasemasu. soshite, doitsugo ga yomemasu.
I can speak Japanese and I can read German.
But, a small word, but... There are other "buts" but demo is the most common. Learn this first and you can pick the others up later.
でも demo - but
nihongo ga suki demo, furansugo wa kirai desu.
I like Japanese, but I hate French.
In English, we have our "um." in Japanese, they have their "eeto." This is the sound you make when you can't think of what to say, but want to say something!
何の動物が好きですか？ nan no doubutsu ga suki desu ka? What animal do you like?
ええと・・・、ねこがすきです。 eeto..., neko ga suki desu. Um..., I like cats.
Sometimes mom's cooking isn't just oishii (delicious) it is VERY OISHII!
Add とても totemo before adjectives to say "very"
totemo oishii desu.
It's very delicious!
totemo ookina ki desu.
It is a very big tree.
OTHER VERY WORDS
非常に hijou ni 超 chou (kind of slang - chou means "super-")
I think と思います
This goes at the end to show that you believe what you say, but are not 100% sure. It is also used to show one's opinion. If there is a desu change it to da which is the more casual form and add to omoimasu
1. The speaker is not totally sure of the accuracy of his info...
kuma no pu-san wa kuma da to omoimasu.
Winnie the Pooh is a bear, I think...
Next is an example of showing one's opinion. It is true for the speaker, but may not be so for the listener.
nattou wa oishii to omoimasu.
I think Natto is delicious
Basically you can say any sentence and if you want to soften it or show you are not sure, or show your opinion add to omoimasu
To want ～がほしい
Saying "I want (something)" is pretty easy. Just say the thing you want and add ga hoshii to it.
nomimono ga hoshii desu.
(I) want a drink.
NOTE: The desu is optional and is usually dropped. nomimono ga hoshii. is perfectly fine in spoken Japanese.
Next, let's ask a question. Can you figure out how to do it? That's right add a ka
ke-ki ga hoshii desu ka.
Do you want cake?
Want to do~ ～たい
First get the ～ます masu form of the verb you want to do. Then drop the ～ます masu and add ～たい tai.
たべます tabemasu (to eat) たべ tabe たべたい tabetai (want to eat)
のみます nomimasu (to drink) のみ nomi のみたい nomitai (want to drink)
します shimasu (to do) し shi したい shitai (want to do)
Of course if you want to say "do you want to..." Just add ka
ke-ki o tabetai desu ka.
Do you want to eat cake?
There is / There are
For inanimate objects (objects, plants...), end the sentence with ～が あります ga arimasu
木です。 ki desu. It's a tree. [lit. tree is.]
木があります。 ki ga arimasu. There is a tree(s).
For living things (people and animals) use ～が います ga imasu.
ねこがいます。 neko ga imasu. There is a cat(s).
To show the negative just add -sen to the end
あります arimasu ありません arimasen Another more casual form of arimasu that you don't have to learn now is... ある aru ない nai
います imasu いません imasen Another more casual form of imasu that you don't have to learn now is... いる iru いない inai
Maybe you know these useful phrases:
お願いがあります。 onegai ga arimasu. I have a favor to ask. 問題ない。 mondai nai. No problem! [this is the casual form of arimasen]
To like... がすき
It is easy to like something and to say it! Just add ga suki after the object that you like:
neko ga suki desu.
I like cats.
[note: Nouns don't change in number (no s) so it could mean "a cat". Also note the desu is often dropped in speech - "neko ga suki." is fine!]
2 ways to say "why" are:
- なぜ naze - why
- どうして doushite - why
They are basically interchangeable and start at the beginning of the sentence and are followed by the question
naze (doushite) watashi no ke-ki o tabemashita ka?
Why did you eat my cake?
[There isn't a "you" but obviously you wouldn't be asking yourself this question.]
なぜなら + reason or excuse + kara
nazenara hara ga hetta kara.
Because, (I'm) starving!
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When first introduced to graphing lines, we often use a table of values to plot points and connect them. There are several other methods of graphing lines, including using a point and the slope. Sometimes graphing lines using an equation involves the same methods as using a table of values. Since we graph lines in the coordinate plane, it is necessary to understand how to connect graphs, tables and equations.
There are different methods you could use to go from an equation to a graph.
Making a table is one of the most fundamental or basic level strategies for graphing a line. And, by the way, making a table will work when you start moving through your high school career and getting into other types of equations like curves. You can make a table for them also.
But let's check it out for lines. When you want to graph a line by making a table, keep in mind any point represents a solution to the equation. And here's what I mean. Every point has an X number and a Y number. When I input an X number into my equation,my Y value's my output. So any point that's on the line is a true solution to that equation. That becomes useful when you're making a table.
Tables usually look like this. You can either make them horizontally or vertically like that, if you want to. Totally up to your preference. And what you do is you choose any X numbers you want to. It's usually a good idea to use some negative values in addition to some positive values. And then what you do is one by one you're going to substitute these X numbers into your equation as inputs to find your corresponding Y value output. Then each one of these is going to turn into a point on your graph and you'll just connect them using a ruler.
One thing I want to make sure I point out to you guys before you start this process is that you want your points to be ruler-straight. Here's what I mean.
Let's say I get my points on there and they kind of look like this and I have one that's kind of like out there. Well, these three are straight. So that's probably what the line looks like. But this point, I probably made an error. If I got three that are perfectly lined up, they're ruler-straight and I used a ruler to draw them and I have this point, that's just like a little bit off, chances are I made an error in my table. So go back to your table and make corrections.
Most people tend to do at least three points in their table to start with. I would recommend for your first tables you start doing, you start by doing about five points. And, again, you're going to substitute your X numbers in to find your Y values and then put those dots on the graph. They should make a ruler-straight line.
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Students discuss and act out their healthy lunch eating routines.
Students will share how preparing and eating lunch makes them feel.
- Gather the students into a circle and instruct them to sit down.
- Ask them why it is important to eat healthy foods for lunch ("go" foods give us the energy to learn and play, etc.).
- Ask them how they feel when they skip lunch (tired, hungry, weak, distracted, etc.). Ask them if they like feeling this way.
- Tell them it is "Lunch Story Time." Tell them about your own lunch ritual. Talk about what you ate for lunch yesterday (or today) and how it made you feel. Describe how the food feels, smells, sounds, and tastes. Use movements to show how you prepare and eat the food.
- Next, ask individual students to tell the story of their own lunch eating routines in the middle of the circle. Guide them with questions:
If a student names a food or drink high in fat or added sugar, gently guide her or him to think of a healthier choice.
Once they finish their stories, invite the students who also enjoy these foods to jump five times in place.
After a few students have had a turn, ask some new students to mime their lunch routines (how they prepare and eat it) in the center of the circle (one at a time) without talking. Have the rest of the class imitate the mimes.
Then, invite the class to guess what the lunch foods are.
Once they have guessed correctly, the students who enjoy these lunch foods should jump all the way around the outside of the circle and back to their spots.
- What will or did they eat for lunch today?
- How does the food look, taste, and smell?
- What do they, their families, or the cafeteria workers do to prepare the food? Does it have to be cooked or toasted, chopped or stirred?
- What are their favorite parts about eating lunch?
- How do they feel after eating?
Because lunch periods are rushed or they donít like the food being served, etc., many students skip lunch or eat unhealthy snacks for lunch. For healthy growth and development, it is essential to eat a balanced meal for lunch. A healthy lunch should be 1/3 of the daily Recommended Dietary Allowance (RDA) for energy and nutrients and contain foods from several food groupings (whole grains; low-fat or skim milk and milk products; fruits; vegetables; and meats, beans, and nuts).
"Go" foods refer to nutritious foods which give the body the energy to go and grow. "Slow" foods refer to foods high in fat and added sugar which can slow the body down.
Healthy ("Go") Lunch Foods and Drinks:
||whole grain pasta
||low-fat string cheese
||low-fat chicken burritos
||100% fruit juice
Less Healthy ("Slow") Lunch Foods and Drinks:
||fried fish sticks
Related National Standards
Further information about the National Standards can be found
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Rationale: Before beginning to read, children must learn to identify phonemes. Short vowels are sometimes hard for young children to recognize and understand. So this lesson has been planned to teach children the short /o/ sound. Students will learn to recognize /o/ in spoken words and by learning a meaningful representation and a letter symbol, and then they practice finding /o/ in words. Children will listen and look along while I read the book that has the short /o/ sound.
Open Up and Say Aaaah!
Materials: Primary paper and pencil; chart with ãOliver had an operation in October, and Oscar gave him an octopus.ä; picture page with illustrations of ox, sock, girl, dog, cat, fox, mop, ham, bat, dot, log, cap; crayon; Doc in the Fog ö publisher: Phonics Readers
1. Explain to the class that words are made up of different sounds and that sounds are represented by letters. Model how we move our mouth to make these different sounds. Today we are going to learn about the letter a, which sounds like /o/.
2. Ask the students: ãHave you ever been to then dentist and he says open up and say aaah?ä Well, when I go to the dentist I open up my mouth wide and say /o/. Can we say /o/ together? This is the same sound we hear in dog. Can you hear the /o/ sound in dog?
3. Now, I am going to say on tongue twister and after I say it I want you to try it. ãOliver had an operation in October, and Oscar gave him an octopus.ä Now, letâs say it again but this time I want you to stretch out the /a/ in each of the words. ãOooliver had an Oooperation in Oooctober, and oooscar gave him an oooctpus.ä
4. Class now we are going to learn how to write the letter a, which makes the sound /o/. So everyone take out a pencil and a piece of primary paper. OK letâs begin·.start at the fence line. Curve around and down and then back up, itâs like making a circle. Now, come back down and draw a stick. Now you have made an a. I want to see everyoneâs a. After I put a smiley face inside youâre a, I want you to make 5 for aâs just like it.
5. Now we will read Doc in the Fog. Listen for the /o/ sound as we read. While reading the book to the book to the children I will ask them to tell raise their hands and tell me some of the words they heard the /o/ sound in. I will write the words on the board so the children are able to see the words in print.
6. Now I will call on students to answer questions. Do you hear /o/ in sock or bell? mob or bend? mad or sod? Oz or ask? ox or bath?
7. For assessment, I will hand out a picture page and ask the students to color in the picture in each row where they hear the /o/ sound.
Refrence: Eldredge, J. Loyd. Teaching Decoding in Holistic
Classrooms. Brigham Young Univesity. Printice Hall, New Jersey (1995)
pages 60, 61, and 184.
Reading Genie Webstie: www.auburn.edu/rdggenie/twisters
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There are different types of graphing transformation, one of which is subtraction a constant from the independent variable. This type of graphing transformation can be written as y = f(x - h). For this graphing transformation, we shift the graph horizontally by h units. We should also know how to recognize vertical shifts and scaling, reflections, and horizontal compression.
I want to talk about the transformation y equals f of x minus h. And to understand what kind of transformation this gives us, let's look at an example where I graph three functions that are all related by this transformation. Notice in these two functions, I've replaced the the x and root x by something else. Here x+4, here x-1.
Let's start by plotting some key points for y equals root x and I've made the substitution u u for x for a reason that you'll see in a moment but let's just write down some numbers here.
Now I like to use perfect squares nice numbers that are easy to take the square root of. So 0, 1 and 4 are pretty nice numbers. And the square roots are 0, 1 and 2.And so we can plot the square root of x really easily just using these three points. 0 0, 1 1 and 4 2 and here's the square root of x. Alright, now let's plot this function y equals root x plus 4. And here I make the substitution u=x+4 and that means x=u-4. What that tells me, excuse me, is that I take the u values from the square root graph and I subtract 4 from them to get my x values for this graph.
So subtract 4, I get -4, subtract 4 I get -3, subtract 4 I get 0. But nothing happens to the y values. This is the square root of u so I just copy these y values over, 0, 1 and 2 and when we plot these three points -4 0, -3 1 and 0 2. -4 0, -3 1 and 0 2 is right here. So that's what happened. This graph has basically shifted to the left four units. Note I had x+4 and the graph has shifted to the left four units. The +4 you might think shifts the graph to the right. It actually shifts the graph to the left. It's the opposite of what you think.
Let's take a look at another example. y equals root x minus one. I'll make the same substitution u=x-1 and I add one to both sides u+1=x. So my x values I get by adding 1 to my u values here. So I add 1 and I get 1, I add 1, I get 2, add 1 I get 5, but this is just the square root of u so nothing happens to the u values I just copy them over. 0, 1 and 2 and here are my points 1 0, 2 1 and 5 2. 1 0, 2 1 and 3, 4, 5, 2. And you could see that the square root of, this is y equals root u x+x-1. The x-1 indicate to shift to the right one unit. Again it's counter intuitive. The x-1 you might think shifts the graph to the left but it shifts it to the right.
So let's just review really quickly what this transformation does. y equals half of x x-h is a horizontal shift. If each is positive it shifts the graph to the right. Like when h was one, we had x-1 the graph was shifted to the right one unit. In this instance you could think of h as being -4. It's like x minus -4 the graph shifts to the left four units. That's how horizontal translation works.
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Have you ever wondered what makes a paper plane fly? Some paper planes clearly fly better than others. But why is this? One factor is the kind of design used to build the plane. In this activity you'll get to build a paper plane and change its basic design to see how this affects its flight. There's a lot of cool science in this activity, such as how forces act on a plane so it can fly. So get ready to start folding!
The forces that allow a paper plane to fly are the same ones that apply to real airplanes. A force is something that pushes or pulls on something else. When you throw a paper plane in the air, you are giving the plane a push to move forward. That push is a type of force called thrust. While the plane is flying forward, air moving over and under the wings is providing an upward lift force on the plane. At the same time, air pushing back against the plane is slowing it down, creating a drag force. The weight of the paper plane also affects its flight, as gravity pulls it down toward Earth. All of these forces (thrust, lift, drag and gravity) affect how well a given paper plane's voyage goes. In this activity you will increase how much drag a paper plane experiences and see if this changes how far the plane flies.
• Sheet of paper
• Large open area in which to fly a paper plane, such as a long hallway, school gym or basketball court. If you're flying your paper plane outside, such as in a field, try to do it when there isn't any wind.
• Something to make at least a one-foot-long line, such as a long string, another ruler, masking tape, rocks or sticks.
• Paper clips (optional)
• Make a standard, "dart" design paper airplane (for instructions, go to the Amazing Paper Airplanes Web page ).
• Fold your paper into the basic dart paper plane. Fold carefully and make your folds as sharp as possible, such as by running a thumbnail or a ruler along each fold to crease it. Do not bend up the tailing edge of the wings (step 6 of the online folding instructions).
• Go to a large open area and, using string, a ruler, masking tape, rocks or sticks, make a line in front of you that's at least one foot long, going from left to right. This will be the starting line from which you'll fly the paper plane.
• Place your toe on the line you prepared and throw the paper plane. Did it fly very far?
• Throw the plane at least four more times. Each time before you throw the plane, make sure it is still in good condition (that the folds and points are still sharp). When you toss it, place your toe on the line and try to launch the plane with a similar amount of force, including gripping it at the same spot. Did it go about the same distance each time?
• Once you have a good idea of about how far your plane typically flies, change the plane’s shape to increase how much drag it experiences. To do this, cut slits that are about one inch long right where either wing meets the middle ridge. Fold up the cut section on both wings so that each now has a one-inch-wide section at the end of the wing that is folded up, at about a 90-degree angle from the rest of the wing.
• Throw your modified paper plane at least five more times, just as you did before. How far does the paper plane fly now compared with before? Why do you think this is, and what does it have to do with drag?
• Extra: Make paper planes that are different sizes and compare how well they fly. Do bigger planes fly farther?
• Extra: Try making paper planes out of different types of paper, such as printer paper, construction paper and newspaper. Use the same design for each. Does one type of paper seem to work best for making paper planes? Does one type work the worst?
• Extra: Some people like to add paper clips to their paper planes to make them fly better. Try adding a paper clip (or multiple paper clips) to different parts of your paper plane (such as the front, back, middle or wings) and then flying it. How does this affect the plane's flight? Does adding paper clips somewhere make its flight better or much worse?
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to enter and enjoy the world of reading, they must be able to recognize
graphemes and know their corresponding phonemes. Before
a child can recognize a phoneme in
written language, they must be able to hear the phoneme in oral
language. In this lesson, they will learn
to recognize the
grapheme and b=/b/ in spoken words by
learning a fun hand gesture and tongue twister and then practicing
finding /b/ in words.
board with tongue twister "Big boy Biscuit was ready for bed" written
- pictures of
objects that have B's in
- a copy of
the book Biscuit, by Alyssa Satin Capucilli, Publisher: HarperCollins,
cards with B and non-B words on them
with dry erase markers
with pictures with B and non-B words
(bat, fish, bed, house, doll,
ball, bottle, clock)
Boys and girls, today we are going to talk
about a new letter. Many of you may
already recognize this letter. Show
the letter b on the white board. Does anyone know what letter this is? Yes,
this is the letter b. Give
specific praise to the students that recognized the letter. Every letter in our alphabet
has a sound. Does anyone know what sound
the b makes? Give
specific praise for student that knows the sound of b. Yes, the letter b says
- Do any of you know any
words that have the /b/ sound in them? (bed,
ball, basket, etc.) Write the words on the
white board and give specific praise. Let's say those words
together. Okay, now let's just say
"bbbbb" and while we are saying the /b/ sound lets pat our chest
like a heartbeat.
- I am going to show you some
pictures of objects that have the /b/ sound in them. When you hear the /b/ sound, pat your
chest like a heartbeat. (Pictures: ball, basket, boat, bottle, bed).
- Who has ever heard of a
tongue twister? Let's look at a tongue
twister to help us hear the /b/. Show the poster board with
the tongue twister "Big boy Biscuit was ready for bed."
I am going to read it once then I want you to
read it with me. Read the
tongue twister. Now I want
us to read it together and listen for the /b/ in the tongue
twister. When you hear the /b/ I
want you to pat your chest like your heart is beating.
Let me repeat this three times to make sure they
understand the /b/ sound.
- We can even write the
/b/ sound by using the letter b. Let's
practice writing a lower case "b". Model
for students how to write a "b". Start at the sky, go down to the grass, and then bounce up to
the fence and back around. Now you try on
your paper. When you think you've got it,
raise your hand and I will come and take a look. Let's
practice writing a "b" ten times on your paper.
Now we will practice writing a capital "B".
Model for students how to write it.
Start at the sky and go straight down to the
grass. Go around for his big chest and
around for his big tummy. When you think you've got it,
raise your hand and I will come and take a look. Now
let's practice writing a capital "B" ten times.
- Let's look at some flash
cards. I want you to tell me if the word
that I show you has the letter "b" in it.
flash cards with B and non-B words. (bat, doll, dress, blue, bed, red, button).
- We are now going to read a
book. Do a book talk for the book
Biscuit. "Biscuit is a cute little dog that gets into
trouble. Let's read the book to find out what type of trouble
Biscuit gets into." While I am reading
the story I want you to listen hard for the /b/ and pat your
chest like your heart is beating every time you hear the /b/ sound. Read book. Can anyone tell me any words in the story that had the /b/
sound? Write the
words on the white board and give specific praise.
- Individual Assessment: I am going to give you
a piece of paper that has different pictures on it.
Some of the pictures will have the /b/ sound in
them and some will not. I want you to
color only the pictures that have the /b/ sound in their
name. After you color the pictures, I want
you to write the name of the objects under their pictures.
If you are not sure what the pictures is raise your hand and
I will share with the class so everyone will know.
will use the student's work sheets in which they have colored the
well as write the name of the object containing the /b/
to Print Letters", The Reading Genie website,
Ashley, "Shelly Goes to Sherman's Shoe Shop",
"La La Lilly",
B., "Baboons Banging Bongos!",
here to return to Voyagers
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- Click on cell Y1 and observe the input bar at the top. You should see =m*X1. The equals sign denotes a formula in a spreadsheet. The value of m is taken from cell W4. The
* signdenotes multiplication. X1 refers to the contents of cell X1.
- Try changing the value in cell W4 to 3. (To do this, put the cursor over the cell, type 3 and hit Enter.) Observe the changes in the Y column. The graph should also change to plot the new values from columns X and Y.
- Experiment with changing the value of m to larger, smaller, and negative values and observe the changes in the table and in the graph. (Don't worry about changing things; you can always reload the page.)
- In cell Z1 enter the formula =2*X1. Highlight cells Z1 to Z11 and under the Edit menu choose Fill, then Down. Notice that the command causes the table to update. Now the line should pass through the square at (5,10).
- Enter formulas in AA1 and AB1 so that the line passes through the points (6,38) and (8,-8) respectively.
- Record your observations and answer the questions in Question Set 1.
- Click on cell Y1, to see the general equation. The equation y=mx+b is entered as the formula =m*X1+b.
- Notice that the value of m in box W5 is 1 and the value of b in cell W6 is 0. What is the equation of the line in the graph?
- In box W6, change the value of b to 2 and note the changes in the Y column and in the graph window.
- What change do you notice?
- Has the slope of the line changed?
- Has the direction of the line changed?
- If m = 1 and b is now 2, what is the equation of the new line in the graph?
- Leaving the value of m alone, change the value of b to cause the line to pass through the coloured squares. When you succeed, write an equation for the new line.
- Using your new equations, type formulas in Z1, AA1 and AB1 and use the Fill Down command to plot the lines.
- Answer the questions in Question Set 2.
- Put your cursor over cell Y1 and see the formula for the equation. You should see =a*X1^n. The
* signis used for multiplication and the ^ signdenotes exponents. Values for a and n are stored in cells W5 and W6. Since a = 1 and n = 2, what is the equation of the curve in the graph?
- Record the y-intercept of the graph.
- Change the value of n until the curve passes through the red square. Remember, you can use decimals. Write the equation down.
- Repeat the procedure in 3 for the other squares on the graph.
- Using your equation from number 3, enter a formula in cell Z1 that will cause the graph to pass through (3,22).
- Using your equations from number 4, enter formulas in AA1, AB1, and AC1 that will cause the graph to pass through (64,42), (5,-25) and (4,-64) respectively.
- Answer the questions in Question Set 3.
- Set the cursor over cell Y1 to note the formula. You should see: =a*(x-p)^2+q. The
^ symbolis used for exponents in a spreadsheet and the * symbolmust be used for multiplication. Note the values of a, p, and q stored in W5, W6 and W7.
- Try altering the values of a, p, and q. It is difficult to see how the parabola changes because the scale automatically adjusts. Therefore, set a = 1, p = 0 and q = 0 and proceed to number 3.
- Make up an equation in the form y=a(x-p)^2+q, and enter the formula in cell Z1. Then use the Fill Down command. For example, you could try =2*(X1-1)^2+1. (To see a larger graph you can touch the plot window and select full screen.)
- Record your values for a,p and q in a chart and also record the y-intercept, the vertex, and whether the vertex is a minimum point or a maximum point.
- Continue in columns AA, AB, AC, AD and AE to enter more equations, leaving p the same and changing a and q.
- After recording your findings, begin at column Z again and this time, change a and p but leave q unchanged.
- Finally, change p and q but leave the value of a unchanged.
- Answer questions in Question Set 4.
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Function Inverse Example 1 Function Inverse Example 1
Function Inverse Example 1
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- So we have f of x is equal to negative x plus 4, and f of x
- is graphed right here on our coordinate plane.
- Let's try to figure out what the inverse of f is.
- And to figure out the inverse, what I like to do is I set y, I
- set the variable y, equal to f of x, or we could write that y
- is equal to negative x plus 4.
- Right now, we've solved for y in terms of x.
- To solve for the inverse, we do the opposite.
- We solve for x in terms of y.
- So let's subtract 4 from both sides.
- You get y minus 4 is equal to negative x.
- And then to solve for x, we can multiply both sides of this
- equation times negative 1.
- And so you get negative y plus 4 is equal to x.
- Or just because we're always used to writing the dependent
- variable on the left-hand side, we could rewrite this as x is
- equal to negative y plus 4.
- Or another way to write it is we could say that f
- inverse of y is equal to negative y plus 4.
- So this is the inverse function right here, and we've written
- it as a function of y, but we can just rename the y as x
- so it's a function of x.
- So let's do that.
- So if we just rename this y as x, we get f inverse of x is
- equal to the negative x plus 4.
- These two functions are identical.
- Here, we just used y as the independent variable, or
- as the input variable.
- Here we just use x, but they are identical functions.
- Now, just out of interest, let's graph the inverse
- function and see how it might relate to this
- one right over here.
- So if you look at it, it actually looks
- fairly identical.
- It's a negative x plus 4.
- It's the exact same function.
- So let's see, if we have-- the y-intercept is 4, it's going
- to be the exact same thing.
- The function is its own inverse.
- So if we were to graph it, we would put it right
- on top of this.
- And so, there's a couple of ways to think about it.
- In the first inverse function video, I talked about how a
- function and their inverse-- they are the reflection
- over the line y equals x.
- So where's the line y equals x here?
- Well, line y equals x looks like this.
- And negative x plus 4 is actually perpendicular to y is
- equal to x, so when you reflect it, you're just kind of
- flipping it over, but it's going to be the same line.
- It is its own reflection.
- Now, let's make sure that that actually makes sense.
- When we're dealing with the standard function right
- there, if you input a 2, it gets mapped to a 2.
- If you input a 4, it gets mapped to 0.
- What happens if you go the other way?
- If you input a 2, well, 2 gets mapped to 2 either
- way, so that makes sense.
- For the regular function, 4 gets mapped to 0.
- For the inverse function, 0 gets mapped to 4.
- So it actually makes complete sense.
- Let's think about it another way.
- For the regular function-- let me write it explicitly down.
- This might be obvious to you, but just in case it's
- not, it might be helpful.
- Let's pick f of 5.
- f of 5 is equal to negative 1.
- Or we could say, the function f maps us from 5 to negative 1.
- Now, what does f inverse do?
- What's f inverse of negative 1?
- f inverse of negative 1 is 5.
- Or we could say that f maps us from negative 1 to 5.
- So once again, if you think about kind of the sets, they're
- our domains and our ranges.
- So let's say that this is the domain of f, this
- is the range of f.
- f will take us from to negative 1.
- That's what the function f does.
- And we see that f inverse takes us back from negative 1 to 5.
- f inverse takes us back from negative 1 to 5, just
- like it's supposed to do.
- Let's do one more of these.
- So here I have g of x is equal to negative 2x minus 1.
- So just like the last problem, I like to set y equal to this.
- So we say y is equal to g of x, which is equal to
- negative 2x minus 1.
- Now we just solve for x.
- y plus 1 is equal to negative 2x.
- Just added 1 to both sides.
- Now we can divide both sides of this equation by negative 2,
- and so you get negative y over 2 minus 1/2 is equal to x, or
- we could write x is equal to negative y over 2 minus 1/2, or
- we could write f inverse as a function of y is equal to
- negative y over 2 minus 1/2, or we can just rename y as x.
- And we could say that f inverse of-- oh, let me careful here.
- That shouldn't be an f.
- The original function was g , so let me be clear.
- That is g inverse of y is equal to negative y over 2 minus 1/2
- because we started with a g of x, not an f of x.
- Make sure we get our notation right.
- Or we could just rename the y and say g inverse of x is equal
- to negative x over 2 minus 1/2.
- Now, let's graph it.
- Its y-intercept is negative 1/2.
- It's right over there.
- And it has a slope of negative 1/2.
- Let's see, if we start at negative 1/2, if we move over
- to 1 in the positive direction, it will go down half.
- If we move over 1 again, it will go down half again.
- If we move back-- so it'll go like that.
- So the line, I'll try my best to draw it, will
- look something like that.
- It'll just keep going, so it'll look something like that, and
- it'll keep going in both directions.
- And now let's see if this really is a reflection over y
- equals x. y equals x looks like that, and you can see
- they are a reflection.
- If you reflect this guy, if you reflect this blue line, it
- becomes this orange line.
- But the general idea, you literally just-- a function
- is originally expressed, is solved for y in terms of x.
- You just do some algebra.
- Solve for x in terms of y, and that's essentially your inverse
- function as a function of y, but then you can rename
- it as a function of x.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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An important concept that comes from sequences is that of series and summation. Series and summation describes the addition of terms of a sequence. There are different types of series, including arithmetic and geometric series. Series and summation follows its own set of notation that is important to memorize in order to understand homework problems.
So a series is just the summation of a sequence. So a sequence is just a bunch of numbers in a row, a series is what happens when we add up all those numbers together. Okay?
So before me I have a general term for a sequence. a sub n is equal to n squared minus 1. And first we're asked to find the first four terms. Okay? So in order to find the first term, we would find a sub 1 which happens when we plug in 1. 1 squared minus 1 that's just 0. So our first term is going to be 0.
To find the second term we plug in 2. a sub 2 is equal to 2 squared. 4-1 which is going to give us 3. Third term [IB] and repeat a sub 3 is 3 squared, 9-1 is 8. And the fourth term a sub 4, plug in 4. 4 squared, 16-1 is 15.
So this right here is a sequence. It's 4 numbers written in order with commons in between. It's just a collection of numbers.
Find the sum of those first 4 terms. So basically we already found the 4 terms, all we have to do is add them together. 0+3 is 3 plus 8 is 11 plus 15 is 26. So 26 is then the series, okay? Series is the way I remember it is, series is a shorter word therefore your answer should be shorter, one number. A sequence is a longer word, it's going to be a collection of data, a collection of numbers, okay?
So basically all the series is is a summation of the sequence.
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5 ways to help your child with decoding
Easy tips for revving up this essential reading skill.
By Bruce Johnson
1. Point to alphabet letters and say their names. Mix the letters and say their names.
2. Look for letters wherever you go. Examples: signs, cereal boxes, book covers.
3. Look at letters, say the letter name, say the letter sound, then say a word that begins with that sound.
4. Make flash cards. Play letter games such as Memory or Go Fish with letters or sounds, and when you find a match say a word that begins with that matched sound. Play Tic-Tac-Toe using letters other than X and O.
5. Go on a letter hunt. Write a letter on top of a sheet of paper, like b. Look for all of the words of objects around the house that begin with that letter or sound. Draw pictures or write words.
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Triple Integrals 1 Introduction to the triple integral
Triple Integrals 1
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- Let's say I wanted to find the volume of a cube, where the
- values of the cube-- let's say x is between-- x is greater
- than or equal to 0, is less than or equal to,
- I don't know, 3.
- Let's say y is greater than or equal to 0, and is
- less than or equal to 4.
- And then let's say that z is greater than or equal to 0 and
- is less than or equal to 2.
- And I know, using basic geometry you could figure out--
- you know, just multiply the width times the height times
- the depth and you'd have the volume.
- But I want to do this example, just so that you get used to
- what a triple integral looks like, how it relates to a
- double integral, and then later in the next video we could do
- something slightly more complicated.
- So let's just draw that, this volume.
- So this is my x-axis, this is my z-axis, this is the y.
- x, y, z.
- So x is between 0 and 3.
- So that's x is equal to 0.
- This is x is equal to-- let's see, 1, 2, 3.
- y is between 0 and 4.
- 1, 2, 3, 4.
- So the x-y plane will look something like this.
- The kind of base of our cube will look something like this.
- And then z is between 0 and 2.
- So 0 is the x-y plane, and then 1, 2.
- So this would be the top part.
- And maybe I'll do that in a slightly different color.
- So this is along the x-z axis.
- You'd have a boundary here, and then it would
- come in like this.
- You have a boundary here, come in like that.
- A boundary there.
- So we want to figure out the volume of this cube.
- And you could do it.
- You could say, well, the depth is 3, the base, the width is 4,
- so this area is 12 times the height.
- 12 times 2 is 24.
- You could say it's 24 cubic units, whatever
- units we're doing.
- But let's do it as a triple integral.
- So what does a triple integral mean?
- Well, what we could do is we could take the volume of a very
- small-- I don't want to say area-- of a very small volume.
- So let's say I wanted to take the volume of a small cube.
- Some place in this-- in the volume under question.
- And it'll start to make more sense, or it starts to become a
- lot more useful, when we have variable boundaries and
- surfaces and curves as boundaries.
- But let's say we want to figure out the volume of this
- little, small cube here.
- That's my cube.
- It's some place in this larger cube, this larger rectangle,
- cubic rectangle, whatever you want to call it.
- So what's the volume of that cube?
- Let's say that its width is dy.
- So that length right there is dy.
- It's height is dx.
- Sorry, no, it's height is dz, right?
- The way I drew it, z is up and down.
- And it's depth is dx.
- This is dx.
- This is dz.
- This is dy.
- So you can say that a small volume within this larger
- volume-- you could call that dv, which is kind of the
- volume differential.
- And that would be equal to, you could say, it's just
- the width times the length times the height.
- dx times dy times dz.
- And you could switch the orders of these, right?
- Because multiplication is associative, and order
- doesn't matter and all that.
- But anyway, what can you do with it in here?
- Well, we can take the integral.
- All integrals help us do is help us take infinite sums of
- infinitely small distances, like a dz or a dx or
- a dy, et cetera.
- So, what we could do is we could take this cube and
- first, add it up in, let's say, the z direction.
- So we could take that cube and then add it along the up and
- down axis-- the z-axis-- so that we get the
- volume of a column.
- So what would that look like?
- Well, since we're going up and down, we're adding-- we're
- taking the sum in the z direction.
- We'd have an integral.
- And then what's the lowest z value?
- Well, it's z is equal to 0.
- And what's the upper bound?
- Like if you were to just take-- keep adding these cubes, and
- keep going up, you'd run into the upper bound.
- And what's the upper bound?
- It's z is equal to 2.
- And of course, you would take the sum of these dv's.
- And I'll write dz first.
- Just so it reminds us that we're going to
- take the integral with respect to z first.
- And let's say we'll do y next.
- And then we'll do x.
- So this integral, this value, as I've written it, will
- figure out the volume of a column given any x and y.
- It'll be a function of x and y, but since we're dealing with
- all constants here, it's actually going to be
- a constant value.
- It'll be the constant value of the volume of one
- of these columns.
- So essentially, it'll be 2 times dy dx.
- Because the height of one of these columns is 2,
- and then its with and its depth is dy and dx.
- So then if we want to figure out the entire volume-- what
- we did just now is we figured out the height of a column.
- So then we could take those columns and sum them
- in the y direction.
- So if we're summing in the y direction, we could just take
- another integral of this sum in the y direction.
- And y goes from 0 to what? y goes from 0 to 4.
- I wrote this integral a little bit too far to the
- left, it looks strange.
- But I think you get the idea.
- y is equal to 0, to y is equal to 4.
- And then that'll give us the volume of a sheet that is
- parallel to the zy plane.
- And then all we have left to do is add up a bunch of those
- sheets in the x direction, and we'll have the volume
- of our entire figure.
- So to add up those sheets, we would have to sum
- in the x direction.
- And we'd go from x is equal to 0, to x is equal to 3.
- And to evaluate this is actually fairly
- So, first we're taking the integral with respect to z.
- Well, we don't have anything written under here, but we
- can just assume that there's a 1, right?
- Because dz times dy times dx is the same thing as
- 1 times dz times dy dx.
- So what's the value of this integral?
- Well, the antiderivative of 1 with respect to
- z is just z, right?
- Because the derivative of z is 1.
- And you evaluate that from 2 to 0.
- So then you're left with-- so it's 2 minus 0.
- So you're just left with 2.
- So you're left with 2, and you take the integral of that from
- y is equal to 0, to y is equal to 4 dy, and then
- you have the x.
- From x is equal to 0, to x is equal to 3 dx.
- And notice, when we just took the integral with respect to
- z, we ended up with a double integral.
- And this double integral is the exact integral we would have
- done in the previous videos on the double integral, where you
- would have just said, well, z is a function of x and y.
- So you could have written, you know, z, is a function of x
- and y, is always equal to 2.
- It's a constant function.
- It's independent of x and y.
- But if you had defined z in this way, and you wanted to
- figure out the volume under this surface, where the surface
- is z is equal to 2-- you know, this is a surface, is z
- is equal to 2-- we would have ended up with this.
- So you see that what we're doing with the triple
- integral, it's really, really nothing different.
- And you might be wondering, well, why are we
- doing it at all?
- And I'll show you that in a second.
- But anyway, to evaluate this, you could take the
- antiderivative of this with respect to y, you get 2y-- let
- me scroll down a little bit.
- You get 2y evaluating that at 4 and 0.
- And then, so you get 2 times 4.
- So it's 8 minus 0.
- And then you integrate that from, with respect
- to x from 0 to 3.
- So that's 8x from 0 to 3.
- So that'll be equal to 24 four units cubed.
- So I know the obvious question is, what is this good for?
- Well, when you have a kind of a constant value within
- the volume, you're right.
- You could have just done a double integral.
- But what if I were to tell you, our goal is not to figure out
- the volume of this figure.
- Our goal is to figure out the mass of this figure.
- And even more, this volume-- this area of space or
- whatever-- its mass is not uniform.
- If its mass was uniform, you could just multiply its uniform
- density times its volume, and you'd get its mass.
- But let's say the density changes.
- It could be a volume of some gas or it could be even some
- material with different compounds in it.
- So let's say that its density is a variable function
- of x, y, and z.
- So let's say that the density-- this row, this thing that looks
- like a p is what you normally use in physics for density-- so
- its density is a function of x, y, and z.
- Let's-- just to make it simple-- let's make
- it x times y times z.
- If we wanted to figure out the mass of any small volume, it
- would be that volume times the density, right?
- Because density-- the units of density are like kilograms
- per meter cubed.
- So if you multiply it times meter cubed, you get kilograms.
- So we could say that the mass-- well, I'll make up notation, d
- mass-- this isn't a function.
- Well, I don't want to write it in parentheses, because it
- makes it look like a function.
- So, a very differential mass, or a very small mass, is going
- to equal the density at that point, which would be xyz,
- times the volume of that of that small mass.
- And that volume of that small mass we could write as dv.
- And we know that dv is the same thing as the width times
- the height times the depth.
- dv doesn't always have to be dx times dy times dz.
- If we're doing other coordinates, if we're doing
- polar coordinates, it could be something slightly different.
- And we'll do that eventually.
- But if we wanted to figure out the mass, since we're using
- rectangular coordinates, it would be the density function
- at that point times our differential volume.
- So times dx dy dz.
- And of course, we can change the order here.
- So when you want to figure out the volume-- when you want to
- figure out the mass-- which I will do in the next video, we
- essentially will have to integrate this function.
- As opposed to just 1 over z, y and x.
- And I'm going to do that in the next video.
- And you'll see that it's really just a lot of basic taking
- antiderivatives and avoiding careless mistakes.
- I will see you in the next video.
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| 4.375 | 5 | 4.112268 | 4.495756 |
<urn:uuid:d04f17e4-7d18-44ec-b2d5-bffe703d8d33>
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Decide which charts and graphs represent the number of goals two football teams scored in fifteen matches.
What can you say about the child who will be first on the playground tomorrow morning at breaktime in your school?
What statements can you make about the car that passes the school
gates at 11am on Monday? How will you come up with statements and
test your ideas?
Here are the lists of first names of the members of Class 5. (They are in alphabetical order of their surnames so they do not seem to be ordered.)
One day when $34$ children were in class, Mrs Clifton, their teacher, said they were going to make some block graphs and other things using their first names. She put the class lists onto the white board.
First, the class made tally charts of the initial letters of their names. They worked in pairs.
The first part of Becky and Selma's tally looked like this:
Can you make a full tally chart using the class names?
Next they all made frequency tables using this information.
This is the first part of Alan and Joe's table:
Can you make a frequency table using all the class's names?
Next they decided which letters of the alphabet were needed and which were not needed to make a block graph of their class names. Then the boys took yellow squares and the girls took pale blue squares, drew a picture of themselves and put the initial of their first name on the square and stuck it onto paper to make a pictogram graph.
The last part of the class's block graph looked like this:
Can you see who was away from school that day from this information?
Next they made true block graphs from the class lists to include anyone who was away that day.
This is part of the middle of the block graph:
Can you tell what letters these were?
Can you make a block graph of all the class?
| 4.34375 | 5 | 4.14256 | 4.495437 |
<urn:uuid:660bdaa4-703d-4f37-aa82-4a917297c222>
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Student: So I have practiced guessing functions and am getting pretty good at it as long as there is one operation. The more complicated functions are harder.
Mentor: Yes, they are. The best way to understand such functions is to study one kind at a time. Let's start with functions of the form:
These functions are called linear functions, and are often written as:
Where m represents the number multiplied to X and b represents the number added to the result.
Student: What's so important about these?
Mentor: These functions increase or decrease steadily. Look at the following function and table of points from the function:
Now, answer some questions for me. What is the value of the function when X is 0?
Mentor: Good. What is the change in the value of the function as X increases by 1?
Student: Well, the value of the function goes from 2 to 6 to 10. So at each step the function increases by 4.
Mentor: Now look at your answers: 2 for the starting point, when X is 0 and 4 for the increase. Do those numbers look familiar?
Student: In the original function, Y = 4 * X + 2, m = 4 and b = 2. The same numbers we got for the starting value and the increasing value. Is this a coincidence?
Mentor: No, it is not a coincidence. This always works. Try some.
Student: Here are a few:
Mentor: Good! But before we begin, let's get the terminology right: The change is called the slope and the starting value is called the intercept. We'll learn why these words are used later when we talk about graphs. Can you build a few tables of ordered pairs to further demonstrate these facts about your functions? You may wish to use Simple Plot to plot the ordered pairs from your table.
| 4.625 | 5 | 3.861158 | 4.495386 |
<urn:uuid:b6703a99-687d-45f6-9e34-8a9b69d01f2e>
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What to do
- Assemble a stack of word index cards. The cards should be a mix of all irregular words learned so far. (Optionally, once students are comfortable with irregular words, you can include some regular words in the pack too.)
- Now let's play a game. We're going to try to go through this stack of cards as fast as we can saying the word on each card. Let's see how fast we can go. My turn first.
- Next, model taking the top card of the stack, showing it to the students, and saying the word after a pause. Continue through the stack.
- Do you think you can go faster than I did? Call on a single student in the group, starting with a student you think may be slower. Show the first card: What's the word? If the student is incorrect, correct him, have him repeat your answer, and move to the next card. Praise correct answers.
- Select the next quicker student and repeat until all students in the group have worked through the stack.
- Okay, now let's go faster. Shuffle the stack of cards and repeat with students in the same order, but encouraging them to go faster.
- If time and focus allow, shuffle and repeat at an even faster pace.
- For students who struggle, give them help and make a note in an Activity Log.
| 4.28125 | 5 | 4.204066 | 4.495105 |
<urn:uuid:a7c1d02e-b66a-48ea-85ad-a72f8e5269b7>
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Permutations Introduction to permutations
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- Let's say I have 3 chairs.
- They'll just be blanks: 1, 2, and 3.
- 3 chairs, and I have 7 people.
- I'll call them people A, B, C, D, E-- how many is that?
- That's 5-- F, G.
- So we have 7 people and what I want to know is how many
- different ways can these 7 people sit in these 3 chairs?
- Well, before anyone sits down if we just pick a chair, these
- are just arbitrary labels for the chairs, but let's start at
- the left with chair number one.
- If no one is sitting down, how many different people could
- sit down in chair one?
- Well, 7 people are standing up, no one is sitting in any of the
- chairs, so 7 different people could sit in chair one.
- So there are 7 possibilities for chair one.
- So 1 of those 7 possibilities is going to sit
- down in chair one.
- So how many people are left to sit in chair two?
- Well, 1 less than 7, right?
- 6 people are going to be left to sit in chair two.
- And then of course, if 2 people are already sitting down, how
- many people are left to sit in chair three?
- Well, there's going to be 5 possibilities.
- So a way to think about it, for each of these possibilities,
- there are 6 possibilities in this chair and 5 possibilities
- in that chair for each of those 6.
- So you would multiply all of the possibilities.
- Hopefully that makes some sense.
- We'll try it out with some examples.
- So the total number of possibilities in this
- case is 7 times 6 times 5, and what is that?
- 6 times 5 is 30.
- 30 times 7 equals 210.
- There's 210 possibilities.
- That's a lot of possibilities.
- Let's do a slightly smaller example.
- I mean we don't have to do people in chairs.
- Let's say we have cups.
- And I'll do the cups in a different color.
- So this is 1 cup, cup one.
- And then I have cup two.
- And then I have 3 balls.
- I have a magenta ball, I have a brown ball, and
- I have a yellow ball.
- And I want to know, how many different ways can I put these
- 3 balls into these 2 cups?
- Well, assuming that I haven't put any of the balls into any
- of the cups as yet, how many balls-- well, let's just
- start with cup two.
- I just want to show you that you don't have to start at the
- cup that happens to be labeled number one sitting on the left.
- If we haven't put any balls into any of the cups, how
- many can we put in cup two?
- Well, there's 3 possibilities, right?
- And for each of those 3 then, how many can
- we put into cup one?
- Well, we would've put 1 into here, so there will be 2
- left to put into cup two.
- So it'd be 3 times 2 possibilities, which
- is equal to 6.
- And let's see if we can draw them out.
- Let me number these cups because it's going to be
- too difficult to keep switching colors.
- So let's say this is A, B, and C.
- I'm going to show you that there are 6 ways of putting
- these 3 balls into these 2 cups.
- So it could be A in cup one, B in cup two.
- It could be B in cup one, A in cup two.
- Right, you could just switch them.
- So we actually care which ball goes into what cup.
- Not just is a ball in a cup.
- It could be A with C.
- A in cup one, C in cup two.
- It could be C in cup one, A in cup two.
- And then finally, you could just have B and C.
- B in cup one, C in cup two.
- Or C in cup one, B in cup two.
- And notice, if we just cared which of the balls were picked,
- but we didn't care whether they were in cup one or cup two, we
- could get rid of this bottom line and there would be 1/2
- as many ways to place them.
- But when we care where the balls are-- we care whether
- they're in cup one or cup two, or in this case we care if
- they're in seat one, two, or three.
- The ways in which we're ordering, we call
- these permutations.
- And up here, the way we would write this permutation, we
- would say, well, how many ways can we fit 7 people into 3
- chairs if we care about what chair they're sitting in?
- So we could write that as 7 people-- and the p isn't
- for people, it's for permutations-- into 3 chairs.
- And another notation for it, you write a big P and you
- say, how many ways can I put 7 things into 3 spaces?
- Or it could be written as, how many ways could you put
- 7 things into 3 spaces?
- And in this case, we got the answer is 210.
- And actually, it will always be 210.
- And I'll show you why in a second.
- How would we write this?
- Well, this would be-- I'll do it in green.
- We had 3 things and we put it into 2 spaces.
- So 3 things into 2 spaces.
- That's the same thing as 3 things into 2 spaces, which
- is equal to 3 things into 2 spaces.
- I'm just showing you the different notations, and we
- figured out that that was 6.
- Let's see if we can figure out a general formula if
- we wanted to evaluate nPk.
- How many ways can we fit n things into k spaces?
- So if we think about it, let's just use some analogy.
- We'll have k spots, so it'll be 1 spot, 2 spots, 3 spots,
- all the way to k spots.
- In the first spot there's n possibilities, just like we
- did in the last two examples.
- There's n possibilities there.
- Then, since 1 person or 1 thing will be placed in spot one,
- there's going to be n minus 1 possibilities for spot two.
- And similarly, n minus 2 possibilities for spot three.
- And then, we could follow that pattern all the way, and how
- many possibilities are there going to be for spot k?
- Well in everything it's n minus 1 thing less than the
- spot number in our case.
- I mean I guess we could have started with spot 0, but this
- is better because we actually numbered all the way to k.
- So it will be n minus k minus 1.
- And that might seem complicated, but
- it makes sense.
- When we did 7 things into 3 spots we went 7 times 6 times--
- we literally put in the top three of you could almost
- say from the factorial.
- 7 factorial will be 7 times 6 times 5.
- I think this will help.
- If this was just 3 was so 7 times 6 times 5 times 4
- times 3 times 2 times 1.
- That's 7 factorial.
- But we only took the first 3 of the factorial.
- And similarly, 6-- well, 6 is also 3 factorial.
- But another way you could view it is we only took the first 2
- of 3 factorial So what we're saying here is we just take
- the first k of n factorial.
- So is there any easy way to write that?
- To write the first k of n factorial.
- Why sure.
- We could write it as n factorial and the formula's
- almost harder than what it's saying.
- We could write it as n factorial-- it;s a lower
- case n-- n factorial over n minus k factorial.
- Let's see if that works.
- Well, what's going to happen?
- So in this case, n factorial was 7.
- So it was 7 times 6 times 5 times 4 times
- 3 times 2 times 1.
- And then what was n minus k factorial?
- Well, in our example, k was the number of spots,
- and there were 3 spots.
- So 7 minus 3 is 4, so 4 factorial.
- 4 times 3 times 2 times 1.
- And of course, this will cancel.
- Let me do that in a different color.
- This will cancel with this, and so you're just left with
- the first 3 of 7 factorial.
- The 3 largest components of 7 factorial.
- I always rederive this because all I think of is what
- we did originally.
- I was like, oh, OK.
- If we're doing permutations, I just start the factorial
- until I run out of spots.
- I do 7 times 6 times 5.
- And let's see if it works out here too.
- So what is 3 factorial because we have 3 different things?
- 3 factorial over-- and then 3 minus 2 factorial.
- Well, that's just 1 factorial.
- So it becomes 3 times 2 times 1 over 1.
- And of course, the 1's cancel out and we got the 3 times 2.
- Hopefully that make sense.
- A lot of people, they learn the permutation notation and they
- say, oh, that's n factorial over n minus k factorial, where
- n is the number of things I need to place and n minus
- the whole thing factorial.
- And k is the number of spots I have.
- And they just memorize it.
- But all this is saying is you start doing the n factorial,
- but you only do the first 3 components of the factorial.
- And it makes sense just from how we started off the video.
- If you 7 things, well, 7 things could go here, 6 things could
- go here, 5 things could go here.
- No more spots?
- Just multiply them.
- And that's all this formula is saying.
- Hopefully I didn't confuse you, and I will see you in the
- next video on combinations.
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| 4.375 | 5 | 4.109246 | 4.494749 |
<urn:uuid:d43e3d63-459c-4c66-a2e1-d36ca871b3a3>
|
This applet demonstrates three rules about angles and parallel lines.
Author and programmer: Ron Barrow
UK Years 7-9, KS3, Foundation GCSE Mathematics - Shape and Space
See also: Angles and crossed lines
Angles, straight lines and triangles
You can move the points A and B by clicking the red dots and dragging them with your mouse.
The lines CD and EF are parallel to each other. By moving A and B you can investigate three important rules (theorems) about angles and parallel lines. You
can choose which rule to investigate from the drop-down list at the top of the page.
The sizes of the angles follow these important rules.
What are the rules? Look at the angles marked with blue and orange as you move the lines,
and try to work out the rules. They are quite simple.
When you think you know, press the "Show the Rule" button at the bottom of the screen and the rules will be revealed. Have a think about why these rules work.
Enjoy yourself while you practise and learn these rules by name.
| 4.5 | 5 | 3.984115 | 4.494705 |
<urn:uuid:7dc48d48-7ac8-48a5-8eb6-5ee38c6ce7e0>
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“Aaaaaaa,” Cries the Baby
A Beginning Reading Lesson
By Janie Colvin
Rationale: This lesson teaches children about the /a/ correspondence, and how to read /a/ by associating it with a crying baby. Students will learn to recognize /a/ in spoken words by learning a meaningful representation (a baby crying) and the letter symbol A. Students will spell and read words containing /a/ in a Letterbox lesson, along with reading a decodable book that focuses on the /a/ sound.
Materials: Graphic image of a crying baby, cover-up critter, letter boxes, primary paper, letter tiles (a,t,h,m,p,d,r,g,c,l,s,s,f,b,n), poster with tongue twister written on it ("Andrew and Alice asked if Annie's animals were agitated."), white board, overhead/document cam, worksheet (listed at the bottom of the page), books for each student (A Cat Nap), and a list of spelling words on a poster or whiteboard for the students to read (lap, mat, Sam, gas, bank, glass, crab, splat)
1. Say: "In order to become expert readers we need to learn the code that tells us how to pronounce words. All letters make different sounds as we move our mouths a certain way. Today class, we are going to learn about the /a/ sound. When I say /a/, I think of a baby crying, "Ahhhhhhh." (Show graphic image).
2. Say: "The letter we are going to learn about today is a." (Have students take out primary paper and pencil). "Let's practice writing a on our primary paper. (Model on the board how to write the letter a). "Start at the fence line and make a curved line down until you touch the sidewalk, but don't stop here. Continue the curve around until you end up where you started. Then draw a straight line back down, and stop on the sidewalk." (As students practice drawing a row of a's, walk around the room observing and checking if they are correctly writing the letter a).
3. Say: "Before we learn about the spelling of /a/, we need to listen for it in some words. When I say /a/ in words, my mouth opens and lengthens, and my mouth looks like a baby's mouth when he/she cries. (Make vocal gesture for /a/.) I'll show you first: class. I heard /a/ and I felt my mouth open and lengthen (make a circle motion around lips). Now I'm going to see if I hear /a/ in school. Hmm, I didn't hear /a/ in school, and my mouth didn't open and lengthen. "That's not it." Do you hear /a/ in head, made, snow, rain, coat, bag, stamp, or lips?" (Have students make a circle motion around their lips when they feel their mouths make the /a/ movement).
4. Say: "Now I am going to teach each of you a tongue tickler that will help you remember the sound that /a/ makes." "Andrew and Alice asked if Annie's animals were agitated." (I will briefly review what the word agitated means before we say the tongue tickler together). "Let's say it together! Now let's say it again, and if you hear the /a/ sound in a word, I want you to raise your hand. (Repeat tongue twister). Now I want each of you to stretch out the /a/ sound. (Ex: Aaaaaandrew aaaand Aaaaalice…) Good Job!"
5. (Have students take out their letterboxes and letters). Say: "We are going to use what we just learned about the letter a to spell words. I will call out a word and you can spell it using the letterboxes. Before each word I call out I will tell you how many boxes to use. Each sound or mouth move in the word will go in a box. For example, the word I am going to spell is hat. I will use three boxes (draw three boxes on the board), because it has three sounds. The first sound I hear is /h/. I will place the letter h in the first box (model on board). Now it might help to say the word again to yourself, hat. The second sound I hear is /a/. We just learned the letter a stands for /a/, so I will place the a in the second box (model on the board). The last sound I hear is /t/. I will place the t in the third box (model on board). I spelled the word hat. Now you try." The words I will call out are: Lap, mat, Sam, gas (3) bank, glass, crab (4), and splat (5). After the students spell a word, the class will spell the word and I will write it on the board. After writing the words on the board, the class will read each word together.
6. Now, I will divide the students into partners. I will give each partner a copy of the book, A Cat Nap. I will ask each partner to go back and forth reading a page to each other. (Remind students if they are reading and get stuck, that there are things they can do to help themselves). Say: "First, try to read the word by covering parts of it up like I demonstrated for you earlier. Then read the sentence all the way through. Think about if the sentence makes sense. Then change words that do not make sense. After you are finished correcting, always make sure you reread the sentence one time through with the corrections that you made. I will be walking around to help you if you need it."
7. To end this lesson, I will read the story to the students and we will discuss and talk about the story as we read. The students will reflect on the story. For the next lesson we will use this book by rereading a familiar text.
8. To assess the students they will each be given a worksheet where they will be asked to circle the picture of the objects that contain the a=/a/ sound. The students must say the name of each picture aloud, and then circle the pictures in which they hear /a/.
"Aaaaaaaaa!" The baby cried. By: Ashley Farrow
Aaaaaaa!! The Crying Baby. By: Hannah Bailey
Book: A Cat Nap. Educational Insights, 1990.
Return to Doorways Index
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this form and investigate how the area and volume of a cube change every time
we double the length of the side. Start with 2 and keep doubling the side. You
might want to make a table of your data to keep track.
use the form, type in any number in one box and then click on either of the other
a graph of length of the side of a square vs. the area of the square (plot length
of side on the x-axis (in cm.) and area in cm2 on the y-axis. What
relationship in physics also show this type of graph?
you know the difference between mass and weight?
| 4) What mass
is needed on the right side to balance the lever on earth? What mass is needed
to balance the lever on the Moon? Assume the two blocks are equal distance from
the fulcrum and the balancing beam has minimal mass. |
A mass is attached to the spring scale on earth. The scale reads 100
g. as shown. The spring scale is now brought to the moon. What mass will be needed
for the scale to read 100 g.? |
Explain your answers.
How is a spring scale different than a triple-beam balance? How is it similar?
the density of a cube with a side of 4 cm. and a mass of 1235 grams. What is the
cube made of?
What is the mass of the cylinder on the left assuming it is made of ice?
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Hiragana is the character alphabet for Japanese native words. Words like "watashi" and "anata" would be spelled out using the Hiragana alphabet (you can use Kanji, too, but we're trying to be basic here.) The other two alphabets are Kanji and Katakana. Those are explained in the other sections, though. In the Hiragana alphabet, there are 46 different basic characters one can use. There are also special variations of certain characters that are also used, changing, for instance, "ka" into "ga" and so on, but we don't need to get into that here.
Before you jump into trying to pronounce half of these, there are a few very important rules you must know. (These rules are the same for the ones for Katakana)
Firstly, the "vowel" sounds in the Japanese language always sound the same. So, the letter "o" always sounds like "Oh" and the letter "e" always sounds like "eh." Here's a little chart that might help:
|"ah" sound as in "cola"|
|i||"E"sound as in "eel"|
|u||"oo" sound as in "food"|
|e||"eh" sound as in "wet"|
|o||"oh" sound as in "cola"|
With this in mind, one should be able to pronounce each of the 46 different Hiragana characters. Just add the consinents to the beginning of each vowel sound, and you basically have it. "ka" is read "kah," "ni" is read "knee," and so forth.
The second thing to keep in mind is the special characters. "chi" "tsu" "shi" and "fu" are the four characters that go against the patterns. For example, the row for the "k" characters reads "Ka, ki, ku, ke, ko..." but the row for the "s" characters reads "sa, shi, su, se, so..." instead of "sa, si, su, se, so." See the difference? It's a very slight difference, but it is noticable. The "t" row is the most complex. It reads "ta, chi, tsu, te, to" instead of "ta, ti, tu, te, to." Another special character is "fu." It is in the "h" row. "Ha, hi, fu, he, ho" instead of "ha, hi, hu, he, ho."
The last thing to keep in mind is the "r" row. It is natural for English speakers to pronounce "r" traditionally, but instead it is prounounced as an "l" sound. So, "rai" would sound like "lai."
I know it may be confusing, but just take your time to look at the chart. It isn't that bad when you get used to it.
Web site maintained by Club
Editor: Eric Friedrich
Updated: November 27, 2007
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Circle the action verbs. Cross out the words that are not action verbs.
Please Use any of the verb worksheets below in your classroom or at home. Just click on the worksheet title to open the PDF and print. Need a verb refresher? Here are some helpful articles on the different types of verbs.
Circle the subject and underline the verb in each sentence.
Choose is or are for each sentence.
Choose will or would to complete each sentence.
Complete the sentences below using the wishful form were.
Choose the correct form of the verb to match each subject.
Complete each sentence by writing the correct form of the verb to be.
Circle the verbs. Write each one in the past tense form.
Underline the adjective or noun.
Choose can, was able to, may or might to complete each sentence.
Choose lie, lay or laid to complete each sentence.
Choose sit, sat or set to complete each sentence.
Choose rise, rose, raise or raised to complete each sentence.
Write the correct past tense form of each verb. Circle the Irregular Verbs.
Read each verb aloud. Decide whether it is a past tense verb or a present tense verb.
Write the correct tense of the action verb to match the rest of the sentence.
Underline the complete verb in each sentence. Circle the helping verb.
Sort out the verbs from the story and write the correct verbs
In each sentence below, underline the subject and circle the simple subject.
Choose the correct tense of the verb to best complete each sentence below.
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Race to Say /A/!
Beginning Reading Design
1.Chart with "Amy bakes cakes all day in May."
2.A zip-lock bag for each student containing the Elkonin boxes and letters needed for the LBL lesson (a,t,e,b,k,e,g,h,u,g,w,v,e,z,p,r,i,c,d,r,o,p,l,n,t,s,c,p)
3.Elkonin boxes for modeling and letters needed to spell the word flake
4.A copy of the decodable book Jane and Babe for each student
5.Primary paper and pencils
6.Copies of attached a_e=/A/ practice worksheet for each student
7.Dry erase board and markers
8. Pseudoword note cards with the following printed on them: FAP, DAKE, DAT, FLAPE, WAT, BAGE, and HADE
1.First, review /a/=a. Then introduce a_e=/A/. Say, "Today we are going to talk about the letter a. We have already learned that a says /a/ in many words such as pat, tap, cat, and nap, but the letter a can also have a different sound. A says its name, the sound /A/, in words when it is followed by a consonant and then the letter e. When you hear this sound /A/ in words, think of somebody saying 'Hello!' or 'AAAAAA!' Let’s all wave to each other and say 'AAAA!' together.” (Say it together).
2."Now let’s say a tongue twister that uses the /A/ sound. (Put the tongue twister on the board so that everybody can read it along together.) Amy bakes cakes all day in May. Let’s say it together. (Say it together.) Now, let’s make the /A/ sound in the words longer. Aaaaaaamy baaaaakes caaaaakes in all daaaaaay in Maaaaaay. Good job!
3."Now I already told you that a says its name and makes the /A/ sound in words when it is followed by a consonant and then the letter e. Let’s look at some of those words on the board. How about the word cane? (Write cane on the board.) We can see that the letter a is followed by the consonant n and the letter e. Do we hear the letter e said at the end of the word? /k/ /A/ /n/…cane! No, the e is silent. The e just lets you know to say /A/ instead of /a/. Now, what if we take off the letter e? (Erase the letter e). What is that word? Can! Right! Let’s try another word. (Write plan on the board.) What word is this? /p/ /l/ /a/ /n/…plan. Right! Now, if I add an e to the end, that changes how we say that word. (Add an e at the end of plan.). Now it says, /p/ /l/ /A/ /n/…plane. Let’s try some more." (Repeat the two sequences with the words made/mad and glade/glad).
4. Now do the letterbox lesson for a_e=/A/. The students will already be familiar with this method of spelling and phoneme correspondence practice. The lesson will consist of some short vowel review words and words relevant to this new correspondence. Model for the students before they begin using your own letterboxes and letters. Say, "Let’s practice spelling some of these words. Today we have learned that a_e=/A/. (Write this on the board). The e is silent, so it will not go in the letterboxes, but just outside the last one. Let me show you how I spell the word flake. Now to spell this word we will need four boxes. The first sound I hear is the /f/, so I will put the letter f in the first letterbox. Now this word has a lot of sounds scrunched up in the beginning so I am going to stretch it out so I can hear each sound really well. FfffffllllAAAAkkkk. The next sound I hear after the /f/ is /l/, so I will put the letter l in the next letterbox. F-l-AAAkkk. The next sound I hear is the long /A/ sound. That means I will put the letter a in the third box. Now I need the e to make the a say its name, so I will put the e outside the last letterbox. I still have not spelled the word flake yet. I still hear the /k/ sound at the end of the word, so I will put the letter k in the fourth and last letter box, just before the e. Now I want you to spell some words". (Hand out bags to each child containing all the letters they will need and the Elkonin boxes.)
The following words will be used for the LBL. Say a sentence out loud that goes along with each word as you call them out for the students to spell. This way, the students will hear and understand the meanings of the words.
2 phoneme words: ate
3 phoneme words: bake, gate, hug, wave, zap
4 phoneme words: brick, drop, plate, tent
5 phoneme words: scrape
Walk around while the students are working to make sure they are using the letterboxes correctly and spelling the words correctly. Give guidance as needed.
Next, write all the words on the board. Call on different students to read them aloud.
5.Pass out individual copies of the decodable book Jane and Babe to each student. Say, "Now we are going to read a good book called Jane and Babe. This book has a lot of words with the /A/ sound in it. I will put you in pairs and you two will find a comfy spot in the room and take turns reading aloud to each other. Help each other if one of you is having trouble. If you both are having trouble decoding a word, raise your hand and I will help you. This story is about a zookeeper named Jane. She takes care of a big lion named Babe. She has to wake him up to feed him and clean his cage. Will Babe be mad when Jane wakes him up? Read to find out!"
6.After reading, students will go back to their desks and take out primary paper and a pencil. Say, "Now it is time for us to write a message. I want you all to tell me in one or two complete sentences what happened in the story you read, Jane and Babe. Was Babe mad when Jane woke him up? What did they do together? What does Jane do to take care of Babe? Write about anything you remembered from the story."
7.Pass out the a_e=/A/ practice worksheet. The worksheet will contain pictures of a cake, a gate, a plane, and a lake. The names of these pictures will be typed underneath them, and the students will also have to write the names of the pictures underneath each. Have students complete the worksheet after they have finished writing their message. Model how to complete the worksheet.
8.For assessment, call each student up to a desk/table individually. Show them flashcards with pseudowords written on each. Students then read the words to check for understanding of a = /a/ and a_e = /A/. Example words are: FAP, DAKE, DAT, FLAPE, WAT, BAGE, and HADE.
James and the Good Day. (Phonics Readers-Long Vowels. Educational Insights. 1990).
Jane and Babe. (Phonics Readers-Long Vowels. Educational Insights. 1990).
Mosley, Merdith. (2006). I Ate Grape Cake
Reinhart, Jennifer. (2008.) A Good Day for ay/ai
here to get back to Solutions
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At The Movies
Work systematically to find all the possible combinations
This problem is first of all about being systematic. This can be done using a number of strategies. You might make an organized list, draw a picture or use equipment. The difficult thing for many students is to keep track of all the possibilities as they go along. This is especially difficult if they use equipment.
The maths behind the problem involves counting all the possible combinations.
John, Jo and Chris have got seats for the movies. In fact their seats are F5, F6, F7. In how many ways can they sit in those seats?
- Use 3 students and 3 chairs to pose the problem.
- Ask the students to work in 3’s to solve the problem.
- Circulate to see that the students are keeping track of their solution.
How are you recording your work?
How do you know that you have found all the possible ways?
How could you convince someone else that you have found all the ways?
- Sharing of solutions
- Focus on the methods that students have used to be systematic.
Extension to the problem
What would the answer be if another two had joined the three friends?
What if your whole class went?
What if the seats were in a circle?
There are 6 ways for the students to sit on the seats.
Here we give every student a chance to sit in F5. There are 3 choices for this seat. For each particular student in F5 we then have two choices for F6. Then we have only one choice left for F7. Note that 3 x 2 x 1 = 6 is the final answer.
Solution to the extension
The extension is possibly ambiguous. We meant to mean that five friends had five seats, though some students might take it to mean that the five students had just three seats. Either way is worth considering.
Here five friends can be seated in five seats in 5 x 4 x 3 x 2 x 1 = 120 ways. If there are 25 in your class, then there are 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. This is a very big number. You might like to let the class calculate it.
On the other hand if the five friends are to be seated in only three seats, then there are 5 ways of putting the first friend in a seat, four ways for the second and three for the third. So it looks as if there are 5 x 4 x 3 = 60 ways. For the 25 members of your class you get 25 x 24 x 23 = something much more manageable than the number in the last paragraph! But then only three get to see the film!
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The first section says: "Clues from the story. The apple tree has....."
The second part says: "I think it looks like:"
The first part of the worksheet was to write down the clues about the apple tree we were given by the author (explicit information). The students recalled what they heard in the story and wrote down the clues:
1. 10 furry toes
2. sharp teeth
3. long pointy ears.
The second part of the worksheet was to draw the picture they saw in their brain. They had to use the explicit information given as well as infer what the rest of their drawing should look like. The kids actually did a really great job with this! Here are a few samples:
He even added labels to his picture!
After they were done, the kids shared their drawings with the group. Then I shared the picture the author used in the story. (It was so funny how they were in such suspense waiting for me to share the picture. They kept trying to sneak a peek while I wasn't looking!) At the end of the lesson, we had a discussion about how each drawing is different, but all are correct visualizations as long as they all contained the details the author gave us.
I created this worksheet on word. This would be a great activity you could use with almost any book, just adapt the worksheet. Have a wonderful evening!! 9 days until Thanksgiving!!!
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The highest surface part of a wave is called the crest, and the lowest part is the trough. The vertical distance between the crest and the trough is the wave height. The horizontal distance between two adjacent crests or troughs is known as the wavelength.
Wave height is affected by wind speed, wind duration, or how long the wind blows, and fetch, which is the distance over water that the wind blows in a single direction. If wind speed is slow, only small waves result. If the wind speed is great but it only blows for a few minutes, no large waves will occur. Also, if strong winds blow for a long period of time but over a short fetch, no large waves form. Large waves occur only when all three factors combine (Duxbury, et al, 2002.)
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Numbers, such as 784, have three digits. Each digit is a different
The first digit is called the hundreds' place.
It tells you how many sets of one hundred are in the number. The
number 784 had seven hundreds.
The middle digit is the tens' place.
It tells you that there are 8 tens in addition to the seven hundreds.
The last or right digit is the ones' place which is 4 in this example.
Therefore, there are 7 sets of 100, plus 8 sets of 10, plus 4 ones in the number 784.
7 8 4
| | |__ones' place
| |_________tens' place
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Ahh! Now That's Refreshing!
Beginning Reading Lesson
Rationale: This lesson teaches children about the short vowel correspondence o = /o/. It is important for students to learn the correspondences between sounds and letters and recognize spellings that map word pronunciations in order to decode words. In this lesson children will learn to recognize, spell, and read words containing the correspondence o. The will learn a meaningful representation, a man saying, "Ahhh" after having a cool drink on a hot day, and will spell and read words with this correspondence in a Letterbox lesson. They will also read a decodable book that focuses on this correspondence.
1. Graphic image of a man drinking a cool drink
2. Cover up critters
3. Whiteboard or smartboard Elkonin boxes for modeling
4. Individual Elkonin boxes for each student
5. Letter manipulatives for each child : a, b, c, f, k, l, m (2), n, o, p, r, s, t
6. Magnetic or smartboard letters for teacher : a, b, c, f, k, l, m (2), n, o, p, r, s,t
7. List of spelling words on poster to read: 2- on, in; 3- rock, mom, lock, bat; 4- stop, flop
8. Decodable text: A Hot Spot
9. Assessment Worksheet
10. Assessment Word List: pop, cog, hot, dob, prom, flock
11. Tongue Tickler poster
11. Tongue Tickler poster
1. Say: In order to become the best readers, we need to learn the secret code that tells us how to pronounce words. Today we are going to crack the code for the letter o (write the letter on the board). Sometimes the letter o makes the sound /o/, kind of like when I take a sip of a refreshing drink on a hot day (show graphic image). Have you ever been really thirsty and then taken a gulf of a drink? Did it make you say "ahhhh"? That is the same sound the letter o makes. Can we all say /o/ together? While you say it, pretend you're drinking a nice cool drink on a hot day with your hands and mouth. We will learn all about this letter today, including the sound it makes, what it looks like, how to write it, and how to read it!
2. Say: Before we learn how to spell /o/, we need to listen for it in some words! When I listen for /o/ in words, I hear the sound coming from the back of my mouth, and my mouth is wide open in an "O" shape! Our tongue stays still. Practice saying /o/ a few times using your cold drink! Let me show you how to find it in a word first: top. I felt my tongue be still and my mouth open wide. There is a short o in top. Now I'm going to see if it's in school. Hmm, I didn't make a sound like I just had a refreshing drink, and didn't open my mouth wide. Now you try. If you hear /o/, put your hand to your mouth like you're drinking your cool drink. If you don't hear /o/ then leave your hands on your desk. Is it in mop, bet, flop, hot, cap? Now listen to this silly tongue tickler for the /o/ sound made with o! (Say the tongue tickler "Oliver had an operation in October, and Oscar gave him an octopus.") Now let's all say it together! Awesome job! Now let's see what words in our tongue tickler have the /o/ sound in them. We're going to read it very slow and drag out each word to see if it has /o/! O-liver had an o-peration in O-ctober, and O-scar gave him an o-ctopus. Great job!
3. Say: Now let's look at the spelling of /o/ that we'll learn today since we know how it sounds. Let me show you how to write the letter o, which makes the sound /o/. (Write it on the board for all students to see). Start at the fence, and curve it down like a little c to the sidewalk, then make another curve from the sidewalk up to the fence on the other side, like this! It should look like a circle! Practice this a few times on your paper. Remember to start at the fence line. Fantastic!
4. Say: Now we are going to use our letter boxes to spell words with the /o/ sound, but we will also review some words with the other vowels we have learned. This will help you pick out the words with the /o/ sound. (Pass out the letter boxes and letter tiles) Remember we use the letter o to represent the /o/ sound! I will show you how to use these first. What if I want to spell the word rock? "I found a new rock for my collection." To spell rock in the letterboxes, first I need to count the phonemes. Let's see, r-o-ck, three! That means I need to use three boxes. I know I heard the /o/ sound in there, so I will need to use the letter o. The first sound I hear is /r/, the word starts with r, so I am going to put it in my first box. Then I heard /o/ so I will put it in the second box. Let's say the word again slowly to stretch out the sound: rrrrooooccckkkk. I think I heard /ck/ at the end so I will put a c and a k in the last box. Now, I want you to try some! When I call out a word, I want you to put the letters in your boxes. I will tell you how many boxes you need for each word, and will be coming around to see if you need any help. I am going to start out easy with two boxes for on. I am standing on the ground. What should go in the first box? (Respond to student's answers). What goes in the second box? Good! Here's another easy one, in. I like to swim in my pool. Make sure you check to see if you need to put an o in the word! (Observe progress). I didn't hear the /o/ sound in the word in, so it should not be in your letter boxes. Remember, some words will be review. You'll need three letterboxes for the next word, and remember to listen for the /o/ sound. Here's the word: mom. I like when my mom bakes me cookies. (Allow children to spell word). Time to check your work. Watch how I spell it in my letterboxes on the board: m-o-m and see if you've spelled it the same way. Try another with three boxes: lock; I need to lock up my bike when I come to school. (Have a volunteer spell it in the letterbox on the front board for children to check their work, and repeat this step for each word.) Next word: bat. Do we hear the /o/ sound? Which sound do we hear? Now let's try 4 letterboxes, or 4 phonemes: stop; My dad said to stop jumping on my bed. One more: flop; I went flop on my bed when I kept jumping.
5. Say: Let's write some of the words we just spelled on the board! I want you to read them to me as a class when I point to them. If you hear the /o/ sound, pretend you are taking a sip of your cool drink! I will show you how to do this first, and then we will do it together. (Write the word sock on the board.) I see the o in the word, which I know says /o/. I am going to use my cover-up to get the first part. It starts with /s/. Then it ends with /ck/. Now let me blend it s-o-ck… oh, sock! (Pretend you are drinking your cool drink as you say it). I am wearing a sock on my foot! Now it's your turn! (Write the words from the letterboxes on the board, along with a few new words.) Great job!
6. Say: Now we are going to read a book called A Hot Spot since you have all done such a good job reading and spelling words for o=/o/. This is a story about a boy named Tim who just wants a cool drink on a hot, hot day. But, there is a pig in the way! Read the story to find out what happens. I want you to whisper read this story to yourself. (Walk around the room monitoring progress. After individual reading, the class reads the story aloud together, stopping between pages to discuss the plot.)
7. Say: That was a fun story! What happened to Tim in the end? Before we finish up with our lesson, I want to see how you can pick out some words with /o/ sounds in them! Color in the words and pictures with the short /o/ sound in them. I will call you up individually to read some words with /o/ sounds!
8. Assessment: I will have a worksheet with words and pictures where some words will have the /o/ sound and some will not. I will instruct student to color in the words and pictures with the short /o/ sound in them. While the students are completing this, I will have each student come up individually and read me a list of words and pseudowords with the short /o/ sound. This will be a good assessment to see if they can decode words with the short /o/ sound.
Murray, G. (2004) A Hot Spot. Reading Genie: http://www.auburn.edu/academic/education/reading_genie/bookindex.html
Johnson, Holly. "Open wide and say Ahhh!" http://www.auburn.edu/academic/education/reading_genie/awakenings/johnsonhbr.htm
Return to the Epiphanies index.
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Aaaaaa it's a snake!!!
need to have an understanding of the
alphabet and the phonemes that letters make to be able to read. When one develops this understanding they are
able to recognize the letters and sounds in print and can read them. Beginning with short vowel sounds is the
first step to teaching phonemes. This
lesson will help children recognize a=/a/.
"Lad and the Fat Cat" by Geri Murray (Powerpoint
from Reading Genie site) http://www.auburn.edu/academic/education/reading_genie/Geniebooks/LadFatCat.ppt
Tongue Twister: "Andrew and Alice asked if Annie's
active animals were angry."
Pictures of different things that have /a/ sound in
(cat, bat, bag, crab, alligator)
Picture of a snake
- Begin the lesson by explaining why it
is important to understand the letters in our language and what sounds
the letters make. Explain that
understanding letters and sounds helps us to read and how important
reading is. Then explain that it is very
important to focus on how our mouth moves when we make certain sounds.
- Ask the students if they have ever
seen a snake and said "Aaaaa!"? Ask, "What
does your mouth do when you make that sound?" Explain
that that is the mouth movement we are looking for in this lesson. Point at a picture of a snake and say, "Aaaa!" Have the students do the same.
- Next try the tongue twister, "Andrew
and Alice asked if Annie's active animals were angry."
Have the students say it with you. Now
let's try it again by stretching out the /a/ in the words.
"Aaaandrew aaaaand Aaaaalice aaasked if Aaaanie's aaaacitve
aaaanimals were aaaangry." Great job! Now let's say it by breaking off the /a/. "/a/ndrew /a/nd /a/lice /a/sked if /a/nnie's
/a/ctive /a/nimals were /a/ngy."
- Next get out the primary paper and
pencils for the students to practice writing. We
need to practice writing a. We
need to start just below the fence, go up and touch the fence, down to
the sidewalk, around and straight down. Now
you practice. I am going to put a snake on
your paper and I want you to write ten a’s.
- Now tell the students to signal that
they saw a snake each time they see the letter a by
itself in a word. Have them yell /a/. Ask the students if they hear /a/ in good or
bad? Tell them that you hear /a/ in baaaad. Then ask the
students which word they hear /a/ in. Bag or purse? Dog or cat? Bat or glove?
- Begin with a book talk about "Lad and
the Fat Cat." Lad is a dog and Scat is a
cat. Lad is mad because Scat has his mat. Lad is mad because Scat can't get up. Why do you think Scat can't get up? To find out you'll have to read "Lad and the
Fat Cat." Each time they hear /a/ tell
them to act scared like when they see a snake. Have
the students write a short message using a word with /a/ in it. Assess by using a running record as they read.
- Assess again by giving them picture
cards with things with /a/ in them and other cards that don’t. Have them mark or color the ones that have /a/
Brittany Williams "Aaaaa! There's
"Lad and the Fat Cat" by Geri Murray
Reading Genie Site
Return to the
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"Watch out for that Choo Choo Train!"
Rationale: In this lesson the children are going to read and spell words with ch in them to help them to be able to recognize the phoneme ch. The children first have to understand that this phoneme is represented by two letters.
Worksheets with pictures and words on them.
(Pictures: chimney, frog, chair, cloud, flowers, chips, and children)
Chart with tongue twister- CHip and CHuck CHewed CHerries.
Letterboxes and Letters for words: Chuck, chap, chop, chart, chick, chin, and chess
Letters needed: ch, i, c, k, a, o, p, r, n, t, e, and s.
Book: Chips for the Chicks by Geri Murray (make copies of this book for your whole class)
1.) Introduction: Today we are going to learn that c and h together make the /ch/ sound when they are put together.
2.) Practice: Does anyone know what kind of sound a train makes? Choo Choo! Very Good! It makes the ch-ch sound. So now I want everyone to raise your arm up like a horn and pull it down like a train horn.
3.) Tongue Twister: Now I am going to read you a sentence off the chart. Chip and Chuck Chewed Cherries. Now I want you to say it with me. While we read it together I want you to listen for the /ch/ sound in the words and remember to pull your horns when you hear the /ch/ sound.
4.) Letterbox Lesson: Pass out the letters and the letter boxes to each student. Now I want everyone to turn your letters to the lower case side. Very Good! Now I am going to model with the word chat. Chat-I hear a /a/ in the middle and it makes the /a/ sound. I hear a /ch/ in the beginning and we have learned that ch makes that sound. At the end of the word I hear /t/ which is the sound for t. Let's look at our ch it is taped together. Does anyone know why it is taped? Because it makes one sound when put together. Now do the letter box lesson (Use short vowels only in the letter box lesson.) Very Good! Now I want everyone to listen while I spell the words and you say them. For ex. Chat. Chat begins with /ch/ and says /a/ in the middle. And the last sound we hear is /t/ so when we blend these sounds we get the word chat. Now I will spell the words and you say them one at a time. Note Miscues.
6.) Assessment: Give each student a worksheet with pictures on one side and words on the other. I want you to match the words with the pictures that have the /ch/ sound and ch in them. Take these worksheets up after the children are through. Do a running record for each child on the book that you previously read to them and that they had the chance to look at and read. (This time children will read it individually to you.)
Murray, Bruce and
Lesniak. "The letterbox
lesson: A hands on approach for teaching
Eldridge, J. Lloyd. Teaching Decoding in Holistic Classrooms. Prentice Hall: 1995 pg. 36.
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|Slide rules HOME page||INSTRUCTIONS||A-to-Z|
Trigonometric calculations (sine and tangent)
Trig scales on front of the slide
It is not the purpose of this site to teach trigonometry, rather how to use trig scales on slide rules. For this purpose we will look at typical examples using trig scales in different positions on the rule. This page is related to rules with the trig scales on the front of the slide.
As an example we use a Pickett N 4P-T. This 5" rule has four trig scales, two for tan (T : 5.6° to 45° and 45° to 84.6°), one for sin (S : 5.6° to 90°) and one for sin and tan for small angles (ST : 0.56° to 5.6°). Relatively few rules have the second tan scale and some do not have the ST scale. We discuss below how to calculate the tan of angles outside the range of the scales. The advantage of a 5" rule is that distances are smaller which makes for more compact diagrams.
This rule has the angles graduated in degrees and decimal fractions of a degree. Other rules may have the angles graduated in degrees and minutes or in grads.
Right angle triangles
To find the length of c given the length of a (2.0) and angle C (30°).
The formula is: c = a tan C
1 on C to 2.0 on D
Cursor to 30.0 on T
Answer (1.16) under cursor on D.
To find the angle C given the length of a (1.2) and b (2.3)
The formula is: C = sin-1 (a/b)
1 on C to 2.3 on D
Cursor to 1.2 on D.
Answer 31.4° under cursor on S.
To find the length c given the angle C (27.0°) and the length b (2.7).
The formula is:
c = b sin C
1 on C to 2.7 on D
Cursor to 27.0 on S
Answer (1.23) on D
To find c given b (2.3) , C (47.0°) and B (32.0°)
The formula is:
c = b sin C / sin B
Cursor to 2.3
32.0 on S to cursor
Cursor to 47.0 on S
Answer (3.17) under cursor on D
Tan and sin of small angles (<5.7°)
For small angles tan and sin are almost equal. To calculate the sin or tan of a small angle multiply the angle by 0.01745. Some rules have a gauge point at this value.
Tan of large angles ( > 45.0°)
For slide rules without a second tan scale align 90 minus the angle with 1 on the D scale, the answer is on the D scale under 1 of the C scale. (Note although this rule has two tan scales, for consistancy this rule is used for the explanation).
The example shows tan 60.
90 - 60 = 30
30 on the tan scale is aligned with 1 on the D scale.
The answer 1.73 is on the D scale against 1 of the C scale.
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Hunting with H
Rationale- This lesson will help children identify /h/, the phoneme represented by H. Students will also understand how their mouth moves when making the /h/ sound. Activities that involve the letter H, along with a piece of literature will help the students remember and learn the letter H.
· Chart with tongue tickler written largely on it: "Harry the hippo had a happy holiday."(1)
· Pictures of a person hiking, bike, house, mouse, a person saying welcome (hello), a person waving (goodbye), hot (sun), cold (snow)-teacher will specify which words are which. They will put together in pairs so that the student can easily compare. The teacher will have these laminated. (1 flip book).
· "A House for Hermit Crab" by: Eric Carle
· Worksheet with pictures (for each student)
· Pencil (for each student)
· Crayons (for each student)
· $2 6-pack sunglasses (of all different shapes)
· Paper (for each student)
1. Introduce the lesson by saying: Class, today we are going to be talking about the letter H! Just like each letter looks different, we have to move our mouths differently to make the sound of that certain letter. The letter H is in quite a few words and we need to know and understand what the letter H looks like and also what it sounds like so that we can read different words.
2. Hand out plastic glasses to the class so that they can practice learning the /h/ sound.Let's pretend you are cleaning off your eye glasses, now hold up your eye glasses to your mouth, like this (shows class) and blow that warm air onto those glasses and say Hhhhhhhhhhhhhhhh, I'm so hhhhhhhhappy. What is your mouth doing while you make the /h/ sound? When I make the sound /h/ my mouth opens up real wide to let all of the hot air out. It looks like this (show class again).
3. Now let's try a tongue tickler to practice saying our new sound (point to the chart). Harry the hippo had a happy holiday. Let's try it together three times (class then repeats tongue tickler three times). Good job! Now let's say it again and stretch out the /h/ sound when we hear it in our tongue tickler. Hhhhhhhharry the hhhhhhhhhhippo hhhhhhhhad a hhhhhhhhappy hhhhhhhholiday.
4. Alright class, now let's see which words we hear the /h/ sound in. I'm going to choose between two words to show you how I know what word has the letter H in it, do I hear the Hhhh in sound or hound? Right! I hear the Hhhh in hound! Good job! Now, who can raise their hand and tell me which word they hear the letter H in? (Flip to first page of pictures) Do you hear the sound /h/ in hike or bike? (Call on student). Explain why you think that word has an H. Good! (Flip to second page to show mouse and house). Mouse or house? (Call on student). Good! Explain why you think H is in that word. (Flip to third page to show hello or goodbye). Hello or goodbye? (Call on student). Good! Explain why you think H is in that word. (Flip to last page that shows hot or cold). Hot or cold? (Call on student). Great job everyone! Explain to students why the /h/ sound is in hot instead of cold.
5. Class, now that we have talked about the different sounds H can make, lets practice writing the letter H. Okay, class, this is how I draw a capital H (teacher demonstrates how to draw the letter H on the board.) Who can come up to the board and practice drawing a capital H? Alright, now class, we are going to write a lower case h, it looks like this (teacher draws lower case h on board). Now, who wants to come up to practice drawing the lower case letter h? Thank you for those who participated. I want you all to draw a upper case H and a lower case h on your paper now.
6. Alright! Now let's all gather around so that we can read a book. The title of our book is called "A House for Hermit Crab" the author of this book is Eric Carle. What /h/ sounds do you hear in the title of this book? I hear that house and hermit both have the /h/ sound. This book is about a Hermit crab that outgrows his shell, but when he moves into his next shell it is so bare that it makes him sad. Then to his surprise all of the beautiful sea creatures come together to make his shell pretty but then he starts outgrowing it again. As we read the book, I want you to remember earlier when we talked about blowing /h/ sound on your eye glasses with the hot air that comes from deep in your lungs. Every time you hear the /h/ sound put on your eye glasses. (Read the book together).
7. Okay class, now it's your turn to show me how much you've learned about the letter H. Pass out worksheet with pictures of different things. Draw a line with your pencil to the /h/ sounding pictures and then I want you to color only the pictures that have the /h/ sound.
Click here for the
Click here for the Awakenings Index
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Roman numerals came originally from Etruscan numerals, but they changed the symbols. The Roman system came into use from the 4th century BC, but the symbols we know today were not fixed until about the 1st century AD.
In our number system (called Arabic numbers), we have ten digits (from 0-9) and we can make as big a number as we want with these. We use all ten digits to count to nine, then we combine them to make bigger numbers. So we never run out of numbers, as long as there is room to write them down! The more digits there are, the longer the number is. The ancient Romans didn't think this. They repeated symbols, so one was I and 2 was II. For larger numbers, they invented new symbols, so five was V, ten was X, and so on. But they didn't have a symbol for zero. They didn't need it.
Click in the first box and type in a whole positive number less than 4000. The Roman number will appear in the other box. Try different numbers, and see how the Romans would write them. If you have a Roman number and you want to find out what it is, click on the Roman box and type it in. Click on Count to watch the numbers change. If you put in a number, you can see a Roman times table in action!
The Romans had different symbols for numbers as they got bigger:
These were the normal symbols, but they could only describe numbers up to 3999. The Romans combined their symbols, so VII meant 5+1+1 or seven. This is called a unary system. However, they found that IIII and VIIII were too confusing (for four and nine), so they introduced another idea. If the I comes after the V then you add it (VI is 6). But if the I comes before the V then you subtract it (IV is four). The rule is that you are allowed to add up to three (VIII is eight), but only subtract one (IX is nine). This means that you have to be very careful what order Roman digits are in. XI is a different number from IX.
You can also do this for larger numbers.
MDCCCLXXXVIII = 1000 + 500 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 1888
MCMXCIX = M CM XC IX or 1000 + (1000 - 100) + (100 - 10) + (10 - 1) = 1999
You have to be good at adding and subtracting for Roman numbers! Also, you can't tell from the length of the number, how big it is (MM is 2000).
How can we remember what these letters are? The easy letters are I, C and M. I is probably a finger. Most people start off by counting on their fingers! The Romans spoke a language called Latin, and the Latin for hundred is Centum. So C was an obvious letter for 100. We still use cent in English words to mean a hundred, so it's easy to remember. Think of a hundred centimetres in a metre, a hundred years in a century or a a hundred cents in a dollar. The Latin for thousand is Mille. So M is the letter for thousand. Think of a thousand years in a millennium or a thousand millimetres in a metre.
Here is a way to remember that V is five. I or II or III are different numbers of fingers held up. So what are five fingers? A whole hand, of course! If you look at a hand (see left), you can see that the thumb and little finger make a V, and it's a lot easier than to draw the whole hand. Perhaps the hand can also explain why the number 4 is written as IV. It is a hand with the thumb turned down. This is a lot easier to do than turning down a couple of fingers, so it could be that's why we only subtract one, not two or three.
Ten fingers are both hands, so the two V's make an X (see right).
|Now for fifty. Fifty is half of a hundred. If you take the symbol for hundred, C, and cut it in half, it looks like an L, which is the letter for fifty.|
|Five hundred is half of a thousand. If you take the symbol for thousand, M, and cut it in half, it looks like a D (sort of), which is five hundred.|
At the top of this page, when using the convertor, I tell you to type a number in which is less than 4000. Why? When we use Roman numbers today, we don't use them for big numbers, so you never see the Roman number for 5000 (and if you don't have that, then you can't write 4000). The Romans agreed on symbols for 1, 5, 10, 50, 100, 500, and 1000, but there were different symbols for 5000 and also for the bigger numbers. Here is one way the Romans wrote these bigger numbers.
So you would write 924,587 like this:
As you can see, it's getting quite messy!
We still use Roman numbers today. One place where you often see Roman numbers is on a clock face. The hours are marked as I to XII. However, there is something odd about these Roman numbers. If you look at four, it is IIII instead of IV. I think that this is because half of the numbers are upside down, since they follow the edge of the clock face round. You can get IV and VI muddled up when they're the right way up. It is even worse when they're upside down! IX and XI are not such a problem, since they are more or less the right way up. In fact, the Romans never had clocks like this, since this type of clock was invented centuries afterwards.
Another place where you see Roman numbers is in the copyright year shown at the end of British TV programmes. Perhaps they do this because most people don't know their Roman numbers very well, so they can't work out how old the programme is!
This is the accepted modern way to count with Roman numbers. The Romans themselves were not so fussy. There is a Roman tombstone in York, England, of Lucius Duccius Rufinius, who was the standard bearer of the VIIII legion (9th), and was XXIIX years old (or 28).
© Jo Edkins 2006 - Go to Numbers index - Go to Romans index
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Code Help and Videos >
In Python code, a string is written withing double quotes, e.g. "Hello", or alternately within single quotes like 'Hi'. Use the
len(s) function to get the length of a string, and use square brackets to access individual chars inside the string. The chars are numbered starting with 0, and running up to length-1.
s = 'Hello' len(s) ## 5 ## Chars are numbered starting with 0 s ## 'H' s ## 'e' s ## 'o' -- last char is at length-1 s ## ERROR, index out of bounds
Python strings are "immutable" which means a string can never be changed once created. Use + between two strings to put them together to make a larger string
s = 'Hello' t = 'Hello' + ' hi!' ## t is 'Hello hi!'
A "slice" in Python is powerful way of referring to sub-parts of a string. The syntax is s[i:j] meaning the substring starting at index i, running up to but not including index j.
s = 'Hello' # 01234 ## Showing the index numbers for the 'Hello' s[1:4] ## 'ell' -- starting at 1, up to but not including 4 s[0:2] ## 'He'
If the first slice number is omitted, it just uses the start of the string, and likewise if the second slice number is omitted, the slice runs through the end of the string.
s = 'Hello' # 01234 s[:2] ## 'He', omit first number uses start of string s[2:] ## 'llo', omit second number uses end of string
Use the slice syntax to refer to parts of a string and + to put parts together to make bigger strings.
a = 'Hi!' b = 'Hello' # Compute c as the first 2 chars of a followed by the last 2 chars of b c = a[:2] + b[len(b) - 2:]
A bad index in Python, e.g. s for the string "Hello", is a runtime error. However, slices work differently. If an index number in a slice is out of bounds, it is ignored and the slice uses the start or end of the string.
Negative Index As an alternative, Python supports using negative numbers to index into a string: -1 means the last char, -2 is the next to last, and so on. In other words -1 is the same as the index len(s)-1, -2 is the same as len(s)-2. The regular index numbers make it convenient to refer to the chars at the start of the string, using 0, 1, etc. The negative numbers work analogously for the chars at the end of the string with -1, -2, etc. working from the right side.
s = 'Hello' # -54321 ## negative index numbers s[-2:] ## 'lo', begin slice with 2nd from the end s[:-3] ## 'He', end slice 3rd from the end
One way to loop over a string is to use the
range(n) function which given a number, e.g. 5, returns the sequence 0, 1, 2, 3 ... n-1. Those values work perfectly to index into a string, so the loop
for i in range(len(s)): will loop the variable i through the index values 0, 1, 2, ... len(s)-1, essentially looking at each char once.
s = 'Hello' result = '' for i in range(len(s)): # Do something with s[i], here just append each char onto the result var result = result + s[i]
Since we have the index number, i, each time through the loop, it's easy to write logic that involes chars near to i, e.g. the char to the left is at i-1.
Another way to refer to every char in a string is with the regular for-loop:
s = 'Hello' result = '' for ch in s: ## looping in this way, ch will be 'H', then 'e', ... through the string result = result + ch
This form is an easy way to look at each char in the string, although it lacks some of the flexibility of the i/range() form above.
CodingBat.com code practice. Copyright 2010 Nick Parlante.
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Shirley loves to SHAKE her SHAKERS
Rationale: In order for children to be successful in phonics, reading and spelling, they need to understand phonemes. Children learn to recognize different phonemes and sounds by matching letters to their vocal gestures in spoken contexts. In this lesson, children will learn the sound and spelling of the consonant digraph /sh/ through an expressive representation and written practice. They will also be able to practice using and spotting the /sh/ sound in both written and spoken language.
Copy of ‘‘A Crash in the Shed’‘ by Geri Murray
Poster with tongue twister (Shirley found a shellfish and shipped it to the shop)
1. Ask a question to get the students interested in the lesson. ‘‘Has anyone ever been to a football game or a basketball game? What are some of the spirit/pep items you see while at the game?
2. Ask students, have you ever had someone ask you to be quiet by saying /sh/? Well, today we are going to focus on the /sh/ sound. Can you say /sh/? Model how to move your mouth to make the /sh/ sound. [Remember to shake your shakers when you hear the /sh/ sound.]
3. Now, we are going to learn how to do a tongue twister with the /sh/ sound. Has anyone ever heard of a tongue twister? Repeat after me, Shirley found a shellfish and shipped it to the shop. Everyone say it three times. Now we will say it again, but this time, I want you to stretch out all of the words so we can hear /sh/. [Remember: Use the motions!] Now, I want you to break off the /sh/ when we say the tongue twister: ‘‘Sh/irley found a sh/ellfish and sh/ipped it to the sh/op.’‘
4. Now is a good time to have students practice writing the letters. Pass out primary paper and pencil to your student(s). It is a good idea to not use mechanical pencils with beginning reading and writing students. Now we are going to use this paper to practice writing the letters s and h. We are going to write the lowercase letter s right now. Form a tiny c up in the air, and then swing back. This makes an s. Next we are going to write the letter h. Observe students and help them if they need help. You can model it again if you need to. Now when you see s or h in a word you can recognize it and remember that it makes the /sh/ sound.
5. Now, I’m going to show you how to find /sh/ in the word wish. I am going to stretch wish out and I want you to listen for the /sh/ like in shakers in this word. w-i-sh. There it is, there is the /sh/. It’s your turn now.’‘
6. Now I’m going to say some words and you are going to shake your shaker every time you hear the /sh/ sound. ‘‘Wish, now put your finger over your mouth when you hear the /sh/ in wish. Do you hear it in bear? Do you hear it in ship? Do you hear it in hops? Do you hear it in wash?’‘
7.’‘Now I’m going to read you the book, A Crash in the Shed by Geri Murray .This is a great book with lots of words with the /sh/ sound. Let’s read and see what this Crash could be in the Shed and see if you can hear the /sh/ sound. Remember to use your shaker every time you hear the /sh/ sound. After reading the book once read it again but this time stop at the end of each sentence and have the students identify the words they heard that have the /sh/ sound in them.
8. For further assessment have the students identify different objects in the classroom that have the /sh/ sound in their name. pencil sharpener, shapes, shoes, etc…
9. For an extension activity each student could make their own personal shaker to use at their very own next AU football game.
A Crash in the Shed by Geri Murray Collection Copyright 2006, The
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Introduction to functions An introduction to functions.
Introduction to functions
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- Welcome to the presentation on functions.
- Functions are something that, when I first learned it, it
- was kind of like I had a combination of I was 1,
- confused, and at the same time, I was like, well what's even
- the point of learning this?
- So hopefully, at least in this introduction lecture, we can
- get at least a very general sense of what a function is
- and why it might be useful.
- So let's just start off with just the overall
- concept of a function.
- A function is something that you can give it an input-- and
- we'll start with just one input, but actually you can
- give it multiple inputs-- you give a function an input,
- let's call that input x.
- And you can view a function as-- I guess a bunch of
- different ways you can view it.
- I don't know if you're familiar with the
- concept of a black box.
- A black box is kind of a box, you don't know what's inside of
- it, but if you put something into it like this x, and let's
- call that box-- let's say the function is called f, then
- it'll output what we call f of x.
- I know this terminology might seem a little confusing at
- first, but let's make some-- I guess, let's define what's
- inside the box in different ways.
- Let's say that the function was-- let's say that f of x is
- equal to x squared plus 1.
- Then, if I were to say what is f of-- let's
- say, what's f of 2?
- Well that means we're taking 2 and we're going to
- put it into the box.
- And I want to know what comes out of the box
- when I put 2 into it.
- Well inside the box, we know we do this to the input.
- We take the x, we square it, and we add 1, so f of 2 is 2
- squared, which is 4, plus 1.
- Which is equal to 5.
- I know what you're thinking.
- Probably like, well, Sal, this just seems like a very
- convoluted way of substituting x into an equation and just
- finding out the result.
- And I agree with you right now.
- But as you'll see, a function can become kind of a more
- general thing than just an equation.
- For example, let me say-- let me actually-- actually not,
- let me not erase this.
- Let me define a function as this.
- f of x is equal to x squared plus 1, if x is even,
- and it equals x squared minus 1 if x is odd.
- I know this would have been-- this is something that we've
- never really seen before.
- This isn't just what I would call an analytic expression,
- this isn't just x plus something squared.
- We're actually saying, depending on what type of x you
- put in, we're going to do a different thing to that x.
- So let me ask you a question.
- What's f of 2 in this example?
- Well if we put 2 here, it says if x is even you do this one,
- if x is odd you do this one.
- Well, 2 is even, so we do this top one.
- So we'd say 2 squared plus 1, well that equals 5.
- But then, what's f of 3?
- Well if we put the 3 in here, we'd use this
- case, because 3 is odd.
- So we do 3 squared minus 1. f of 3 is equal to 8.
- So notice, this was a little bit more I guess you could
- even say abstract or unusual in this case.
- I'm going to keep doing examples of functions and
- I'm going to show you how general this idea can be.
- And if you get confused, I'm going to show you that the
- actual function problems you're going to encounter are
- actually not that hard to do.
- I just want to make sure that you at least get exposed
- to the general idea of what a function is.
- You can view almost anything in the world as a function.
- Let's say that there is a function called Sal, because,
- you know, that's my name.
- And I'm a function.
- Let's say that if you were to-- let me think.
- If you were to give me food, what do I produce?
- So what is Sal of food?
- So if you input food into Sal, what will Sal produce?
- Well I won't go into some of the things that I would
- produce, but I would produce videos.
- I would produce math videos if you gave me food.
- Math videos.
- I'm just a function.
- You give me food and-- and maybe, actually, maybe
- I have multiple inputs.
- Maybe if you give me a food and a computer, and I would
- produce math videos for you.
- And maybe you are a function.
- I don't know your name.
- I would like to, but I don't know your name.
- And let's say if I were to input math videos into you,
- then you will produce-- let's see, what would you produce?
- If I gave you math videos, you would produce A's on tests.
- A's on your math test.
- Hopefully you're not taking someone else's math test.
- So that's interesting. If you give...
- Let's take the computer away.
- Let's say that all Sal needs is food.
- Which is kind of true.
- So if you put food into Sal, Sal of food, he
- produces math videos.
- And if I were to put math videos into you, then you
- produce A's on your math test.
- So let's think of an interesting problem.
- What is you of Sal of food?
- I know this seems very ridiculous, but I actually
- think we might be going someplace, so we might be
- getting somewhere with this kind of idea.
- Well, first we would try to figure out what is Sal of food?
- We already figured out, if you put food into Sal, Sal of
- food is equal to math videos.
- So this is the same thing as you of-- I'm trying to confuse
- you-- you of math videos.
- And I already determined, we already said, well, if you put
- math videos into the function called you, whatever your name
- might be, then it produces A's on your math test.
- So that you of math videos equals A's on your math test.
- So you of Sal of food will produce A's on your math test.
- And notice, we just said what happens
- when we put food into Sal, you know.
- This could-- would be a very different outcome if you put,
- like, if you replaced food with let's say poison.
- Because if you put poison into Sal, Sal of poison-- not that I
- would recommend that you did this-- Sal of poison
- would equal death.
- No, no, I shouldn't say something so... no no no no.
- Well you get the idea.
- There wouldn't be math videos.
- Let me move on.
- So with that kind of-- I'm not so clear whether that would be
- a useful example with the food and the math videos.
- Let's do some actual problems using functions.
- So if I were to tell you that I had one function, called f of x
- is equal to x plus 2, and I had another function that said g
- of x is equal to x squared minus 1.
- If I were to ask you what g of f of 3 is.
- Well the first thing we want to do is evaluate what f of 3 is.
- So if you-- the 3 would replace the x, so f of 3 is equal to
- 3 plus 2, which equals 5.
- So g of f of 3 is the same thing as g of 5, because f
- of three is equal to 5.
- Sorry for the little bit of messiness.
- So then, what's g of 5?
- Well, then we take this 5, and we put it in in place of this
- x, so g of 5 is 5 squared, 25, minus 1, which equals 24.
- So g of f of 3 is equal to 24.
- Hopefully that gives you a taste of what a function is all about.
- And I really apologize if I have either confused or scared you
- with the Sal / food / poison video example.
- But in the next set of presentations, I'm going to do
- a lot more of these examples, and I think you'll get the idea
- of at least how to do these problems that you might see on
- your math tests, and maybe get a sense of what functions
- are all about.
- See you in the next video.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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Licking Our Lips With L
Rationale: This lesson will help children identify /l/, the phoneme represented by L. Students will learn to recognize /l/ in spoken words by learning a meaningful representation (licking their lips) and the letter symbol L, practice finding /l/ in words, and apply phoneme awareness with /l/ in phonetic cue reading.
Materials: chart paper with tongue twister written on it, primary paper, pencils, chart paper with Lizards in a Log, plain white paper, assessment worksheet
1. Say: Our written language is a secret code. The tricky part is learning what letters stand for –the mouth moves we make as we say words. Today we're going to work on spotting the mouth move /l/. We spell /l/ with the letter L. The letter L looks like where your pointer finger and thumb come together, and /l/ sounds like licking your lips.
2. Say: Let's pretend to lick our lips, /l/, /l/, /l/. [Pantomime licking lips] Notice what your tongue does? The tongue starts on the roof of the mouth behind the front teeth. The tongue sometimes rolls down at the end of the /l/ sound for certain words. If the /l/ sound is at the end of the word, your tongue will start resting on your bottom teeth and then roll up to the roof of your mouth. Your mouth is also open for both /l/ sounds.
3. Say: Now I want to show you how to find the /l/ sound in the word like. I am going to say the word and stretch it out as slow as I can and you are going to listen for the "licking our lips" sound. Llll-iii-k-e. Let's all say it together now even slower. Lllllll-iiiiii-kk-e. Did you feel how your tongue started at the top of your mouth and rolled down? I felt it!
4. Say: Let's try a tongue twister [on chart]. "Lisa lost the large lemon for the lizard Lenny loved." Now let's say it three times together. Now let's say it again and stretch out the /l. sound at the beginning of each word. "Lllisa lllost the lllarge lllemon for the lllizard Lllenny llloved." We are going to say it one last time and this time break off the word: "/l/isa /l/ost the /l/arge /l/emon for the /l/izard /l/enny /l/oved."
5. [Pass out primary paper and pencil to each student].Say: We use the letter L to spell /l/. Let's practice writing capital and lower case letter L. I am going to write capital and lowercase L on the board. To write a capital L you "pull down a line and add a lap. Lie down, lazy! It's time for a nap!" I want everyone to write a capital L. After I come by and put a star next to it, I want you to make ten more just like it. Once students are done introduce lowercase letter L. While writing a lower case L on the board say "little l looks like a number one. Just draw a line and you are done!" Next I want everyone to write a lowercase L. After I come by and put a star next to it, I want you to make five more just like it.
6. Say: Now I am going to say some words and I want you to tell me if you hear the /l/ sound. [Call on students to answer and tell how they knew]. Do you hear /l/ in lake or ocean? Lamp or fan? Ball or bat? Candle or fire? Let's see if you can see my mouth move in some /l/ words. Lick your lips if you hear /l/: The, little, lamb, walked, slowly, up, the, hill.
7. Say: Let's sing a song called "Lizards in a Log". [Display the lyrics on chart paper]. [Teacher should sing first].
Five lizards live in a log. (Hold up five fingers cover them with other hand)
One left to live with a frog (Fold thumb down)
One left to live with a dog. (fold index finger down)
Two left to live with a hog (Fold middle and ring finger down.)
One little lizard living in the bog (Fold little finger.)
Is a little lonely living in a log (Make a sad face.)
Have children join in and sing the song three times.
8. [Pass out plain white paper to each student]. Say: On your piece of paper, I want you to draw five lips. Think of words that have the /l/ sound. Inside each drawing of lips, I want you to a word with the /l/ sound. [Students are encouraged to use inventive spelling]. [Once each student is done, have them share their /l/ words with the class.
9. For the assessment, have students color the pictures that begin with the letter sound /l/ on the activity sheet.
Resource: Lick Your Lollipop with L by Kelly Meyer http://www.auburn.edu/academic/education/reading_genie/awakenings/meyerel.htm
Assessment Worksheet: http://www.tlsbooks.com/letterl_1.pdf
Return to Epiphanies Index
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So, let's start of with some basic strings and print statements. If you want Python to print something, you just type this into a python interactive shell:
print 'message goes here'
When you use print, you are passing it a string between the ' '. This string is then printed underneath the command. But what if you want to use ' in your message? well, python will also accept " as quotation marks.
print "message goes here"So, we know how to print just one line of stuff, but what if you want to print a few lines of stuff? Well, for this you can use three " to tell python that you want to use multiple lines.
print """Lots and lots of lines more lines Another line!"""This is really simple stuff, so lets move on. In your program, you often want to add variables into your strings. There are a few ways to do this in python. One way is to use the a comma. In the example below, I will use a loop to demonstrate using a comma to add in a variable.
for i in range(5): #this sets up our for loop print 'this is loop number: ', i
When you run this code you should get:
this is loop number 1
this is loop number 2, etc.
You can also put another string in after the variable as well by using the comma again and the putting in the string.
print 'this is loop number: ', i, ' another string.'
It would then print like this: this is loop number 1 another string.
More variables in strings
Another way to add variables into strings is by using the +. You need to be careful when you use the + because if the variable you are trying to add in is not a string, it won't work. If you have a number, you can
use this to make sure it will work as a string str(variable). This will convert the variable into a string. So, for example:
num = 99 print 'The number is'+str(num) #makes num a string
If you tried to print without the str(), you would get this error:
Traceback (most recent call last):
File "<input>", line 1, in <module>
TypeError: cannot concatenate 'str' and 'int' objects
You can also put another string after the variable just like the comma.
print 'number: '+str(num)+' more text'
If the you are trying to add a variable into the string which is already a string, you don't need the str(), I mainly use it for adding numbers into strings. The other way (and probably the most favored way) of adding a variable into a string is using the % symbol. This way allows you to add variables into strings without closing the string. %s is for strings, %i for integers, %f for floats. See the example below:
string = 'message' integ = 99 floatNum = 88.59 print 'this is a %s, this is an int %i, this is a float %f' %(string, integ, floatNum)
When you print it, you should see all of the variables in the string. If you only have one % variable in the string, you don't need the %() for the variable.
var = 'message' print 'this is a %s' %var
That will print: this is a message. If you want to use the % sign in a string, python can detect that your not trying to put a variable into the string because there will be no variables listed at the end of the string. One other thing which you may find handy is limiting the number of decimal points on a float.
temp = 15.735363873475 print 'The temperature is: %.2f' % temp
It should print only two decimal places. Another thing you may notice is that it will print 15.74 instead of 15.73. This is because python has automatically rounded the number for you. So, lets take what I've talked about today and use it in some code.
print 'program started' #basic string var_a = 'Marry has a little lamb' print 'This is from a nursery rhyme !', var_a #using , for variable var_b = 10 var_c = 51.453 print 'Can you count to '+str(var_B)/>+ '? Because I can!' #using + to add in # a variable and using str() to make it a string for k in range(10):#making a for loop num = k + 1 #computers start counting from 0 so it is now 1 - 10 print 'number %i' %num #using % to put a variable in a string print "I'd like to go to markets, I'd like to go!" #using ' in a string by #changing to " for defining the string print """She moved quietly around the corner, when she saw the number %f on the computer screen. She turned and ran away, that boy had been back to his coding tricks again!""" #printing multiple lines in one print statement print 'That''s all for now!'
In part two, I will talk about formatting strings, joining strings, getting strings from lists and searching strings.
Good luck programming!
If you have any questions, feel free to ask them!
This post has been edited by JackOfAllTrades: 16 October 2010 - 04:44 AM
Reason for edit:: Fixed syntax error
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Shhh Here and There
Just as students need to learn how to recognize each vowel sound, they also need to learn the concepts of vowel and consonant digraphs to become a fluent reader. Students must begin with an understanding that letters represent phonemes, which are the vocal gestures they hear, as well as an understanding that vocal gestures are represented by graphemes, which are the letters that are seen. Phonemes can either be represented by a single letter or by a combination of letters. A digraph is a combination of letters that make one single sound. The goal for this particular lesson is to help students understand that digraphs are made up of more than one letter but only produce one vocal gesture. The digraph taught in this lesson is /sh/. The children will learn how to identify the digraph /sh/, its spelling, and its use in words and language. Students will be able to recognize audibly and visually the phoneme and grapheme /sh/ in text as well as learn to spell and read /sh/ words through the use of letterboxes.
Chart with tongue twister
Elkonin boxes for each student
Letter tiles of the letters [a, b, c, e, f, h, i, l, l, o, p, r, s, t, u, w]
Copy of the “Baa, Baa, Black Sheep” poem for each student
One Fish, Two Fish, Red Fish, Blue Fish by Dr. Seuss- enough for each pair of students
Primary paper for each student
Pencil for each student
Copy of the shark coloring page for each student
Copy of the sheep coloring page for each student
Crayons for each student
TV and VCR
One Fish, Two Fish, Red Fish, Blue Fish, video
Copy of the /sh/ assessment worksheet for each student
1. Introduce the lesson by explaining that more than one letter can represent a phoneme. “Today we are going to talk about a special phoneme. We already know the sounds s and h make when they are by themselves, but today we are going to find out the sound that they make when they are together. Whenever s and h are together, they make the special sound /sh/, like in sheep and shark. When two letters are put together to make one sound, it is called a digraph. We are going to participate in several activities to learn more about the digraph sh and the sound that it makes.”
2. “If you want someone to be quiet, what sound do you make? "Shhh!" When you make that sound, do you usually put your fingers in front of your mouth? Let’s all make the /sh/ sound together. What do you feel? You feel air."
3. Model how to make the /sh/ sound. “To properly make the /sh/ sound, put your teeth together and blow out of your mouth. As you make the /sh/ sound bring one of your fingers to your lips. All together say shhh. Can you think of any words that make the /sh/ sound?”
5. “For our next activity, we are going to spell and read some words that contain the consonant digraph sh. Take out you letter boxes and fold them until you have only three boxing showing.” Model by holding up three boxes. “Also, take out your bag that contains the letter tiles [a, b, c, e, f, h, i, l, l, o, p, r, s, t, u, w]. Before we begin the activity tape the s and h together because they make one sound. Listen carefully to my instructions and watch as I model the activity for you. I am going to say a word then you are going to spell the word in your letterboxes. Place the letters that make up one sound in one box. For example, if I say ship, you would put sh in the first box because s and h make the /sh/ sound. Next, you would put i in the middle box because i makes the /i/ sound. Lastly, you would put the p in the last box because the /p/ is only one sound and it is the last sound in the word ship.” Demonstrate on the board by drawing three boxes and placing the correct phonemes in each box. “Now remember that our /sh/ makes one sound so this is why the two letters are taped together; because it makes one sound, it goes in one box. Now let's begin. I am going to say a word and I want you to spell it using the letters in front of you. Remember only one sound for each box.” While saying each word walk around the room monitoring the student’s progress. 3 phonemes- [shell, fish, cash, shop, wish, bash]; 4 phonemes- [brush, flush, trash]; 5 phonemes-[splash]. “Now I am going to spell the words on the board and I want you to read them aloud. For example, if I put sh-i-p on the board, you say each sound together to make the word ship. The first sound is /sh/, the second sound is /i/, and the third sound is /p/. Now say the sounds together until you say the word ship.” Write each word on the board and have the students read them as a class.
6. “Now, I am going to read a poem called “Baa, Baa, Black Sheep” and I want you to listen for the /sh/ sound.” Read the poem aloud to students.
Baa, baa, black sheep,
Have you any wool?
Yes, sir, yes, sir,
Three bags full:
One for my master,
One for my dame,
And one for the little boy
Who cries in the lane.
Baa, baa, black sheep,
Have you any wool?
Yes, sir, yes, sir,
Three bags full.
7. Pass out copies of the book One Fish, Two Fish, Red Fish, Blue Fish to each pair of students as well as a piece of primary paper and a pencil. “For our next activity, I am going to divide you into pairs. Take turns reading a page from the book to each other. After you finish reading the book, write down all the words that have sh and make the /sh/ sound.”
8. After each pair of students has created a list of words that contain sh, have each group share a word from their list. Write the words on the board so that each student can visually identify the sh consonant digraph in several different words.
9. Pass out the /sh/ coloring book pages of a shark and a sheep as well as crayons. Let each student pick out which picture he or she would like to color. “Now everyone is going to color a picture of an animal whose name begins with /sh/. What animal is this?” Hold up the picture of the shark. “What animals is this?” Hold up the picture of the sheep.
10. “As you color your /sh/ picture, I am going to let you watch and listen to the book we just read, One Fish, Two Fish, Red Fish, Blue Fish, on video. Try to listen for the words we just identified that contain the /sh/ sound.” Play the One Fish, Two Fish, Red Fish, Blue Fish video for the students.
11. In order to assess each student’s understanding of the consonant digraph /sh/, give each student a worksheet with several pictures on it. Have several pictures that contain the consonant digraph /sh/ on it as well as a word box with the pictures’ names in it. Instruct the students to match each picture to the correct word and write the word underneath the picture. “For our last /sh/ activity, each one of you will complete this /sh/ worksheet. Follow the directions: Match the word from the word box to the correct picture. Write the word in the space underneath the picture.”
Click here to return to Constructions.
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In this free music lesson we’ll look at the basics of counting notes, a skill you can use for both reading and writing music. It’s one thing to be able to feel music and another to be able to write down what you compose so that other people can play it.
Counting in music is like eating pie. You can eat the whole thing (yum!), only 1/2 of it (still yummy), 1/4 of it (good if you’re less hungry), or 1/8th of it.
So there are:
• Whole notes – like a whole pie
• Half notes – like half of it
• Quarter notes – 1/4 of the pie
• Eighth notes – 1/8th of the pie
There are also 16th notes, 32nd notes, etc. but we’re not going to look at them in this lesson.
Some countries call these notes by other names:
• whole note (semibreve)
• half note (minim)
• quarter note (crotchet)
• sixteenth note (semiquaver)
Here’s what whole, half, quarter and eighth notes look like…
Whole notes look like a whole pie.
Half notes look like a pie with a handle or stem.
Quarter notes look like half notes but are filled in (“pie filling).
Eighth notes look like quarter notes, but they have a “flag” on the stem.
For now, we’ll assume the piece of music we’re looking at is in 4/4 time. So we’re going to count in fours: 1-2-3-4, then 1-2-3-4 again, etc.
A note that lasts half as long as a whole note is a half note. A note that lasts a quarter as long as a whole note is a quarter note. A note that lasts an eighth as long as a whole note is an eighth note.
A whole note gets 4 counts.
A half note gets 2 counts.
A quarter note gets 1 count.
An eight note gets only ½ a count.
So when you play a whole note, you hold it for 4 counts: 1-2-3-4.
When you play a half note, you hold it for 2 counts: 1-2
When you play a quarter note, you hold it for 1 count: 1
When you play an eighth note, you hold it for ½ a count: 1/2
So if you have two half notes, one after the other, you count 1-2 for the first half-note, and 3-4 for the second half-note.
If you have four quarter notes, one after the other, you count 1-2-3-4 (one count for each one).
If you have eighth notes, you start counting ANDS, like 1-AND is how you count two eighth notes in a row.
If you have four eighth notes in a row, you’d count 1-AND-2-AND…
1 for the first eighth note, AND for the second eighth note, 2 for the third eighth note, AND for the fourth eighth note.
Of course, this is only a quick introduction to counting notes in music, but that skill will carry you quite far if you pick it up.
All the best,
BellaOnline’s Musician Editor
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As we learn how to graph, we will need a thorough knowledge of the fundamentals of graphing: plotting points and identifying coordinates. One of the most important things to know is the terminology of what we call the Cartesian coordinate system, or an xy graph. Plotting points will be useful when we start to interpret graphs and graph lines using a table of values.
One of the things you guys will quickly learn about math class if you haven't already is that it's like a whole other language. There's so much vocabulary to keep your head wrapped around. One of the important things to learn about in your early algebra studies is how we talk about what's called the Cartesian Coordinate Plane, which pretty much means a graph. What the story is that this guy who is a French mathematician. His name is Rene Descartes.
Supposedly, he was lying in his bed and then there was this little fly up on the ceiling and he was trying to describe where the fly was going. And so what he did is he used the ceiling tiles. And he would say, OK. He went over two, up one. He's at the point (2, 1), supposedly. I don't know if that's true or not.
But, that's why we call it the Cartesian Coordinate Plane after him. What the coordinate plane looks like is this. It's these rectangular boxes, that actually if it were perfect they'd be squares. We called the rectangular coordinate system, because it's made up of these little squares.
And there are a couple of vocabulary things you want to keep in mind. The first thing is that this center point where the two... It's called axis cross. It's called the origin. And we label it with the coordinates (0, 0). You guys probably already know that the first number represents your X value, your side to side. The second number represents your Y value. That's your up and down.
So, we call this the X axis, the horizontal axis. We call that vertical part the Y axis. And every dot just like the Descartes' fly has two numbers, over two up one would be something that would look like that. Two is the X number. One is the Y number.
So that's important, how you get the points on there. The other thing, and my friends, this is one of like the weirdest things in math is how we name the quadrants. This graph is broken into four pieces. We call them quadrants. And we name them in a counter clockwise method, which to me is kind of confusing.
Here's what it looks like. This we call quadrant one. And you use the Roman numeral one which looks like a capital "I." This is quadrant two, Roman numeral two. Three and quadrant four is "IV." I'm not sure why we use Roman numerals.
But, quadrants are named in a counter clockwise method like this, quadrant one, two, three and four. It's important that you guys keep all of that vocabulary in your brain throughout your entire math careers, not only in algebra, but for now on.
The Cartesian coordinate system with rectangular coordinates, the origin, the X and Y axis', and the naming of the quadrants, one, two, three and four.
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To help students learn to write their names and also to see who is at school today, I get my students to practise every morning when they come into the classroom. I printed each student's name out in dotted font and then laminated them. Students come in and find their name on the board, and then trace over it with a whiteboard marker. They then they put it onto the correct side of the chart. When we begin our mat session we use the chart in a variety of different ways.
- Count the boys and the girls and then how many kids in the class altogether. Write a number story to match.
- Read through the names together to help students recognise their friend's names.
- Discuss names on the chart and how many letters are in them. Who has the longest name?
- Use the names to reinforce inital sounds and what sound/letter is at the start of names.
- Use the names to practise clapping syllables.
- Pull a name off each day and look at the name. Discuss features of it. Then 'interview' the child to find out more about them.
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To use this tutorial, you will need a "JAVA-enabled" web browser.
Just below you will see a drawing; the vector labeled c is being calculated according to your specifications for the vectors a and b. You move these by clicking on their tips and dragging them around the plane with the mouse. You can also "spin the plane" by clicking and dragging on other parts of the picture.
In the drawing you see three vectors a, b,
and c. The vector c
is calculated from the vectors a and b
using the vector cross product. In mathematical notation you write:
c = a x b
Magnetic forces are described using the vector cross product. So are the "torques" governing spinning and rotating objects. And there are still more examples.
It is important to understand that any two vectors a and b lie in some plane. This is the plane indicated in the applet's output. The vector c calculated using the cross-product rules is always perpendicular (or "normal") to this plane. To help you understand these relationships, you can spin the plane shown in the figure. Place the mouse on some spot on the plane, click, and move the mouse around. The plane and the three vectors all rotate to accomodate the new perspective. We'll discuss how to figure out if c points "up" or "down" later on.
Vectors have been denoted here using boldfaced characters.
We denote the magnitude (or length) of the vector a
as just "a" (without boldface). Note that a magnitude
is always a positive number.
The magnitude c of the cross product is given by the formula c = ab sin(\phi), where \phi is the angle included between a and b.
The direction of c has only been defined as perpendicular to the plane of a and b. To determine whether c points up or down from the plane, you use a "right-hand" rule.
The right hand rule is difficult to explain in words, but try the following exercise. Point the four fingers of your right hand so that they point in the same direction as the vector a. Now get your hand organized so that you can swing the palm of your hand from a to b. If you succeeded, then your thumb will point along c. See if you can make sense of this right-hand rule by checking it against the applet's output.
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In this chapter rotational motion will be discussed. Angular displacement, angular velocity, and angular acceleration will be defined. The first two were discussed in Chapter 5.
Angular Displacement: The symbol generally used for angular displacement is θ pronounced "teta" or "theta." θ is the angle swept by the radius of a circle that points to a rotating mass, M, under study. Below, the symbol ω is pronounced "omega" is used to denote angular velocity.
Example 1: An object travels around a circle10.0 full turns in 2.5 seconds. Calculate (a) the angular displacement, θ in radians, and (b) its average angular speed, ω in (rd/s).
Solution: (a) θ = 10.0 turns ( 6.28 rd / turn ) = 62.8 radians.
(b) ω = Δθ / Δt = 62.8 rd / 2.5s = 25 rd/s.
Angular Velocity (ω): Angular velocity is defined as the change in angular displacement, θ, per unit of time, t.
ω = Δθ/Δt ; [rd/s]
Angular Acceleration (α): Angular acceleration is the change in the angular velocity, ω, per unit of time, t.
α = Δω/Δt ; [rd/s2]
The symbol α is pronounced " Alpha."
Example 2: A car tire is turning at a rate of 5.0 rd / sec as the car travels along a road. The driver increases the car's speed, and as a result, each tire's angular speed increases to 8.0 rd /sec in 6.0 sec. Find the angular acceleration of the tire.
Solution: α = Δω / Δt ; α = (ωf - ωf) /Δt ; α = ( 8.0 rd/s - 5.0 rd/s ) / 6.0s = 0.50 rd/s2.
As can be seen, there is an excellent correspondence between the linear formulas we learned in Chapter 2 and the angular formulas defined here. The following chart, shows the one-to-one correspondence between the linear and angular variables and formulas:
Variables: x, t, v, and a
v = Δx / Δt.
a = Δv / Δt ; a = ( vf - vi ) / Δt.
x = (1/2) a t2 + vi t.
vf2 - vi2 = 2 a x.
θ, t, ω,
ω = Δθ / Δt.
α = Δω / Δt ; α = ( ωf - ωi ) / Δt.
θ = (1/2) α t2 + ωi t.
ωf2 - ωi2 = 2 α θ.
The Relations between Linear and Angular Variables:
Each of the angular variables θ, ω, and α is related to its corresponding linear variable x, v, and at by factor R, the radius of rotation.
x = Rθ ; v = Rω ; at = Rα . (at means tangential acceleration).
This can be easily verified by the following simple mathematics:
Starting with s = Rθ, or x = Rθ and writing as Δx = RΔθ, and then dividing both sides by Δt, yields:
Δx/Δt = RΔθ/Δt ; the left side is v and the right side is ω ; therefore, v = Rω.
If v = Rω is divided through by Δt , yields:
Δv/Δt = R Δω/Δt ; the left side is at and the right side is α ; therefore, at = Rα.
s = Rθ
v = Rω
at = Rα (tangential acceleration)
Note in the 3rd figure that there are two types of acceleration in rotational motion. One type is at , the tangential acceleration that is responsible for the change in the magnitude of the linear velocity, v. Pushing a merry-go-round, gives it tangential acceleration because the push is tangent to a circular path.
The other type is ac, the centripetal acceleration that is responsible for the change in the direction of v. This acceleration is always directed toward the center of rotation (not shown here to keep the diagram more clear). It was discussed in Chapter 5.
Example 3: As a car starts accelerating ( from rest ) along a straight road at a rate of 2.4 m/s2, each of its tires gains an angular acceleration of 6.86 rd/s2. Calculate (a) the radius of its tires, (b) the angular speed of every particle of the tires after 3.0s, and (c) the angle every particle of its tires travels during the 3.0-second period.
Solution: (a) Since a linear variable and its corresponding angular variable are given, the radius of rotation can be
calculated. at = Rα ; R = at /α ; R = [2.4 m/s2] / [6.86 rd/s2] ; R = 0.35m = 14 in.
(b) α = (ωf - ωi)/Δt ; α Δt = ωf - ωi ; ωf = ωi + α Δt ; ωf = 0 +(6.86rd/s2)(3.0s) = 21 rd/s.
(c) θ = (1/2)α t2 + ωi t ; θ = (1/2)( 6.86 rd/s2)(3.0s)2 + (0) (3.0s) = 31 rd.
Example 4: The canister of a juicer has 333 grams of pulp distributed over its inside wall at an average radius of 8.00cm. It starts from rest and reaches its maximum angular speed of 3600.0 rpm in 4.00 seconds. For the pulp, determine (a) the angular acceleration, (b) the angle (radians) it travels during this period, (c) the tangential acceleration, (d) the linear velocity at t =2.00s and t = 4.00s, (e) the centripetal acceleration at t = 2.00s and t = 4.00s, and ( f ) the tangential and centripetal force on it at t = 2.00s and t = 4.00s.
Solution: (a) First calculate ω in (rd/s) ; ω = 3600 [rev/min] [6.28 rd/rev] [1 min / 60s] = 377 rd /s.
α = (ωf - ωi) /Δt ; α = ( 377- 0 ) / (4.00s) = 94.3 rd/s2.
(b) θ = (1/2) α t2 + ωi t ; θ = (1/2)(94.3 rd/s2)(4.00s)2 + 0 = 754 rd.
(c) at = Rα ; at = (0.0800m)(94.3 rd/s2) = 7.54 m/s2. (Refer to at in the above figure).
For Part (d), the values for final angular speed, ωf , must be calculated both at t = 2.00s and t = 4.00s.
α = (ωf - ωi) /Δt ; α Δt = ωf - ωi ; ωf = ωi + α Δt ; (ωf)1 = 0 +(94.3rd/s2)(2.0s) = 189 rd/s.
From the problem, at t = 4.00s, ω = 3600 rpm = 377 rd/s or, (ωf)2 = 0 +(94.3rd/s2)(4.0s) = 377 rd/s.
(d) v1 = R(ωf)1 ; v1 = (0.0800m) (189 rd/s) = 15.1 m/s.
v2 = R(ωf)2 ; v2 = (0.0800m) (377 rd/s) = 30.2 m/s.
(e) (ac)1 = v12 / R ; (ac)1 = (15.1 m/s)2 / 0.0800m = 2850 m/s2.
(ac)2 = v22 / R ; (ac)2 = (30.2 m/s)2 / 0.0800m = 11400 m/s2.
(f) Ft = Mat ; ( Ft )1 = ( 0.333 kg )( 7.54 m/s2 ) = 2.51 N ; ( Ft )2 = 2.51 N (Constant tangential force)
Fc = Mac ; ( Fc )1 = ( 0.333 kg )( 2850 m/s2) = 949 N
( Fc )2 = ( 0.333 kg )( 11400 m/s2) = 3800 N (3 sig. figures) ( Variable centripetal force)
Chapter 8 Test Yourself 1:
1) In Fig. 1, the angular displacement of mass M is (a) arc AB = S (b) ω (c) angle θ. click here
2) In Fig. 1, the linear displacement of mass M is (a) arc AB = S (b) ω (c) angle θ.
3) The relation between angle θ and arc S, the arc opposite to it, is (a) S = 2Rθ (b) S = Rθ (a) S = πRθ.
4) The symbol for angular speed is (a) θ (b) ω (c) S. click here
5) The relation between angular speed and linear speed is (a) S = Rθ (b) V = Rω (c) S = 2πR.
Problem: The angular speed of a wheel is such that it makes 80.0 turns in 20.0 seconds. The radius of the wheel is 35.0cm.
Answer the following questions:
6) The angular speed of the wheel is (a) 240 rpm (b) 4.00 turns/s (c) 25.1 rd/s (d) a, b, & c. click here
7) The linear speed of any point on the outer edge of the wheel is (a) 879 cm/s (b) 8.79 m/s (c) a & b.
8) The angular acceleration of the wheel is (a) half of its centripetal acceleration (b) a nonzero constant (c) zero, because the angular speed is constant. click here
9) The tangential acceleration of the wheel is (a) half of its centripetal acceleration (b) a nonzero constant (c) zero, because the linear speed is constant.
10) The centripetal acceleration of any point on the outer edge of the wheel that is at a radius of R = 35.0cm is (a) 25.1 m/s2 (b) 221 m/s2 (c) 221 rd/s2.
11) The variables in uniformly accelerated motion (motion along a straight line at const. velocity) are: x, t, v, and a. Write down the counterpart variables for rotational motion. Ans.: .................................... click here to check your answer.
12) Without referring to Table 1 above, try to write down the formulas you know for linear motion from Chapter 2. Then write down the corresponding angular formulas. Pay attention to the one-to-one correspondence between the variables and formulas.
Problem: Make sure you perform all calculations even if they seem obvious to you. We all know that our planet completes one revolution about its own axis every 24 hours. Answer the following questions:
13) The angular speed of the Earth in revolving about its own axis is (a) 1 rev./24h (b) 2πR/ 86400s (c) 6.28 rd/86400s (d) 7.27x10-5 rd/s (e) a, c, & d. click here
14) Any person who lives on the equator is at a radius of rotation of R1 = 3900 miles. He/she has a linear speed of (a) 0.283mi/s (b)456m/s (c) both a & b.
15) Any person who lives exactly at the North Pole or the South Pole where the Earth axis passes through, is at a radius of rotation of R4 = (a) 3900mi (b) almost 0 (c) neither a, nor b.
16) Whoever lives exactly at the North Pole or the South Pole, has an angular speed of (a) 7.27x10-5 rd/s (b) almost 0 (c) neither a, nor b. click here
17) A person who lives exactly at the North Pole, has a linear speed of (a) 456 m/s (b) almost 0 (c) neither a, nor b.
18) The radius of rotation of a person who lives in between the equator and the North Pole is (a) less than 0 (b) more than 3900mi (c) less than 3900 miles.
19) The radius of rotation for the people who live 45º above the equator is R2 = (a) [3900/2] miles (b) [3900/45º] miles (c) 3900cos45º miles. click here
20) The linear speed of the people who live 45º above the equator is (a) 323 m/s (b) 0.200 mi/s (c) both a & b.
21) The tangential acceleration of any person on this planet because of Earth motion about its own axis is (a) 9.8 m/s2 (b) 0 (c) 456 m/s2.
22) The centripetal acceleration of a person living on the equator because of the Earth's rotation about its own axis is (a) 9.8 m/s2 (b) 0 (c) 0.0331 m/s2. click here
23) Because of the Earth motion about its own axis, the direction of the centripetal acceleration vector for those who live on the equator is (a) parallel to the direction of g (b) perpendicular to the direction of g (c) neither a, nor b.
24) The direction of the centripetal acceleration vector for those who live 45º above the equator is (a) parallel to the direction of g (b) perpendicular to the direction of g (c) neither a, nor b.
25) The direction of the centripetal acceleration vector for those who live close to the North Pole (a) parallel to the direction of g (b) almost perpendicular to the direction of g (c) neither a, nor b. click here
Problem: Again, make sure you perform all calculations even if they look obvious to you. We all know that our planet completes one revolution about the Sun every year. Assume circular orbit for simplicity. Answer the following questions:
26) The angular speed of the Earth in its rotation around the Sun is (a) 2πR/yr (b) 6.28 rd/yr (c)1.99x10-7 rd/s (d) b&c.
27) Knowing that the average Earth-Sun distance is 150,000,000km, the linear speed of the Earth in its motion around the Sun is (a) 30mi/h (b) 30 km/s (c) 19 mi/s (d) b & c. click here
Problem: In the TV game "Price is right", suppose a person gives an initial angular speed of 2.0 rd/s to the wheel and the wheel comes to stop after 1.5 turns. Answer the following questions:
28) The final angular speed is (a) 2.0 rd/s (b) 0 (c) 1.5 rd/s. click here
29) The angular displacement, θ, before the wheel comes to stop is (a) 9.42 rd (b) 0.80rd (c) 6.28 rd.
30) Since time is not given, one good way to solve for the angular acceleration, α , is to use the equation.............................. . Write the equation first, and then check your answer. For answer, click here.
31) The value of α is (a) 0.21 rd/s2 (b) -0.21 rd/s2 (c) -0.21 rd/s.
32) The elapsed time is (a) 2.8s (b) 1.4s (c) 9.5s.
Problem: A car is traveling at a constant speed of 18.0m/s. The radius of its tires is 30.0cm. Answer the following:
33) The linear speed of every point on the outer edge of its tires that perform circular motion is (a) 18.0 rd/s (b) 18.0 m/s (c) neither a, nor b.
34) The angular speed ω of each tire is (a) 60.rd/s (b) 30. rd/s (c) 30. cm/s.
35) The angular acceleration of each tire is (a) 540 rd/s2 (b) 18 rd/s2 (c) 0.
36) The equation of its angular motion is (a) θ = αt2 + (60.0 rd/s)t (b) θ = (60.0rd/s)t (c) θ = ωt.
37) The angle each tire rotates in 45 seconds is (a) 2700 turns (b) 2700º (c) 2700 rd.
1) Calculate (a) the average angular speed of the Moon about the Earth that completes each turn in about 29 days, and (b) its average linear speed in its motion about the Earth. The average distance from here to the Moon is 384,000km.
2) A juicer reaches its maximum angular speed of 3600rpm, 2.00s after start. Find (a) its angular acceleration, (b) maximum linear speed of its porous cylinder wall if its radius is 12.0cm, (c), the centripetal acceleration of points on its inner cylinder wall when at maximum speed, and (d) the angular displacement of any point on its cylinder during the acceleration period.
3) A car tire is spinning at 377 rd/s in a tire balancing equipment. If it is slowed down to 251 rd/s in 3.00s, calculate (a) its angular acceleration, (b) the angle traveled during slowing down, (c) the number of turns made during slowing down, (d) the equation of its rotation, and (e) the angle traveled during the 3rd second.
4) Starting from rest, a mother pushes her daughter in a merry-go-round uniformly for 1/4 of a turn where she reaches a running speed of 6.0m/s. If the daughter's seat is at an average radius of 5.0m, calculate (a) her initial and final angular speeds, (b) her angular acceleration within the 1/4 turn, (c) the elapsed time, and (d) her tangential and centripetal acceleration when at 1/4 turn position.
5) For rotation about the axis of the Earth, find (a) the angular speed, (b) the linear speed, (c) the angular acceleration, (d) the tangential acceleration, and (e) the centripetal acceleration of the people who live at the 60.0º latitude above the Equator. Draw a sphere, select a point at the 60º latitude, and show both of centripetal acceleration and the gravity acceleration vectors at that point. Note that people at the Equator are at 0º latitude and the people at the North pole are at +90º latitude. The radius of rotation at the Equator is 6280km( the radius of the Earth), and the radius of rotation at each of the poles is zero. The radius of rotation about the Earth's axis at 60º latitude is (6280km)cos60 =3140km.
Answers: 1) 2.5x10-6 rd/s, 960m/s 2) 188 rd/s2, 45.2m/s, 1.70x104m/s2, 377 rd
3) -42.0 rd/s2, 942 rd, 150 turns, θ = ½ α t2 + ωi t, 272 rd
4) 0 and 1.2rd/s, 0.46 rd/s2, 2.6s, 2.3m/s2 and 7.2m/s2
5) 7.27x10-5 rd/s, 228m/s, 0, 0, 0.0166m/s2
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Activity: Lengths of Leaves
this Activity you are going to
investigate the lengths of leaves and work out the mean (average)
You are also going to learn a method to find an estimate of the mean length.
The first thing you need to do is to find some leaves ...
What kind of leaves?
You can use leaves from any tree or plant; but if it's a tree, then choose one that is easy to reach (we don't want any accidents), and don't take your neighbor's leaves without asking! Also it's best to use simple leaves. Don't try to use leaves with strange shapes. The kind of leaves you see in the photograph below are ideal.
Some of the rules you might want to consider are:
- I must choose all my leaves from the same tree or plant.
- I must make sure the leaves are whole - broken leaves just won't do.
- I must try to get a random sample of leaves - not all big ones and not all small ones.
The following photograph shows four leaves of different sizes that I collected from a tree in my garden:
You will see that some leaves are small and some are larger.
The next thing you need to decide is how many leaves to pick and how to get a random sample.
You could pick as many as you like. Ideally you would use all the leaves on the tree, but that would be rather a large number to measure, and your parents might not be very happy if you stripped the tree bare!
So let's try 100 leaves.
to get a random sample?
Here is one way you could get a random sample:
taking all the leaves on one branch of the
tree. After you've discarded any that are broken, then see how many
there are. If there are less than 100, then get the leaves from another
branch until you have more than 100. Then write a different number
(starting with 1) on each leaf
with a marking pen.
- Write the same numbers on small pieces of paper.
- Fold the pieces of paper.
- Put them into a hat and mix them up.
- Draw 100 pieces of paper (without looking) from the hat. The first 100 pieces of paper you draw would give you the numbers of the leaves to use in the experiment.
how accurate your measurements should be:
How to measure?
Keeping your leaves flat, use a ruler to measure the length of each leaf from the pointy part at one end of the leaf to the point where the leaf joins the stalk at the other end. Maybe your leaves bend a bit, but don't follow the main rib of the leaf as this would make measurement too difficult.
Just measure in a straight line as shown in the following diagram:
You should measure the length
of each leaf to the nearest millimeter.
Now you're ready to begin.
Measure the length of each leaf to the nearest millimeter and record you results in a table, as follows:
(5 columns of 20 each equals 100 measurements)
Add up each column, then add those sums together for the grand total:
_______ + _______ + _______ + _______ + _______ = _________
Finding the Mean
Now you should be able to calculate the mean length of your leaves. Simply divide the sum of lengths by 100.
|Mean (= Grand Total / 100):|
Is There Another Way?
There is a way to estimate the mean length by grouping your results.
This makes the calculation quicker, but is not as accurate.
|20 - 29||3|
|30 - 39||8|
|40 - 49||15|
|50 - 59||26|
|60 - 69||23|
|70 - 79||16|
|80 - 89||7|
|90 - 99||2|
If this is not clear, then let me explain:
The three shortest leaves in my sample were leaves of lengths 22 mm, 25 mm and 27 mm respectively. These were all between 20 mm and 29 mm, so each of them contributed one tally mark for the group 20 - 29.
So there were three tally marks altogether () in the group 20 - 29, and the frequency for this group was 3 (i.e. there were 3 leaves in this group).
Similarly, there were eight leaves whose lengths were between 30 mm and 39 mm, so there were 8 tally marks for this group and the frequency was 8.
And so on.
Once you've grouped your lengths, how can you estimate the mean?
What we do is we assume all leaves in a group have the same length, which is the average for that group. This value is called the midpoint of the group and is simply found by taking the average (mean) of the smallest and greatest lengths in that group.
The midpoint for the group 20 - 29 is (20 +29)/2 = 49/2 = 24.5
The midpoint for the group 30 - 39 is (30 +39)/2 = 69/2 = 34.5
So, returning to my example, I am going to assume that there are 3 leaves with a mean length of 24.5 mm, 8 leaves with a mean length of 34.5 mm, 15 leaves with a mean length of 44.5 mm, etc. I can then work out my estimate of the mean length from a frequency table, as follows:
|f × x|
|20 - 29||24.5||3||73.5|
|30 - 39||34.5||8||276.0|
|40 - 49||44.5||15||667.5|
|50 - 59||54.5||26||1,417.0|
|60 - 69||64.5||23||1,483.5|
|70 - 79||74.5||16||1,192.0|
|80 - 89||84.5||7||591.5|
|90 - 99||94.5||2||189.0|
|Σf = 100||Σ(f × x) = 5,890|
So the estimate of the mean length = Σ(f × x)/Σf = 5,890/100 = 58.9 mm
This value differed a little from the exact value of the mean that I obtained earlier. It's important to understand that this is just an estimate, but it can be much quicker to calculate.
Try using the method for your sample and see how good an estimate you get.
You can use this table. You will have to decide which length groups to use. You may have to use fewer groups or more groups than we did. For example, if you had a leaf of length 105 mm, then you will need an extra group 100 - 109. On the other hand, you might not have any leaves as short as mine, so you might not require the group 20 - 29. Everyone's results will be different, so you will have to decide what are the right groups for you to use.
|f × x|
× x) =
Divide Σ(f × x) by Σf to get the mean length:
Σ(f × x) / Σ(f) = ________ / 100 = _________
Why use an Estimate?
Faster! Easier! (But less accurate.)
It might not have made much difference in our example, with only 100 leaves, but it could be a useful method to use when the number in a sample is much much larger.
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Music is most commonly notated using the Staff (and tablature.) The staff consists of five horizontal lines on which musical notes lie. The lines and the spaces between the lines represent different pitches. Lower pitches are lower on the staff and higher pitches are higher on the staff.With the blank staff we can't yet tell what notes to play. We use Clefs to tell us which notes correspond to which lines or spaces. The most common clefs are the Treble Clef (also known as the G Clef) and the Bass Clef (or F Clef).
The Treble Clef spirals around the second line from the bottom. This spiral tells us that notes on this line are G.
From here we can figure out the other note names simply by going forward or backward through the musical alphabet: A,B,C,D,E,F,G.
The note names in Bass Clef are:
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Dong, It's D!
Anna Beth Sanders
recognition is one of the best predictors
of a child's future reading achievement (Adams
36). To read, children must be able to
automatically recognize letters. In this
lesson, children are taught how to recognize D, write uppercase and
D, and the sound and mouth move that D=/d/ makes.
Materials: Primary writing
paper and pencils for each
student, dry erase or chalk board with marked primary writing lines,
with tongue twister: Ding Dong, David's Daddy is at the door, picture
deer, door, diamond, dog, cat, hat, dinosaur, sun, and rope, and the
book The Doorbell Rang, by Pat Hutchens.
- Introduce the letter D. "Today
we are going to learn about the letter D. Ding
Dong begins with D. Lets all say Ding Dong
together, and ring the door bell( show motion). Do
you hear the D=/d/? Lets say ding dong
making the D=/d/ sound like a machine gun, like this, dddding ddddong. Now you try. What
does your mouth do when you say D=/d/? Did
you feel the tip of your tongue just barely touch the roof of your
mouth, right behind your top teeth, and then did you feel your mouth
open a little bit and your tongue pop down? That
is what our mouths do when we say D=/d/. Let's say Ding Dong and ring
the doorbell together and see if we feel it. Ding Dong."
- Name words to the
whole class, some beginning with d, some not, some ending with d, some
not. Ask the class to ring the door bell
when they hear D=/d/. Teacher rings doorbell on the first couple of
D=/d/ words to model for the students. "Now I am going to call out some
words. If you hear D=/d/ in the word, I
want you to ring the door bell. You may
here D=/d/ at the beginning or end of a word. Deer,
dog, cat, man, bed, mad, happy."
- Introduce the tongue
twister, Ding Dong, David's Daddy is at the door. Tongue
twister is written on chart paper for the class to see. Repeat tongue
twister with the class. "Here is a tongue twister with
D=/d/: (point to chart) Ding Dong, David's Daddy is at the door, let's
say it together. Ding Dong, David's Daddy is at the door.
Did you hear D=/d/ in that tongue twister?
This time when we say it, ring the door bell when you hear
D=/d/. Ding Dong, David's Daddy is at the
- Model and instruct how
to write D and d. Use dry erase or chalk board with primary lines. Have the children use their primary paper. "We
Know what D=/d/ sounds like, now we will learn how to write the letter
D. Take out your paper and pencil and
watch what I do. (Model while instructing) For big D we start at the roof, go straight
down, pick up, and go around. Now you try
to make a D, start at the roof, go straight down, pick up, and go
around. Good. For
little d, first we make little c, then little d. Now
you try, first make little c, then little d. Continue
to make big D and little d, while I walk around the room to see how
well you are doing. (Teacher will help
those having trouble).
- Introduce and read The Doorbell Rang. Ask children to ring the doorbell
every time they hear D=/d/ in the book. "Now we are going to read The Doorbell Rang, this is a book about some kids who
are trying to share cookies, and more people keep coming to the door,
so they have to keep sharing the cookies with more and moor people. What sound does a doorbell make when it rings? And when we say ding dong we say D=/d/, don't
we? Every time you hear D=/d/ in this
story I want you to ring the doorbell.
- Assess the children
using the picture page. "Now
I am going to pass out a page with some pictures on it.
If the picture begins with D, like duck, I want you to
circle the picture. If the picture does
not begin with D, like cow, do not circle it.
Adams, Marilyn-Jager. (1990) Beginning to Read:
Thinking and Learning
About Print. Center for the study off Reading
and the Reading
Research and Education
University of Illinois
Hutchins, Pat. The Doorbell Rang. Mulberry
Adams, Whitney, Duh! It's D!: http://www.auburn.edu/rdggenie/discov/adamsel.html
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