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Age Range: 7 to 11
1) Draw a square on the board. Tell the children that you want them to think of that square as one unit.
2) Split the square into ten rectangular sections. Ask them what fraction of the unit each of these sections is worth (i.e. tenths).
3) Now split each of the ten sections into ten squares (there should now be 100 small squares inside the large square). Explain that we can split tenths up even more. The smaller sections are called hundredths.
4) Explain the following concepts:
There are ten hundredths in one tenths and one hundred hundredths in one unit.
Hundredths are written to the right of the tenths column when writing numbers in figures, i.e.
Hundredths are said in the following way:
7.53 = Seven Point Five Three (NOT seven point fifty three)
9.39 = Nine Point Three Nine (NOT nine point thirty nine)
4.70 is the same as 4.7. We don't have to write in the zero, but it is good practice to.
There are five follow-up activities which you might like to try when the children are confident with the above concepts.
A) Identifying Hundredths on a Number Line
This activity is based on worksheet (in PDF format only) here . Children should look at the number line and write in the table the numbers (in fractions and decimals) shown by each letter.
Answers (only shown in decimals) for this worksheet are:
B) Counting Units, Tenths and Hundredths
Children will need to use the worksheet here and work out the values of the numbers shown in the pictures. Units are indicated by large squares, tenths by rectangles and hundredths by small squares. When they have worked out the value of each picture, they can write the answer (in figures and in words) in their books, or on the worksheet here.
|1) 3.63||2) 2.19||3) 2.43||4) 0.66|
|5) 2.35||6) 3.07||7) 0.09||8) 1.27|
C) Which is Bigger?
This is a simple exercise which uses the worksheet here. It requires children to look at the pair of numbers in each row and decide which of them is bigger. They can indicate their answer by circling the larger number.
Answers are as follows: (larger numbers are underlined)
D) Sequencing Activity
Another simple exercise, which asks children to put a set of numbers in order (from smallest to largest). It can be found on the worksheet here. The correct answer is:
E) Matching Exercise
This exercise (on the worksheet here) is similar to previous exercises involving tenths (see other pages in the decimals section). Children should fill in the blank spaces on the table, showing how numbers of the same value can be written in different ways. The completed table should look like this:
|Fraction (words)||Fraction (figures)||Decimal (figures)||Decimal (words)|
|6 units, 8 tenths and 9 hundredths||6 89/100||6.89||Six Point Eight Nine|
|2 units, 7 tenths and 1 hundredth||2 71/100||2.71||Two Point Seven One|
|3 units, 4 tenths and 2 hundredths||3 42/100||3.42||Three Point Four Two|
|7 units, 9 tenths and 1 hundredth||7 91/100||7.91||Seven Point Nine One|
|1 unit, 3 tenths and 4 hundredths||1 34/100||1.34||One Point Three Four|
|1 ten, 9 units, 4 tenths and 2 hundredths||19 42/100||19.42||Nineteen Point Four Two|
|8 units, 6 tenths and 4 hundredth||8 64/100||8.64||Eight Point Six Four|
|9 units, 1 tenth and 2 hundredths||9 12/100||9.12||Nine Point One Two|
|3 units, 0 tenths and 2 hundredths||3 2/100||3.02||Three Point Zero Two|
|3 units, 4 tenths and 0 hundredths||3 4/10||3.4||Three Point Four|
If the children have completed the previous matching exercises, it is important to remind them that the rows in this table are not in order. The other tables went in numerical order (e.g. 1/10, 2/10, 3/10 etc). The numbers on this table are jumbled.
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PatrickHaller/fineweb-edu-plus
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Rationale: In order to read and spell words children must have
"This is the ability to identify phonemes or vocal gestures from which words are constructed, when they are found in their natural context—spoken words." This lesson will help children recognize the /i/ sound. They will learn this through practice and writing activities.
Materials: Primary paper and pencil, Tin Man Can Fix It by Sheila Cushman (phonics readers), pictures cut from magazines (fish, lip, dish, mitt), chalk, chalkboard and a worksheet of pseudo words (lig,clib,gib,blid,crig,id,kip,ip,hig).
1. Introduce the lesson by explaining to the children that they are going to learn a new mouth move. "Today class we are going to talk about one new mouth move /i/." "At first it may seem tricky and kind of hard, but we will get lots of practice at saying it, writing it and finding it in words."
2. I will explain to them and show them the phoneme /i/. "Class, has anyone ever seen a bug and gone /i/?" I will model for them this sound. "Can all of you go /i/?"
3. "Lets try a tongue twister with /i/ mouth move." Icabod’s igloo is icky. "Okay class, you try to say it." "Good, lets do it one more time, but faster." "Lets stretch out the /i/ in all the words." Model this for children. "IIIcabod iiiigloo iiiis iicky." "Okay, children now you do the same thing."
4. "I am going to show you some pictures and I want you to tell me which one has /i/ sound in it." The teacher holds up a picture of a bat and a fish. "Good, lets try a few more." The teacher will hold up several pictures.
5. "Now students it is time to practice writing the lowercase i." "Look up at the board and watch me." "You start your pencil on the sidewalk and make a line up to the road and place a dot above the road." "Okay class, I want you to get out your paper and pencil and practice."
6. "Okay, children we are going to practice spelling words with the phoneme /i/." [Teacher will write large squares on the board.] "Okay, we are going to use these boxes to spell words using our mouth moves." "Each box will hold one mouth move." "For example, if we spell sit, you hear three mouth moves so, we will use three boxes, one for each letter." The teacher would ask the students to spell it, in, fit, fix, bit, spin, and clip using the letterboxes.
7. I will read Tin Man Can Fit It. I will read it a second time, but this time have them raise their hands when they hear /i/. Teacher will write the words on the board.
8. For assessment: Give them pseudo words to pronounce out loud to check for awareness of /i/.
Reference: The Reading Genie
Click here to return to Elucidations
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PatrickHaller/fineweb-edu-plus
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A linear function, we have seen is a function whose graph lies on a straight line, and which can be described by giving its slope and its y intercept.
There is a special kind of linear function, which has a wonderful and important property that is often useful. These are linear functions whose y intercepts are 0 (for example functions like 3x or 5x). This means their graphs pass right through the origin, (the point with coordinates (0, 0)). Such functions are called homogeneous linear functions. They have the property that their values at any combination of two arguments is the same combination of their values at those arguments. In symbols this statement is:
f(ax + bz) = af(x) + bf(z)
Do ordinary linear functions have any such property?
They do. Any linear function at all has the same property when b is 1 - a. Thus for any linear function at all we have
f(ax + (1 - a)z) = a f(x) + (1 - a) f(z)
But be careful, linear functions that are not homogeneous do not obey the general linearity property stated several lines above.
Properties like these mean that once you know the value of a linear function at two arguments you can easily find its value anywhere else it is defined.
The property here described is often called the property of linearity. This is not really a sensible way to describe it because perfectly good linear functions which have y intercept that is not 0 do not obey the more general version of the property (the first one above.)
Anyway, realize that most functions DO NOT have either of these properties.
3A Describing Linear Functions on a Spreadsheet
Suppose we have a linear function, say, f(x) = 5x + 3.
We now address the following questions:
1. How can we evaluate this function at an arbitrary argument, x, on
2. How can we evaluate it at a whole lot of arguments?
3. How can we plot it?
Will see that once the first of these questions is addressed, the rest are quite easy to do. They were harder in the old days.
One nice feature of what you can do is that if you set this up once, you can change the linear function at will and watch how the plot changes instantly, as in the applet.
Just in case you want to keep what you are doing you will be wise to give it labels so at some future time you will know what you have.
So as a preliminary, you might enter in box A1 the title: Linear Functions.
Some more preliminaries: in A2 write the word slope, and in B2 enter the
number 5 (later on you can change this to anything else you want)
In A3 enter the words: y intercept, and in B3 enter the number 3.
In A4 enter: starting argument and in B4 enter -1
In A5 enter: spacing and in B5 enter .01.
(When you want to plot your function, you can only do it over a finite interval, and these last lines are useful for creating an interval.)
Now you are ready to start.
In A9 enter the symbol x and in B9 enter f(x). These are labels for the columns
In A10 enter =B4
In B10 enter =B$2*A10 +B$3
You now have the answer to the first question. The number that appears in box B10 will be the value of your function at the argument given in B4 (at this point that argument is -1, and with function 5x + 3 the value in B10 should be -2.)
You can evaluate this function anywhere else you please, by changing the entry in B4 to whatever you please.
Suppose I want to change the slope or the y intercept of my function?
You can do that by changing the entries in B2 or B3. The value of the changed function at the argument in A10 will appear in B10.
What are these funny dollar signs that I have put in A10 and B10?
To answer the second and third questions above we are going to copy the instruction in B10 into other boxes as well. When we do that, the references which do NOT have dollar signs in front of them will change . Those with dollar signs will stay the same.
How do the references change? What do you mean?
Suppose we copy B10 to B11. Then what will appear in B11 will not be exactly what is in B10, but instead it will be =B$2*A11 +B$3. Because the A10 had no dollar sign in it, when we copied it down one row the 10 turned into an 11. The other terms did not change because we put dollar signs in front of them.
What happens if you copy to a different column?
The same kind of thing will happen. That is, if you copy what is in B10 to C11, you will get =C$2*B11 +C$3. All the column indices that do not have dollar signs in front of them will shift over one column, because you shifted over one column. The same goes for shifting any number of rows or columns.
This property is what allows us to look at a function over a range and plot it by copying. Our plan is: have the argument increase by d from row to row, which can be accomplished by putting one entry in A11 and copying it down the A column Then copying B10 down the B column. That is all there is to answer the second question.
OK, what goes into A11?
We can enter =A10+B$5. This will increase the entry in column A in each row we copy it to by the amount in B5 over what it was in the previous row. If we do this in Column A, say down to row 500, and copy B10 also down to row 500, you will have a set of pairs for your function all ready to plot.
OK, how do I copy?
This varies somewhat from spreadsheet to spreadsheet. For many or most you do the following:
1. Highlight the box you want to copy.
2. Press [Ctrl] and c at the same time
3. Highlight the boxes you want to copy to.
4. Press [Ctrl] and v at the same time.
There is another way that is easier if you are copying several columns down from the same row at once; it is called fill or fill down on the edit menu. Try it. You can also fill sidewise. (Here you could copy B10 into B11 and then fill A11 and B11 both together down to A500 and B500.) Experiment with these things until you get them to work. If you can't get them to work on your spreadsheet, ask someone how.
OK, how do I get a graph of my function?
Highlight columns A and B from row 10 or 11 to row 500 (or to wherever you copied to) and click on "chart" in the insert menu. You will get to another menu with lots of options. Click on "x-y xcatter", and you will get to your plot. You will be asked about inserting labels on it and asked where you want it. You can put it anywhere, but if you put it on the same sheet as your calculation, you can change the function or domain by changing what is in B2,...,B5 and see the results immediately. There are ways to adjust the size of the graph and where it is, that you have to figure out for yourself. I generally screw them up.
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PatrickHaller/fineweb-edu-plus
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How to practise spellings at home.
Use the Look, Say, Cover, Write, Check system.
This helps children to remember the words and gets them used to practising writing the word.
As Mrs Edwards always says "Practise makes perfect!"
Look- look at the word carefully. Look at each letter of the word. Trace over the word with
your finger as you read it.
Say-Say the word slowly.Listen to each sound in the word. Say each letter of the word as
you trace over the letters with your finger.
Cover-Cover the word. Try to see the word in your head or write it with your finger.
Write- Now write the word.
Check- Check to see if you were right. If you didnt get it right don't worry, try again.
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PatrickHaller/fineweb-edu-plus
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This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Some time ago I was walking past a garage. Down on the ground
was the big sign that they have that tells motorists how much the
petrol will cost. You've probably seen them yourselves and you may
have been asked to look out for the cheapest petrol around. The
signs usually tell you the price for the different kinds of petrol.
Since we measure in litres it's the price for one litre.
Well, this sign was being prepared to be put up by the side of
the garage. I went over and looked at the part that shows the
price. I was interested in how the numbers were shown and how they
altered when the price changed. This particular one, like so many,
showed the numbers like they are on a calculator display.
The little lines on a calculator display can be called
'light bars'. This is how they generally look for the
figures 0 through to 9:-
In this sign they were brightly coloured flaps which on one side
showed the colour and on the other side were blank. As I walked
away from the garage I got thinking. This is the challenge that
came to my mind.
If we had 16 light bars we could only make certain numbers. For
So, my challenge to you is to find all the numbers you can make,
using 16 light bars all the time and forming the figures in the
same way as I did them for 0 to 9.
When you've done a few you may be able to think of a method or
system for helping you along the way. When you do, do write and let
us know what it was, as well as sending us your solutions.
The last word, as usual, is to say when you are happy with what
you have got, "I wonder what would happen if ...?''
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PatrickHaller/fineweb-edu-plus
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Distance Formula How to find the distance between lines using the Pythagorean Formula
⇐ 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.
- In this video, we're going to learn how to take the distance
- between any two points in our x, y coordinate plane, and
- we're going to see, it's really just an application of
- the Pythagorean theorem.
- So let's start with an example.
- Let's say I have the point, I'll do it in a darker color
- so we can see it on the graph paper.
- Let's say I have the point 3 comma negative 4.
- So if I were to graph it, I'd go 1, 2, 3, and
- then I'd go down 4.
- 1, 2, 3, 4, right there, is 3 comma negative 4.
- And let's say I also have the point 6 comma 0.
- So 1, 2, 3, 4, 5, 6, and then there's no movement in the
- We're just sitting on the x-axis.
- The y-coordinate is 0, so that's 6 comma 0.
- And what I want to figure out is the distance between these
- two points.
- How far is this blue point away from this orange point?
- And at first, you're like, gee, Sal, I don't think I've
- ever seen anything about how to solve for a
- distance like this.
- And what are you even talking about the Pythagorean theorem?
- I don't see a triangle there!
- And if you don't see a triangle, let
- me draw it for you.
- Let me draw this triangle right there, just like that.
- Let me actually do several colors here, just to really
- hit the point home.
- So there is our triangle.
- And you might immediately recognize
- this is a right triangle.
- This is a right angle right there.
- The base goes straight left to right, the right side goes
- straight up and down, so we're dealing with a right triangle.
- So if we could just figure out what the base length is and
- what this height is, we could use the Pythagorean theorem to
- figure out this long side, the side that is opposite the
- right angle, the hypotenuse.
- This right here, the distance is the hypotenuse of this
- right triangle.
- Let me write that down.
- The distance is equal to the hypotenuse
- of this right triangle.
- So let me draw it a little bit bigger.
- So this is the hypotenuse right there.
- And then we have the side on the right, the side that goes
- straight up and down.
- And then we have our base.
- Now, how do we figure out-- let's
- call this d for distance.
- That's the length of our hypotenuse.
- How do we figure out the lengths of this up and down
- side and the base side right here?
- So let's look at the base first. What is this distance?
- You could even count it on this graph paper, but here,
- where x is equal to-- let me do it in the green.
- Here, we're at x is equal to 3 and here we're at x is equal
- to 6, right?
- We're just moving straight right.
- This is the same distance as that distance right there.
- So to figure out that distance, it's literally the
- end x point.
- And you could actually go either way, because you're
- going to square everything, so it doesn't matter if you get
- negative numbers, so the distance here is going to be 6
- minus 3, right?
- 6 minus 3.
- That's this distance right here, which is equal to 3.
- So we figured out the base.
- And to just remind ourselves, that is equal to
- the change in x.
- That was equal to your finishing x minus your
- starting x.
- 6 minus 3.
- This is our delta x.
- Now, by the same exact line of reasoning, this height right
- here is going to be your change in y.
- Up here, you're at y is equal to 0.
- That's kind of where you finish.
- That's your higher y point.
- And over here, you're at y is equal to negative 4.
- So change in y is equal to 0 minus negative 4.
- I'm just taking the larger y-value minus the smaller
- y-value, the larger x-value minus the smaller x-value.
- But you're going to see we're going to square it in a
- second, so even if you did it the other way around, you'd
- get a negative number, but you'd still get the same
- answer, so this is equal to 4.
- So this side is equal to 4.
- You can even count it on the graph paper if you like.
- And this side is equal to 3.
- And now we can do the Pythagorean theorem.
- This distance is the distance squared.
- Be careful.
- The distance squared is going to be equal to this delta x
- squared, the change in x squared plus
- the change in y squared.
- This is nothing fancy.
- Sometimes people will call this the distance formula.
- It's just the Pythagorean theorem.
- This side squared plus that side squared is equal to
- hypotenuse squared, because this is a right triangle.
- So let's apply it with these numbers, the numbers that we
- have at hand.
- So the distance squared is going to be equal to delta x
- squared is 3 squared plus delta y squared plus 4
- squared, which is equal to 9 plus 16, which is equal to 25.
- So the distance is equal to-- let me write that-- d squared
- is equal to 25.
- d, our distance, is equal to-- you don't want to take the
- negative square root, because you can't have a negative
- distance, So it's only the principal root, the positive
- square root of 25, which is equal to 5.
- So this distance right here is 5.
- Or if we look at this distance right here, that was the
- original problem.
- How far is this point from that point?
- It is 5 units away.
- So what you'll see here, they call it the distance formula,
- but it's just the Pythagorean theorem.
- And just so you're exposed to all of the ways that you'll
- see the distance formula, sometimes people will say, oh,
- if I have two points, if I have one point, let's call it
- x1 and y1, so that's just a particular point.
- And let's say I have another point that is x2 comma y2.
- Sometimes, you'll see this formula, that the distance--
- you'll see it in different ways.
- But you'll see that the distance is equal to-- and it
- looks as though there's this really complicated formula,
- but I want you to see that this is really just the
- Pythagorean theorem.
- You see that the distance is equal to x2 minus x1 minus x1
- squared plus y2 minus y1 squared.
- You'll see this written in a lot of textbooks as the
- distance formula.
- And it's a complete waste of your time to memorize it
- because it's really just the Pythagorean theorem.
- This is your change in x.
- And it really doesn't matter which x you pick to be first
- or second, because even if you get the negative of this
- value, when you square it, the negative disappears.
- This right here is your change in y.
- So it's just saying that the distance squared-- remember,
- if you square both sides of this equation, the radical
- will disappear and this will be the distance squared is
- equal to this expression squared, delta x squared,
- change in x-- delta means change in-- delta x squared
- plus delta y squared.
- I don't want to confuse you.
- Delta y just means change in y.
- I should have probably said that earlier in the video.
- But let's apply it to a couple more, and I'll just pick some
- points at random.
- Let's say I have the point, let's see, 1, 2, 3, 4, 5, 6.
- Negative 6 comma negative 4.
- And let's say I want to find the distance between that and
- 1 comma 1, 2, 3, 4, 5, 6, 7, and the point 1 comma 7, so I
- want to find this distance right here.
- So it's the exact same idea.
- We just use the Pythagorean theorem.
- You figure out this distance, which is our change in x, this
- distance, which is our change in y.
- This distance squared plus this distance squared is going
- to equal that distance squared.
- So let's do it.
- So our change in x, you just take-- you
- know, it doesn't matter.
- In general, you want to take the larger x-value minus the
- smaller x-value, but you could do it either way.
- So we could write the distance squared is equal to-- what's
- our change in x?
- So let's take the larger x minus the smaller x, 1 minus
- negative 6.
- 1 minus negative 6 squared plus the change in y.
- The larger y is here.
- It's 7.
- 7 minus negative 4.
- 7 minus negative 4 squared.
- And I just picked these numbers at random, so they're
- probably not going to come out too cleanly.
- So we get that the distance squared is equal to 1 minus
- negative 6.
- That is 7, 7 squared, and you'll even see it over here,
- if you count it.
- You go, 1, 2, 3, 4, 5, 6, 7.
- That's that number right here.
- That's what your change in x is.
- Plus 7 minus negative 4.
- That's 11.
- That's this distance right here, and you can count it on
- the blocks.
- We're going up 11.
- We're just taking 7 minus negative 4 to get
- a distance of 11.
- So plus 11 squared is equal to d squared.
- So let me just take the calculator out.
- So the distance if we take 7 squared plus 11 squared is
- equal to 170, that distance is going to be the square root of
- that, right? d squared is equal to 170.
- So let's take the square root of 170 and we get 13.0,
- roughly 13.04.
- So this distance right here that we tried to
- figure out is 13.04.
- Hopefully, you found that helpful.
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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PatrickHaller/fineweb-edu-plus
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Rationale: Children have to be able to read whole sentences and have phoneme awareness. The next step is for them to become more independent readers. This is achieved by becoming more fluent readers. Children must learn to read quickly, silently, with expression and smoothly. The only way to achieve this is by practicing reading. In this lesson I will show children how to read fast by repeated readings.
Materials: ''If You Give a Pig a Pancake'', ''The Cat in the Hat'', ''The Giving Tree'' Minute timers, two per child, class library, pencil and paper.
1. ''Today we are going to learn ho to read a book fast without all the choppy sentences. Everyone listen. I am going to read a few sentences the wrong way, then I will read these sentences the right way.'' ''If….you….g-I-ve….a p-I-g….a…. pan-ca..ke, she….will…w-a-nt…some-th-ing….to go… with… it.'' ''This is the right way, If you give a pig a pancake, she will want something to go with it. ''Which one sounds better?'' The second one right! How do you think you can learn to read faster? Well the only way I know how is to read a lot. Today we are going to read the book of your choice over and over again until it sounds like the second example.
2. ''Boys and Girls, what do you do when you come to a word you do not understand? Take your finger and cover up the word except for the first letter, say the sound to yourself. Once you can read the first sound then go on to the next few letters, until you can read the whole word. If you still cannot read the word, reread the sentence over again and try to guess the word based on what the sentence says.'' Do not skip a word if you cannot read it. Just ask the teacher.
3. I will do three book talks to get the children interested in reading independently. I will do the books ''If You Give a Pig a Pancake'', ''The Cat in the Hat'', and ''The Giving Tree.'' Listen carefully to everything I say about the books because it might be the one you want to pick for yourself. If you do not find one of these books interesting then you can pick from the library. You can only choose from the books that have the blue sticker on them. How do you think you choose a book? By its cover? No. You choose a book by reading the back of the book or reading the first few sections. This helps you get an idea of what the book is about. If you find that there are more than two words on a page that you do not understand, the book might be too hard for you. This is a very good way to get the children interested in reading. They get to choose the book they want to read.
4. Once they have chosen their book I will put them in groups of two and have them read the book to each other. Each group will have the same book. One child reads the book once, and then the other child reads the book. They will continue this until each child has read the book three times. This repeated reading will enhance their fluency.
''We will now play a game. You have now had time to practice reading your book, your partner will time you. This will help you to know how fast you are reading your book. Remember that you cannot skip over any words. Practice cover up and rereading to understand a word.'' Do this three times and record your time to see who wins.
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PatrickHaller/fineweb-edu-plus
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LESSON 4: Ready to solve the equation
|Introduction to Elementary Algebra
Help on solving algebra math problems
Simple step by step method
We are now ready to start solving the equation below.
Solving means to know the value for 'x'.
We know the value of 'x' when we can say: 'x' is equal to …
the left side of the equal sign.
Most important rule: Because both sides of an equation are EQUAL,
any operation we do on one side must be done on the other side.
So let’s start
We already got an x of the left side. But we don’t want the x on the right side.
What can we do?
We know from the previous lesson
that we can make the +2x disappear
if we use
On the right side of the equation.
Because it is the opposite operation.
But remember: to keep things legal we must do the same thing on the
left side also.
Let’s do it
On the right side of the equal sign
Is equal to zero.
The equation becomes
On the left side we can put the 'x's together like this
It’s easy to see that
Now the equation becomes
Which is the same as
This is where we are now
If we can make the -4 disappear we finally get the x alone on the left side of the
equal sign and we can say that we solved the equation.
The opposite of -4 is +4 so let’s do it on BOTH sides.
On the left side: -4 + 4 is equal to zero.
On the right side: 7 + 4 is equal to 11.
The equation is solved !
If we use 11 in place of 'x' we will get that both sides of the equation are EQUAL.
In rapid motion...
Bye for now. More answers to algebra problems examples in a few days.
3x - 4 - 2x = 7 + 2x - 2x
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PatrickHaller/fineweb-edu-plus
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Although school buses are the safest way for children to get to school, children can still be seriously hurt—especially when approaching or leaving the bus.
Walk your child to the bus stop on the first day of school. Point out where it’s safe to walk and stand. Teach him these rules about school bus safety:
• Allow plenty of time to get to the bus stop. Children who are late may be tempted to run into a busy street.
• Wait in a safe place away from the traffic. Sometimes, children play games while they wait for the bus. They should be sure these games never involve running near the street.
• Get in line and wait your turn when the bus arrives. Children who push and shove to get on the bus can get hurt.
• Never walk behind the bus.
• Follow the rules. Children should be taught to respect bus drivers as they do teachers and other school staff members.
• Don’t stick hands, heads or objects out bus windows.
• Don’t push and shove to get off of the bus.
• Walk three “giant steps” (six feet) away from the side of the bus.
• If your child drops something near the bus, tell the bus driver before picking it up. Drivers can’t always see children.
• Wait until the driver says it’s safe when getting off the bus. Before crossing in front of the bus, take at least five “giant steps” (about 10 feet) until your child can see the driver’s face. Then the bus driver will also be able to see your child.
Copyright © Parent Institute
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PatrickHaller/fineweb-edu-plus
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One of the first lessons for a beginning bass guitar player is how to learn the names of the notes on a bass. You can play by ear, follow tabs, or mimic a lead guitarist, but at some point you really need to know the notes to advance your skills. Fortunately, they are very easy to learn.
Note Name Basics
The vast range of musical pitches is split up into units called octaves. An octave is the distance between two notes that have the same pitch (such as A and the next A). For example, play an open string on your bass, and then play the note you get from putting a finger down on the 12th fret (marked with a double dot). That note is one octave higher.
Each octave is divided into twelve notes. Seven of these notes, called the "natural" notes, are named with the letters of the alphabet, A through G. These correspond to the white keys on a piano. The other five notes, the black keys, are named using a letter and a sharp or flat sign. A sharp sign, ♯, indicates one note higher, while a flat sign, ♭, indicates one note lower. For example, the note in between C and D is called either C♯ (pronounced C-sharp) or D♭ (D-flat).
As you may have noticed, there are too many natural notes to have a sharp/flat in between every pair of neighbors. B and C natural have no note in between them, and neither do E and F. On a piano, these are the places where two neighboring white keys have no black key in between. So (except in advanced music theory) there is no such thing as a B♯, C♭, E♯, or F♭.
To recap, the names of the twelve notes in an octave are:
A, A♯/B♭, B, C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭, A...
Note Names on the Bass
Now that you know the note names, it's time to look at your instrument. The lowest, thickest string is the E string. When you play it without any fingers down, you are playing an E. When you play it with your finger down on the first fret, you are playing an F. Next is an F♯. Each consecutive fret raises the pitch by one note.
The simplest way to learn note names is to continue playing the note on each fret and naming it aloud as you go up. Notice that when you reach the fret marked with a double dot (12th fret), you've come back around to E again. Try this on all the strings. The next string is the A string, followed by the D string and the G string.
You may have noticed that certain frets are marked with single dots. These are good reference points to memorize first. For example, if you are going to play a song in the key of C, it will be useful to immediately know that the first dotted (3rd) fret on the A string is a C. Work out what notes the dots are on each string. The dots up past the double dot are the same notes as the ones below, only an octave higher.
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PatrickHaller/fineweb-edu-plus
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I started the unit by reading a couple of books about teeth. I read this adorable book about how a moose has a loose tooth and all of the animals try and help him pull it. After I read the story, we made a class graph based on how many teeth we have lost. I was surprised that most kids have not lost any teeth yet!
We talked about keeping our teeth healthy, what types of foods are good for our teeth, and what we use our teeth for. Here are some of their ideas.
I made a worksheet where the children had to sort food and items that are good and bad for our teeth. They cut and pasted the pictures to group them accordingly.
We also wrote sentences about how we can keep our teeth clean. They had to write 1-4 sentences based on their ability and draw a picture that corresponded with their sentence. Here are some examples:
Lastly, we made this adorable toothbrush and tooth craft! I let each student make one tooth and one toothbrush.
After a week of fun activities, we know how to keep our teeth clean and healthy!
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PatrickHaller/fineweb-edu-plus
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How you can help at home: Have your child come up with household rules and learn about the importance of rules.
By Miriam Myers , GreatSchools Staff
In this social studies activity your child comes up with rules for your household.
What you'll need:
Here's How to Do it
Rules are important aspects of a community. Discuss with your child different types of rules, such as classroom rules, rules of games she plays and laws in your community. Talk about why rules are important and what might happen if there were no rules. Discuss who makes different rules and who enforces them. Are there good rules and bad rules? What's the difference? Have your child come up with household rules such as locking the door when you leave the house and cleaning up after yourself. Have your child write down the rules. Talk about why these rules are important.
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PatrickHaller/fineweb-edu-plus
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“R, R, RRRRR," Is What the Tigers Say!
Emergent Literacy Design
By: Sarah Leslie Smith
Rationale: This lesson will help children identify the letter R. The sound /r/. They will recognize the phoneme. The representation is the visual growling like a tiger and showing your claws and the sound will be the actual growling like a tiger. Students will be able to pick the /r/ sound out of words when they are spoken or heard. Students will also recognize the word in writing and be able to write words with the letter R.
Materials: 1 sheet of primary paper per child.
1 pencil per child.
Notecards with words, CARD, PAPER, RAGE, PARTNER, RAGTOP.
Board to write words from number 9 on to show students where the letters come in. Book, “Pat’s Jam”
1. Say: There are many sounds that make up our language. What language do we have? That’s right, English! Today we are going to look at one specific sound. That sound is made by the letter R. It sounds like a tiger growling. Everyone practice making their tiger “RRRRR”.
2. Now let’s pretend like we are tigers in the jungle or tigers on the football field and say “”RRRR””!! That was scary! We say RRR by closing our mouth and almost putting our teeth together with rounded lips. Our tongue curves around.
3. I am going to say a word then I will find the R in the word. I will listen for the tiger RRR. Ccccc-aaaa-rrrrr-dddd. Card. Where was it? It was carrrrd. I found it!
4. Now you try. I will say this word and you say it and look for the RRR. PPPP-aaa-pppp-eeee-rrrr. Where was the RRR? Say it again slowly to yourselves. It’s at the end! We found it! RRR! Now growl like a tiger! Show me your fangs and your claws!
5. Now we will learn to write the letter R. Take out primary paper and pencil. Draw a straight line with a cup around the top and a leg coming out of the cup. There you have an RRR. RRR like a tiger! Now practice writing that letter 10 times!
6. Now write the word RAGE on your paper. Underline the RR in that word. Do the same with Partner and Ragtop. Have these words written so children can copy them.
7. Ask students if they hear R in rip or slip? What about car or map? Watch my mouth when I say the word CAR. Look for the tiger RRR.
8. Practice reading from some pages from the book “Pat’s Jam”. Read the page with the word “rat”. Have them find the RR word. Read the page with the word “car”. Have them find the R.
9. Show them how to decide is R in a word. Show them Rap. Help them decide if it is Rap or Tap. Show them deliberately how you move your mouth to find the sound. Do the same with Run. Run or Fun? Ripe. Ripe or Pipe?
10. Assessment. Give children for them to practice. Assess as you move through the lesson. Take notes on children that seem eager and children that aren’t speaking up. You can learn a lot throughout the lesson by watching the children. Let children the worksheet. When they finish have them individually read the words and show you the RRR by making a tiger RRR .
Book Reference: Decodable text, “Pat’s Jam”
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PatrickHaller/fineweb-edu-plus
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Lesson on Addition for a first grade classroom
2. At the end of this lesson the students should be able to add different objects
together to find out how many objects there are total
1. The students should be able to explain up to 3 different reasons that being able
to add is important
1. 5 colorful building blocks
2. 5 pieces of paper with the numbers 1 through 10 on them
The teacher should start out by explaining that addition is simply the combination of 2 or more different groups of numbers. For example if you have a pile with 2 objects in it and another pile with one object in it you get three. The teacher should count the separate piles, then put the piles together and count them again. Next the teacher should get five students to come up to the front of the room. The students should be split up into 2 groups one with 3 individuals and the other with 2. The students in the first group should each get pieces of paper with the numbers 1, 2 and 3 written on them. The students in the second group should get the numbers 4 and 5. The class should then count the students in the first group. The teacher should then say that we are now going to add 2 and 3 together. As the group of two moves to the group of three the teacher should say that we have just added 2 to 3. The students should then count the this new group and come up with the number five. The teacher should not move on if the students do not readily recount the new group and do not seem to understand that the groups have now been combined.
The teacher should now talk to the students about the different ways we can use addition in our everyday lives. The teacher should give the example of figuring out how many fish are in the fish tank. The fish could be separated in several ways depending on what fish are in the tank. If there is 1 black fish and 2 gold fish this is an easy number for the children to add. The teacher should then have the students take turns going around the room and looking for things they could add together. The teacher should be accepting of most anything the students want to add. If one student want to add three block and one desk that is ok.
The teacher should then ask the students about things in their homes that they can add and ask everybody to think of something at home tonight that it could be beneficial to add.
As a conclusion to this lesson the teacher should have several different objects that she has gathered for the students to add. Each student should get a chance to do this. If any students make a mistake the teacher should correct them and help the students by having them count each pile and then count the piles together.
The students should be informally evaluated based on how the teacher has observed them answering questions. A short quiz could be used as well, but should not take more then five minutes to finish.
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Talk to your child.
Use everyday events, like taking a bath, getting dressed, or brushing teeth as a chance to talk with your child. Ask lots of questions, use short sentences and lots of words. This helps your child learn words and build vocabulary.
Play a rhyming game.
We’ve all been there. Your child is bored, fighting with a sibling or asking, “Can we go now?” To help pass the time, play a rhyming game with your child. If you are in a car or on a bus, find objects outside of the window, like a tree. Then, have your child think of another word that rhymes with tree. Rhyming helps your child learn sounds and words.
Play the alphabet detective game.
Help your child find an “a” on a sign, a “b” on a license plate, and so on. This game helps your child learn to find letters in words, which is an important step in learning to read.
Find the first letter of your child’s name.
Show your child the first letter of his or her name. Then, while you are in the grocery store, find labels that are spelled with that letter. This game is another fun way for your child to recognize letters in words.
Write a grocery list together.
Have your child “help” you write a grocery list. Say the words of the items you need as you write them down. This shows your child how letters form words and shows how we use writing in our everyday lives.
Keep lots of crayons, pencils and paper in easy reach.
Kids love to draw and write their name. Have crayons and paper ready for them at home or when you are traveling. Drawing is one of the first steps to writing. Drawing can also keep your child busy and happy.
Have your child draw a picture and tell you a story.
Kids have wonderful imaginations. Encourage your child to draw and make up his or her own stories. Having your child tell you a story will help develop language skills.
Tell your child stories.
Your child might enjoy hearing about the day he or she was born, or how you spent your time when you were his or her age. Telling your child stories can help him or her understand other stories and become familiar with more words. It also encourages your child to tell you stories.
Songs are a fun way for your child to learn and remember words. You can sing along to the radio in the car, or you can make up songs together as you make dinner.
Point out common words you see everyday.
There are words all around you. Point out simple words, like stop, exit, and welcome, as you shop or travel with your child. Have your child repeat the words. This helps your child learn to recognize everyday words.
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PatrickHaller/fineweb-edu-plus
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- 1. Is reality closer to the top video or the bottom?
- 2. Using your finger, show just how long it takes light to get from the Earth to the Moon.
- 3. What information will you need to know to solve the problem?
- 4. If it were bright enough, how long would it take Dan's flashlight to reach Pluto?
- 5. Choose an object in the universe and find out how long it will take the light from Dan's flashlight to reach it.'
- 6. If the light takes a month to reach a certain point in space, where might that point be?
- 7. How far does light travel in ten years? (A: Ten light-years. Introduce a new unit of distance.)
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PatrickHaller/fineweb-edu-plus
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Using Language to Learn
What Do Preschoolers Do?
- Listen to stories and to conversations.
- Talk to adults and to other children in complex sentences.
- Master many rules of grammar.
- Make up silly words and stories.
- Use language to think, to share ideas and feelings, and to learn new things.
- Enjoy the same books over and over and look at new books.
- Retell familiar stories to themselves and others.
- Think about what the characters in a book might feel or do.
- Draw and write with pencils, crayons, and markers.
- See print around them and watch adults read and write.
- Imitate adult writing by scribbling.
- Copy shapes and some letters.
How Do Preschoolers Learn?
Gina bounces out of bed and hurries to the kitchen. She opens the cabinet, takes out a box of cereal, then puts it back. She takes out another box and says, "Grandpa, this is my cereal. It has a big P and lots of stars."
Grandpa says, "That's good thinking." Gina points to a letter on the box, "That's a P." She traces the letter in the air and says, "P as in Peter. Peter's name starts with a P. It's on his cubby."
Grandpa makes an offer. "Today, we can have our regular story time and then write together. I need to write a letter to a friend. You can write, too."
Gina puts her empty bowl in the sink and runs to find her mother. "Mom, I'm gonna read and write with Grandpa." Her mother says, "That sounds like fun. When I take you to family child care, I'll tell Ms. Jenkins that you like to write. You can write at her house and at home."
Like many preschoolers, Gina is learning language:
- She knows that letters (the P) and pictures (the stars) have meaning.
- She knows there is a P on her cereal box and at the beginning of Peter's name.
- She knows that people take turns when talking to each other.
Gina's family helps her learn about language:
- They have a regular story time every day.
- Grandpa encourages her thinking, so Gina continues exploring the letters on the box.
- Grandpa offers to write with Gina.
- Mom talks to Ms. Jenkins, so that Gina can write at family child care and at home.
Source: America Reads Challenge: Ready*Set*Read for Families
More on: Activities for Preschoolers
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PatrickHaller/fineweb-edu-plus
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Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Investigate the different ways you could split up these rooms so
that you have double the number.
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How many triangles can you make on the 3 by 3 pegboard?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
We need to wrap up this cube-shaped present, remembering that we
can have no overlaps. What shapes can you find to use?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
An activity making various patterns with 2 x 1 rectangular tiles.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Can you find ways of joining cubes together so that 28 faces are
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
How many models can you find which obey these rules?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
In how many ways can you stack these rods, following the rules?
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Try continuing these patterns made from triangles. Can you create
your own repeating pattern?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
An investigation that gives you the opportunity to make and justify
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
Ben has five coins in his pocket. How much money might he have?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
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PatrickHaller/fineweb-edu-plus
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To see what the graph
of y = |x| looks like, let’s create a table
these values, simply plot the points and see what happens.
Whenever you have an absolute value
graph, the general shape will look like a “v” (or in some cases, an upside down “v” as we will see later). Let's Practice:
- Graph y = |x+2| We know what the general shape should look like, but let’s create a table of values to see exactly how this graph will look.
|-3|||-3 + 2| = |-1| = 1|
|-2|||-2 + 2| = |0| = 0|
|-1|||-1 + 2| = |1| = 1|
|0|||0 + 2| = |2| = 2|
|1|||1 + 2| = |3| = 3|
|2|||2 + 2| = |4| = 4|
|3|||3 + 2| = |5| = 5|
So our graph of y = |x + 2| looks like
Notice that the graph in this example looks almost identical to the graph of y = |x| except that it was shifted to the left 2 units. This will be important as we try to make generalizations later in the lesson.
- Graph y = |x| - 4 The table of values looks like this:
|-5||5 - 4 = 1|
|-4||4 - 4 = 0|
|-3||3 - 4 = -1|
|-2||2 - 4 = -2|
|-1||1 - 4 = -3|
|0||0 - 4 = -4|
|1||1 - 4 = -3|
Which makes the graph look like this:
Notice that the graph in this example is the same shape as except that it has been moved down 4 units.
- Graph y = -|x| In creating the table of values, be careful of your order of operations. You should find the absolute value of x first and then change the sign of that answer.
So the graph of looks like:
In this example, we have the exact same shape as the graph of y = |x| only the “v” shape is upside down now.
Based on the examples we’ve seen so far, there appears to be a pattern
when it comes to graphing absolute value
- When you have a function in the form y = |x + h| the graph will move h units to the left.
When you have a function in the form y = |x - h| the graph will move h units to the right.
- When you have a function in the form y = |x| + k the graph will move up k units.
When you have a function in the form y = |x| - k the graph will move down k units.
- If you have a negative sign in front of the absolute value, the graph will be reflected, or flipped, over the x-axis.
Keep in mind that you can also have combinations that change the absolute value graph
more than once. You can practice these transformations with this EXCEL Modeling
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PatrickHaller/fineweb-edu-plus
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Let the Air out of the Balloon
Rationale: It is
important for children to understand that the letters in the alphabet
phonemes that make up words. Before
students can match the letters to their phoneme however they have to be
recognize the phonemes in spoken words.
This way, they understand the connection between the sound and
written letter. This lesson is to help
students learn the consonant "S" and
the /s/ sound that it makes. Through the lesson, the students will
recognize the phoneme in spoken words and then recognize the written
that represents the sound. They will
practice finding /s/ in words.
Paper with, "Sssarah
sssea while sssitting in the ssssand."
a balloon with the letter "S" printed underneath it
Siena at the Store; the sound of S by
Cecilia Minden and Joanne D Meier
Picture page with sun, bug, star, window, snake, flower,
sword, table, chair, purse, sock, computer
- Begin the lesson by explaining that
our written language can be very tricky. "It
is like a code that every one needs to learn to crack. Once you have
cracked the code you are open to endless possibilities. You can
understand symbols all around you. You can
write messages to your friends and family and they will understand what
you mean. Our mouths move when we say words and the sounds that come
out represent letters which make up words. Today
we are going to work on the sound /s/ and notice the way our mouth
moves when we say it."
- Ask students: "Have you ever heard the
air come out of something? Like a balloon or a tire? It makes the /s/
sound. When you make the sound of air
coming out of a balloon that is the /s/ mouth movement we are looking
for. Let's pretend we see a balloon flying
around that has the air coming out of it. Move your hand in the air and
point to the imaginary balloon and let's make the /s/ sound together."
[Point up in the air and make a figure 8 like you are trying to keep
your finger on a moving balloon].
- "Now that we have learned the sound
and mouth movement of /s/, everyone look up here at the board! Here is a tongue twister I want you to try
(pass out sheet with tongue twister on it). Tongue
twisters can be tricky, but they are also fun, Listen to me read it
then we will say it together!" I say, "Sssarah ssscanned the sssea
while sssitting in the ssssand. Let's read
it together!" (We read it together.) "Now
let's read it again, but this time slower and break the /s/ sound off
the word: "/s/ arah /s/ canned the /s/ ea while /s/ itting in the /s/
- [Have students take out primary paper,
pencils and pass out the picture of a balloon with air coming out and
the letter "S" written under it.] "Remember
how I told you that the sounds that come out of our mouths are
represented by letters. The letter "S" is
used to spell the /s/ sound. Let's
practice writing the letter "S". Watch me
write it on the board. You start halfway
between the rooftop and the fence and curve up towards the roof. Once you get to the roof curve back to the
fence and then curve down to the sidewalk. Once
you get to the sidewalk curve back up and end in-between the sidewalk
and the fence. It weaves around kind of like a snake!
This is a capital "S" or a big "S". To
make a lower-case "S" or a little "S" you only use the area from the
fence to the sidewalk. Now I want everyone
to try a capital "S" on your paper (repeat the directions). I am going to walk around and see
snaky "S"s. When I put a sticker on your paper I want you to write nine
more "S"s on your paper. Now when you see
the letter "S" in a word, you know that it will make the /s/ sound".
- "Now I am going to show you how to
find /s/ in words. Listen to the word basket, I'm going to stretch out the word for you and I
want you to listen for /s/ like the balloon that is loosing air! B-b- b- a- a- S- S- S . . . .
* Do you hear it? There is the /s/! There
is the air blowing out of the balloon in basket!"
- Call on different students to tell
what they think is the answer and how they knew:
"Do you hear the /s/ in say or cut? Glass or bowl? Basement or attic?
Desk or table? Snake
or bear?" [Tell the students to use their balloon
picture] Hold up your balloon if you hear the /s/ sound in any of the
words I'm about to say. Sam,
packed, his, suitcase, to, ride, a, bus, to, Seattle, to, see, Aunt,
- Say: "Siena
and her mother go to the store to buy sandals. When
they get there they end up buying a lot more! They
buy surprises for their entire family! To find out what surprises Siena and her mother buy we have to read, Siena at the Store. Read Siena at
the Store and talk about the story". Read it again and have the
students raise their hands when they hear words with /s/.
List the words they hear on the board. Next
have the students write a message about the store and what they would
buy if they went using invented spelling! Display their work.
- Assessment: [Pass
out worksheet to each student] Say, "Get out your pencil and I want you
to circle every picture that has the mouth move /s/ in it".
Bruce. The Reading
Genie; Making Friends with Phonemes. http://www.auburn.edu/academic/education/reading_genie/phon.html.
here to return to the Voyages Indes
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An exponent is a number that tells how many times the base number is
used as a factor. For example, 43 indicates that the base number 4
is used as a factor 3 times. To determine the value of 43, multiply
4*4*4 which would give the result 64.
Cubes indicate that the exponent has a value of three. The term cube comes
from the geometrical shape that has the same width and length and height. To find
the volume of a cube you would multiply the width times the length times the height.
Exponents are written as a superscript number (e.g. 43) or preceded
by the caret (^) symbol (e.g. 4^3).
Some facts about exponents:
- Zero cubed is zero (e.g. 03 = 0)
- One cubed is one (e.g. 13 = 1)
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Birds of Prey in Year 2
Year 2 have also been learning about birds of prey this week;
Nell wrote – There are loads of different owls. There is a Barn owl, a Snowy owl, an Eagle owl, aTawny owl. It looks like owls turn their heads all the way round but they actually turn their heads 180 degrees. Their feathers are so soft that when
they hunt at night they fly silently so their prey can’t hear it coming. Owls swallow their prey whole and then they spit the bones out and that’s called an owl pellet. They have facial discs which help them hear in the dark.
Yelena wrote – Did you know some owls have two feathers on the top of their head. Owls are a bird of prey. There are lots of owls in the world. Tawny, Horn, Snowy and a Barn owl but the rarest is the Sokoke Scops. Owls are nocturnal that means that they are awake at night. Some owls have red eyes and yellow and they have great eye sight to see their prey. They can fly silently so their prey can’t hear them. After owls have eaten they spit it our and that is called an owl pellet. If you look at it you can see what it’s eaten.
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Rational: Letter recognition is one of the most important steps toward children learning to successfully read and write. The goal of this lesson is to teach the students to recognize the letter p in print and the phoneme /p/ in spoken words. Another goal for this lesson is for the students to recognize both upper and lower case P, and to successfully participate in the mouth movement involved with P.
1. Large picture of Peanut and
2. Poster board with tongue twister: “Peanut please pass the pink pitcher to
3. Primary Writing Paper
4. Pencils (for students)
5. Dry erase marker
6. Dry erase board
7. Peanut and
8. Picture cards with words that begin with p and words that do not begin with p. (Ex. Prince and Queen)
9. Worksheet for assessment with pictures of words beginning with p and pictures of those not beginning with p. (Ex. Pea, moon, pear, dog)
1. The teacher introduces the lesson by explaining that language is like a secret code and that we all must first learn to recognize what each letter stands for.
2. First, we will review the letter we have already learned. “I am going to write a letter on the board and when I snap my finger I want you all to make the sound that each letter creates.” Have the students give examples of words that start with each of these letters. “Great job class, I loved the way everyone participated and came up with their own words for these sounds.”
3. Tell the students, “Today we are going to talk about the letter p and the sound that it makes.” Show the students the chart with the letter p written on it. Now ask the students what their mouth does while we make the /p/ sound.
4. Let the students practice the /p/ sound until everyone has got it down. Next, ask a student to tell you the movements their mouth makes as they pronounce the sound.
5. “Okay now I am going to pronounce two words. You will choose which word in the pair has the /p/ sound. Let’s try one together. Does pen or mat have the /p/ sound? P-e-n, m-a-t, I hear /p/ in pen. Do you all agree? Now give the students the opportunity to answer the questions.
6. Bring out poster with the Tongue Twister on it. State the expectations: "Now we are going to practice a tongue twister using the /p/ sound. I am going to say it first and then we will say it together." When reading the tongue twister say it with much expression and encourage students to do the same. "Listen, Peanut please pass the pink pitcher to
7. Next, the students will practice writing the letter p. Students now should take out primary paper and pencil and model what you do. "First, I am going to model it then I want you to try. To write a p put your pencil on the fence, go straight down to the ditch, come up and put his chin on the sidewalk. Now let me see you try on your paper." Allow them to practice making the letter p along a line of primary paper.
8. At this point, I will have students listen as I read the story “Peanut and
9. “Everybody did a great job!” For assessment, I am going to pass out the worksheet with pictures on it. The students will circle the picture with the /p/ sound.
Harrington, Meagan. "P is for Popcorn". http://www.auburn.edu/academic/education/reading_genie/encounters/harringtonel.html
Dotlich, Rebecca. Peanut and Pearl's Picnic Advewnture. (2006). Harper Collins.
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Unit 17 - WE GO WHERE Where are we going?
The students will recall classroom instructions and will learn the vocabulary for places around a school.
If you have not already done so, make a poster of the classroom instructions you want them to use and put it on the classroom wall. The poster will remind your students of the language you want them to integrate naturally into their NZSL learning.
Play clip 17.1a, in which the presenters sign some vocabulary relating to places around a school. Have the students practise their signing along with the presenters.
Hand out worksheet 17.1 to the students for their reference.
Distribute copies of a map of your school, one per pair of students. While one student points to a place on the map, the other signs its name. Or one student could sign the name and the other could point to the place on the map.
This task will help your students to create meaning by making a direct sign–object link.
Where am I going?
The students will learn how to give and follow directions.
Understanding signed directions can take some practice. Once a starting point has been established, NZSL expresses directions using the signing space like a "map". Signers usually give instructions by starting with a general location (that they both know) and moving to a specific location, for example:
YOU KNOW LIBRARY IX-loc, NEXT IX-loc CLASSROOM
Remind your students that a signer usually gives directions from their own perspective (as the starting point), so the viewer has to mentally turn the directions on the signed map around in order to understand how to follow them.
Find out how many location words (place prepositions) your students can remember from Unit 7, when they learned some signs for classroom objects and for where items can be located in a classroom. Play clip 7.1b to help them with their recall.
Play clip 17.1b, in which the presenters model the vocabulary for indicating direction. Have the students sign the words along with the presenters. Write the prepositions from worksheet 17.2 on the board in English. As you point to one of them, have the students sign the word. Hand out worksheet 17.2 for their reference.
Project all or some of the sentence patterns from the Unit 17 overview. Play clip 17.2a so that the students can use these as models for dialogues in which they give and follow directions. This will take them some time and you may need to replay this clip many times. They can change the names of places using the vocabulary from worksheet 17.2. Their partners respond by giving an imagined location for the place, for example:
How do I get to the library?
[Gloss: IX-me GO-TO LIBRARY HOW; Non-manual signal: whq]
The library is ahead on the left.
[Gloss: LIBRARY IX-loc; Non-manual signal: t] IX-you STRAIGHT TURN-LEFT
Extension task: Take the students outside and have them practise giving and responding to directions, in groups or as a class. For example, you or a student could give the instruction
The students respond by turning left.
Making meaning through physical movement will build their conceptual understanding. They will learn to link the signs with their meaning in NZSL without using English.
Where am I?
The students will follow instructions and directions to locate places on a map.
Play scene Q, in which the girls are communicating on a street outside a shop. Ask the students how much they understand. Replay the scene and check whether the students understand more with each viewing.
Hand out copies of the scene Q transcript and have the students role-play the scene. Replay the scene so that the students can focus on the communicative expression now that they have grasped the meaning. Challenge the students to perform their role-plays without the prompt of a script.
Introduce the ordinal numbers from FIRST to FIFTH. Play clip 17.2b and have the students practise their signing. Encourage them to use these numbers as they give and respond to directions in the next task.
Pair task: Laminate enough copies of worksheet 17.3 for the students to have one per pair. Have them take turns to give instructions while the other person uses a non-permanent pen to draw the route on the map. This can then be wiped off before the next turn.
To make the task more interactive, show (by projecting them onto the board) sentences like the following for the students to use when they see their partner going in the wrong direction:
No, that’s the wrong way.
[Gloss: "wave no" WRONG; Non-manual signal: neg]
No, don't turn right. Turn left.
[Gloss: "wave no" TURN-RIGHT WRONG; Non-manual signal: neg], [Gloss: TURN-LEFT; Non-manual signal: nod]
Stop. Go back.
"wave no" GO-BACK
Repeat the task but have one student follow the directions on their copy of the map this time and then tell the person giving the directions which building they arrive at.
Group task: Repeat the task outlined above but first have the students work in pairs to develop a set of instructions for locating a particular place. Each pair takes turns to give the instructions to the other pair, who respond by drawing the route on the map.
Pair task: Have the students take turns to give directions. Reproduce copies of your own school’s map or use copies of worksheet 17.3. Have one student give directions for how to get to a place on the map but not tell their partner what the place is. The partner follows the directions and gives their location in response to this question:
Where are you?
[Gloss: IX-you WHERE IX-you; Non-manual signal: whq]
If the response is not correct, the students review the directions together until they agree on the finishing point.
The students will assess their progress across the outcomes to be achieved.
Discuss the learning outcomes for the unit with your students and make sure they have copies of the assessment criteria. Discuss how they will carry out the assessment. For example, they could record the role-plays on DVD and then assess:
- their own performance
- each other’s performances.
You could use the recordings to assess individual progress.
Get your students to make up role-plays and perform them before the class. Have two possibilities for them to choose from:
A student has just arrived at your school and has made friends with someone in another class. You arrange to meet at lunchtime at a particular place. The new student needs directions for how to get there.
Your students have been chosen to show some visitors around the school. Make up a series of directions to guide the people around.
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Parts of Speech
Verbs: All the Right Moves
Verbs are words that name an action or describe a state of being. Verbs are seriously important, because there's no way to have a sentence without them.
While we're on the topic, every sentence must have two parts: a subject and a predicate.
There are four basic types of verbs: action verbs, linking verbs, helping verbs, verb phrases.
You Could Look It Up
Verbs are words that name an action or describe a state of being.
The action of an action verb can be a visible action (such as gamble, walk, kvetch) or a mental action (such as think, learn, cogitate).
Quoth the Maven
To determine if a verb is transitive, ask yourself, “Who?” or “What?” after the verb. If you can find an answer in the sentence, the verb is transitive.
Action Verbs: Jumping Jack Flash
Action verbs tell what the subject does. For example: jump, kiss, laugh.
An action verb can be transitive or intransitive. Transitive verbs need a direct object.
Intransitive verbs do not need a direct object.
Chain Gang: Linking Verbs
Linking verbs join the subject and the predicate. Linking verbs do not show action. Instead, they help the words at the end of the sentence name and describe the subject. Here are the most common linking verbs: be, feel, grow, seem, smell, remain, appear, sound, stay, look, taste, turn, become.
Although small in size as well as number, linking verbs are used a great deal. Here are two typical examples:
Quoth the Maven
To determine whether a verb is being used as a linking verb or an action verb, use am, are, or is for the verb. If the sentence makes sense with the substitution, the original verb is a linking verb.
Many linking verbs can also be used as action verbs. For example:
Mother's Little Helper: Helping Verbs
Helping verbs are added to another verb to make the meaning clearer. Helping verbs include any form of to be. Here are some examples: do, does, did, have, has, had, shall, should, will, would, can, could, may, might, must.
Verb phrases are made of one main verb and one or more helping verbs.
Identify each of the verbs in the following sentences. Remember to look for action verbs, linking verbs, and helping verbs.
One more time, with gusto! Underline the verbs in each of these sentences.
Excerpted from The Complete Idiot's Guide to Grammar and Style © 2003 by Laurie E. Rozakis, Ph.D.. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.
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|Activity Type: Build Accuracy|
|Activity Form: Game|
|Group Size: Small Group, Whole Class|
|Length: 10 minutes|
|Materials: Magnetic or felt letters|
|Goal: Given a written regular word or nonsense word, the student can sound out and then say the word ( abc -> "aaabbbcc" -> "abc").|
|Items: All letters whose sound has been learned so far (or a subset of consonants and vowels)|
What to do
- Let's play the Alien Word Game. We're going to make some words with these letters, and you have to tell me whether the word is a real one or an alien one. Alien words are words that don't make any sense to you or me. Ready?
- First, let's review the sounds for these letters. Point at each letter in a random order and have students say its sound. Give several students individual turns until you are sure all students know the letter sounds for these letters.
- Make a real word from the letters, say dot. Sound out this word with me by saying it slowly: dooot. What's the word? Right! Dot. Is dot a real word or an alien word? Students: A real word. It may help to emphasize the real word by using it in a sentence: You can make a dot on paper with a pencil.
- Next, switch out one of the letters (replace d with g, for instance). Okay, now we have a new word. Let's find out if it's a real word or an alien word. First, sound it out. Students: gooot. What's the word? Students: got. Right: got. Is got a real word or an alien word? Students: a real word. Emphasize the real word by using it in a sentence: Nico got a sticker today!
- Now switch again (for instance, replace g with z). Is this a real word or an alien word? First, sound it out. Students: zzzooot. What's the word? Students: zot. Right: zot. Is zot a real word or an alien word? Students: an alien word. That's right. Zot is a make-believe word. It might be a new word that someone makes up some day. Let's try another.
- Continue switching letters (including the medial vowel and the last letter), making words and non-words. Watch for students who are struggling and give them an individual turn, perhaps modeling for them again. Make a note of students who continue to have trouble in an Activity Log. If a student can say the word slowly but not fast, you may need to go over oral blending with them.
- As students become more confident with sounding out, you can fade that part of the activity so that they are reading words with sounding out.
Related activities
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Rationale: In order to develop a child's phonemic awareness, children must have an understanding of short vowel sounds. For students to be successful fluent readers, they must accomplish decoding skills for unfamiliar words. In this lesson, students will learn the short a sound: a=/a/. Through language experience activities, tongue twisters, buddy reading, and print concepts students will learn to read and write /a/ words.
Materials: Primary paper, pencil, chart paper with tongue twister on it (Allie the ant and Alison the alligator are actors), two pieces of chart paper for language experience activity, easel, marker, each student needs a copy of A Cat Nap (Educational Insights), one flashcard for each child with pictures with the short a sounds as well as other pictures that do not have the short a sound (apple, ate, last, cat, cab, rat, cap, fat, stand, rag, ran, hand, dog, roof, pig, book, chick, red, pet, hen, six, up, rip, stop, hop, and frog), picture worksheet
1.) Ask the class: "What noise do you make when you sneeze? Your right. Aaa-aaa-aaa-choo! The aaa sound is the sound the short /a/ sound makes. Today we are going to learn about the letter /a/ and the sound it makes by reading and writing words with the short /a/ sound."
2.) Read the tongue twister aloud to the students. "Now as I point to each word of the tongue twister on the chart paper, I want everyone to read aloud with me. Allie the ant and Alison the alligator are actors. Now lets read it again, and I want everyone to stretch out the /a/ at the beginning of the words. A/a/a/a/llie the a/a/a/nt a/a/a/nd a/a/a/lison the a/a/a/lligator are /a/a/a/ctors. Awesome job! Now lets try it again but only this time break /a/ off each word. /a/llie the /a/nt and /a/lison the /a/lligator are /a/ctors. Great job!"
3.) Have the class sit together on the floor. Set up a piece of chart paper on an easel. Ask the class: "Can anyone think of other words with the short /a/ sound?" As students say each word, write them down, even if they do not have the short /a/ sound. Afterwards go through the list and ask the students: "Does everyone agree that each word on the list has the short /a/ sound? If there are some words that do not, which ones are they?" If there are other words that do not have the short /a/ sound, make another list of other words. When the short /a/ word list is correct, ask the students: "Now we are going to read all the short /a/ words we came up with and lets stretch out the /a/ sound in each word."
4.) "Now we are going to practice writing the letter a. Everyone take out your primary paper and pencil. Now everyone follow me as I model how to write the letter a. Don't start at the fence. Start under the fence. Go up and touch the fence, then around and touch the sidewalk, around and straight down. Now everyone practice a row of a's just the way we practiced and when you are down come show me."
5.) "Next we are going to read A Cat Nap with a buddy." Have the class predict what they think the story will be about based on the cover. Afterwards, give a book talk. "Tab the cat likes to take naps but when he woke up from his nap he was somewhere new. You must read the book to find out where Tab was. Now I would like everyone to find a buddy and take turns reading a page aloud to one another. I will walk around and listen to everyone read."
6.) "Now, I am going to pass out one flashcard to everyone. On some cards there are pictures with the short /a/ sound and on some cards there are pictures that do not have the short /a/ sound. I want the people that have the short /a/ words on this side of the room and the people who have the cards with other words on the other side of the room." Pass out the cards and tell the student what the picture is if they do not know. When the students move to their respected side of the room, have each student read what their picture is of and to stress the short /a/ sound in the word.
7.) Have the students return to their seats. "Now class I want everyone to look at their worksheet on their desk. There are two pictures in each box and I want you to circle the picture that has the short /a/ sound in the word. When you are done put the worksheet in the reading basket."
A Cat Nap. Educational Insight.
Adams, Marilyn Jager. Beginning to Read. Center for the Study of Reading, 1990. page 51-71.
(Web page entitled Aaa-aaa-aaa-choo!! By: Paige Parker)
Click here to return to Inspirations
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- Equation SolverFactoring CalculatorDerivative Calculator
A line can be expressed algebraically in several forms. The easiest to learn is called slope-intercept, and is written in the form of y=mx+b. The letters x and y represent the coordinates on the graph, m is the slope, and b is the y-intercept. The slope is the steepness of the line, and the y-intercept is where the line crosses the vertical axis. A slope of 5 is a very steep line, and a slope of 1/5 is almost flat. A y-intercept of 4 means that the line contains the point (0,4), which is on the y-axis. Here is the graph of y=1x+2:
As you can see, the line crosses the y-axis (vertical line) at the point (0,2). You might also notice that for every point that the line moves right, it moves 1 point up, which is a slope of 1. The basic idea of a slope is that the amount you move up is on the top and the amount to move right is on the bottom. A slope of 1/2 means go up 1 and right 2, and a slope of 4 (or 4/1) means go up 4 for every 1 you go right. To understand slopes further, read our lesson on the slope of a line.
The easiest way to graph a line is to first plot the y-intercept. In the equation y=2x + 1, the y-int. is 1, which means that the point (0,1) is part of the line. Next, you should look at the slope. A slope of 3/1 means that you should go up 3 and right 1, giving you another point of (4,1). Connect these two points and continue the line, and you're done!
Another common way of writing lines involves using point-slope form. This way you are given one point and the slope to calculate the others. A line would be given like this in slope-intercept form: y - y1 = m(x - x1)
If you know the point (1,2) is on the line and the slope is 1/2, you can easily write the line as y - 2 = 1/2(x - 1). To graph it, just start at the given point (1,2) and move up 1 and right 2. For more information on this subject you might want to continue browsing our site or perform a search on Google for graphing Lines. There are other lessons on graphing lines available on other websites
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What you need:
stiff cardboard , pencil, scissors, water, a plastic bag, tape
What you do:
1. draw the shape of a magnifying glass on the cardboard.
2. Cut around the outline and then cut out a circle from the middle.
3. Cut a piece of the plastic bag to fit the hole in the middle.
4. Carefully stretch the plastic tightly over the hole and secure it with adhesive.
5. Put a drop of water on to the plastic and hold the lens over a page in a book. You will see that you have made a magnifying glass.
What happened:Water acts as a magnifier for this experiment. A lens can be any clear substance that has a definite shape and will bend light rays as they pass through it. Glass, plastic, and liquids can bend light. This is called refraction. When you look at objects through these materials they look different. A microscope is used for looking at very small objects. It has lenses that are a special shape. A convex lens makes objects look bigger. A concave lens makes objects look smaller.
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An exponent is a number that tells how many times the base number is
used as a factor. For example, 32 indicates that the base number 3
is used as a factor 2 times. To determine the value of 32, multiply
3*3 which would give the result 9.
Squares indicate that the exponent has a value of two. The term square comes
from the geometrical shape that has the same width and length. To find the area
of a square you would multiply the width times the length.
Exponents are written as a superscript number (e.g. 32) or preceded
by the caret (^) symbol (e.g. 3^2).
Some facts about exponents:
- Zero squared is zero (e.g. 02 = 0)
- One squared is one (e.g. 12 = 1)
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Electricity and magnetism
The dot product Introduction to the vector dot product.
The dot product
⇐ 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 learn a little bit about the dot product.
- The dot product, frankly, out of the two ways of multiplying
- vectors, I think is the easier one.
- So what does the dot product do?
- Why don't I give you the definition, and then I'll give
- you an intuition.
- So if I have two vectors; vector a dot vector b-- that's
- how I draw my arrows.
- I can draw my arrows like that.
- That is equal to the magnitude of vector a times the
- magnitude of vector b times cosine of the
- angle between them.
- Now where does this come from?
- This might seem a little arbitrary, but I think with a
- visual explanation, it will make a little bit more sense.
- So let me draw, arbitrarily, these two vectors.
- So that is my vector a-- nice big and fat vector.
- It's good for showing the point.
- And let me draw vector b like that.
- Vector b.
- And then let me draw the cosine, or let me, at least,
- draw the angle between them.
- This is theta.
- So there's two ways of view this.
- Let me label them.
- This is vector a.
- I'm trying to be color consistent.
- This is vector b.
- So there's two ways of viewing this product.
- You could view it as vector a-- because multiplication is
- associative, you could switch the order.
- So this could also be written as, the magnitude of vector a
- times cosine of theta, times-- and I'll do it in color
- appropriate-- vector b.
- And this times, this is the dot product.
- I almost don't have to write it.
- This is just regular multiplication, because these
- are all scalar quantities.
- When you see the dot between vectors, you're talking about
- the vector dot product.
- So if we were to just rearrange this expression this
- way, what does it mean?
- What is a cosine of theta?
- Let me ask you a question.
- If I were to drop a right angle, right here,
- perpendicular to b-- so let's just drop a right angle
- there-- cosine of theta soh-coh-toa so, cah cosine--
- is equal to adjacent of a hypotenuse, right?
- Well, what's the adjacent?
- It's equal to this.
- And the hypotenuse is equal to the magnitude of a, right?
- Let me re-write that.
- So cosine of theta-- and this applies to the a vector.
- Cosine of theta of this angle is equal to ajacent, which
- is-- I don't know what you could call this-- let's call
- this the projection of a onto b.
- It's like if you were to shine a light perpendicular to b--
- if there was a light source here and the light was
- straight down, it would be the shadow of a onto b.
- Or you could almost think of it as the part of a that goes
- in the same direction of b.
- So this projection, they call it-- at least the way I get
- the intuition of what a projection is, I kind of view
- it as a shadow.
- If you had a light source that came up perpendicular, what
- would be the shadow of that vector on to this one?
- So if you think about it, this shadow right here-- you could
- call that, the projection of a onto b.
- Or, I don't know.
- Let's just call it, a sub b.
- And it's the magnitude of it, right?
- It's how much of vector a goes on vector b over-- that's the
- adjacent side-- over the hypotenuse.
- The hypotenuse is just the magnitude of vector a.
- It's just our basic calculus.
- Or another way you could view it, just multiply both sides
- by the magnitude of vector a.
- You get the projection of a onto b, which is just a fancy
- way of saying, this side; the part of a that goes in the
- same direction as b-- is another way to say it-- is
- equal to just multiplying both sides times the magnitude of a
- is equal to the magnitude of a, cosine of theta.
- Which is exactly what we have up here.
- And the definition of the dot product.
- So another way of visualizing the dot product is, you could
- replace this term with the magnitude of the projection of
- a onto b-- which is just this-- times the
- magnitude of b.
- That's interesting.
- All the dot product of two vectors is-- let's just take
- one vector.
- Let's figure out how much of that vector-- what component
- of it's magnitude-- goes in the same direction as the
- other vector, and let's just multiply them.
- And where is that useful?
- Well, think about it.
- What about work?
- When we learned work in physics?
- Work is force times distance.
- But it's not just the total force
- times the total distance.
- It's the force going in the same
- direction as the distance.
- You should review the physics playlist if you're watching
- this within the calculus playlist. Let's say I have a
- 10 newton object.
- It's sitting on ice, so there's no friction.
- We don't want to worry about fiction right now.
- And let's say I pull on it.
- Let's say my force vector-- This is my force vector.
- Let's say my force vector is 100 newtons.
- I'm making the numbers up.
- 100 newtons.
- And Let's say I slide it to the right, so my distance
- vector is 10 meters parallel to the ground.
- And the angle between them is equal to 60 degrees, which is
- the same thing is pi over 3.
- We'll stick to degrees.
- It's a little bit more intuitive.
- It's 60 degrees.
- This distance right here is 10 meters.
- So my question is, by pulling on this rope, or whatever, at
- the 60 degree angle, with a force of 100 newtons, and
- pulling this block to the right for 10 meters, how much
- work am I doing?
- Well, work is force times the distance, but not just the
- total force.
- The magnitude of the force in the direction of the distance.
- So what's the magnitude of the force in the
- direction of the distance?
- It would be the horizontal component of this force
- vector, right?
- So it would be 100 newtons times the
- cosine of 60 degrees.
- It will tell you how much of that 100
- newtons goes to the right.
- Or another way you could view it if this
- is the force vector.
- And this down here is the distance vector.
- You could say that the total work you performed is equal to
- the force vector dot the distance vector, using the dot
- product-- taking the dot product, to the force and the
- distance factor.
- And we know that the definition is the magnitude of
- the force vector, which is 100 newtons, times the magnitude
- of the distance vector, which is 10 meters, times the cosine
- of the angle between them.
- Cosine of the angle is 60 degrees.
- So that's equal to 1,000 newton meters
- times cosine of 60.
- Cosine of 60 is what?
- It's square root of 3 over 2.
- Square root of 3 over 2, if I remember correctly.
- So times the square root of 3 over 2.
- So the 2 becomes 500.
- So it becomes 500 square roots of 3 joules, whatever that is.
- I don't know 700 something, I'm guessing.
- Maybe it's 800 something.
- I'm not quite sure.
- But the important thing to realize is that the dot
- product is useful.
- It applies to work.
- It actually calculates what component of what vector goes
- in the other direction.
- Now you could interpret it the other way.
- You could say this is the magnitude of a
- times b cosine of theta.
- And that's completely valid.
- And what's b cosine of theta?
- Well, if you took b cosine of theta, and you could work this
- out as an exercise for yourself, that's the amount of
- the magnitude of the b vector that's
- going in the a direction.
- So it doesn't matter what order you go.
- So when you take the cross product, it matters whether
- you do a cross b, or b cross a.
- But when you're doing the dot product, it doesn't matter
- what order.
- So b cosine theta would be the magnitude of vector b that
- goes in the direction of a.
- So if you were to draw a perpendicular line here, b
- cosine theta would be this vector.
- That would be b cosine theta.
- The magnitude of b cosine theta.
- So you could say how much of vector b goes in the same
- direction as a?
- Then multiply the two magnitudes.
- Or you could say how much of vector a goes in the same
- direction is vector b?
- And then multiply the two magnitudes.
- And now, this is, I think, a good time to just make sure
- you understand the difference between the dot product and
- the cross product.
- The dot product ends up with just a number.
- You multiply two vectors and all you have is a number.
- You end up with just a scalar quantity.
- And why is that interesting?
- Well, it tells you how much do these-- you could almost say--
- these vectors reinforce each other.
- Because you're taking the parts of their magnitudes that
- go in the same direction and multiplying them.
- The cross product is actually almost the opposite.
- You're taking their orthogonal components, right?
- The difference was, this was a a sine of theta.
- I don't want to mess you up this picture too much.
- But you should review the cross product videos.
- And I'll do another video where I actually compare and
- contrast them.
- But the cross product is, you're saying, let's multiply
- the magnitudes of the vectors that are perpendicular to each
- other, that aren't going in the same direction, that are
- actually orthogonal to each other.
- And then, you have to pick a direction since you're not
- saying, well, the same direction that
- they're both going in.
- So you're picking the direction that's orthogonal to
- both vectors.
- And then, that's why the orientation matters and you
- have to take the right hand rule, because there's actually
- two vectors that are perpendicular to any other two
- vectors in three dimensions.
- Anyway, I'm all out of time.
- I'll continue this, hopefully not too confusing, discussion
- in the next video.
- I'll compare and contrast the cross
- product and the dot product.
- 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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about the site
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PatrickHaller/fineweb-edu-plus
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Here's a sort of code you may have seen before.
If you exchanged each letter of your name for a number, what would the code be?
Mine is Lynne so my code is 1 4 1 1 1 . The numbers add up to 8 which is not much!!
What is your name worth using this code?
Try some other names - what names are worth the most and which are worth the least?
Are longer names always worth more?
Can you work out why certain letters are worth a lot and why others are only worth one?
Some children may recognise that the 'code' is based on the values of the Scrabble tiles. Those values are based on the frequency of letters in written English and so this activity is a gentle introduction into the sort of data analysis which underpins much code breaking.
If this is your first code-related acivity you may wish to use the task 'What's in a name?' first.
Display the table or show this Powerpoint slide. Ask the children to write down their own name and work out what letters would represent it using the code. What do they notice?
Draw up an alphabet table on the board, and tell the children you are going to collate the letters from each child's name (using a five bar gate, or whatever way of recording is familiar to the children). Ask the children to predict what they think will happen.
Once complete, compare their predictions with the actual table. Unless you have a lot of non-English names in your class, the frequency distribution is likely to mirror the Scrabble table.
If they haven't already spotted it, make connections to Scrabble and how the Scrabble values were derived. If you have a Scrabble set in the classroom, children could check that the table is correct.
Ask the children to add up the numbers in their names: whose name is worth the most/least?
Can they work out a short, high value name?
What about a long, low value name?
Let the children explore other sorts of words - can they make some short, high value words and some long, low value ones?
Which letters do you think will have the highest frequency?
Are long words always worth more than short ones? Why or why not?
If you have some Scrabble tiles they can be used to support children who need to manipulate the letters. You can download a set of blank alphabet tiles for children to make their own Scrabble set.
Use some of the texts familar to the children and ask them to analyse a short section to see if the frequencies are the same.
Here are some translations of the same text into other languages ( courtesy of Google Translate). How do these frequency tables compare?
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PatrickHaller/fineweb-edu-plus
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How to find the slope of f(x) times g(x) ? Use the Product Rule.
The slope of f(x)g(x) has two terms:
f(x) times (slope of g(x)) PLUS g(x) times (slope of f(x))
The Quotient Rule gives the slope of f(x) / g(x) . That slope is
[[ g(x) times (slope of f(x)) MINUS f(x) times (slope of g(x)) ]] / g squared
These rules plus the CHAIN RULE will take you a long way.
Professor Strang's Calculus textbook (1st edition, 1991) is freely available here.
Subtitles are provided through the generous assistance of Jimmy Ren.
Lecture summary and Practice problems (PDF)
PROFESSOR: OK. This video is about derivatives. Two rules for finding new derivatives. If we know the derivative of a function f-- say we've found that-- and we know the derivative of g-- we've found that-- then there are functions that we can build out of those. And two important and straightforward ones are the product, f of x times g of x, and the quotient, the ratio f of x over g of x. So those are the two rules we need.
If we know df dx and we know dg dx, what's the derivative of the product? Well, it is not df dx times dg dx. And let me reduce the suspense by writing down what it is. It's the first one times the derivative of the second, we know that, plus another term, the second one times the derivative of the first. OK. So that's the rule to learn. Two terms, you see the pattern. And maybe I ought to use it, give you some examples, see what it's good for, and also some idea of where it comes from. And then go on to the quotient rule, which is a little messier.
OK. So let me just start by using this in some examples. Right underneath, here. OK. So let me take, as a first example, f of x equals x squared and g of x equals x. So then what is p of x? It's x squared times x. I'm multiplying the functions. So I've got x cubed, and I want to know its derivative. And I know the derivatives of these guys.
OK, so what does the rule tell me? It tells me that the derivative of p, dp dx-- so p is x cubed. So I'm looking for the derivative of x cubed. And if you know that, it's OK. Let's just see it come out here. So the derivative of x cubed, by my formula there, is the first one, x squared, times the derivative of the second, which is 1, plus the second one, x, times the derivative of the first, which is 2x. So what do we get? x squared, two more x squared, 3x squared. The derivative of x cubed is 3x squared. x cubed goes up faster than x squared, and this is a steeper slope.
Oh, let's do x to the fourth. So x to the fourth-- now I'll take f to be x cubed, times x. Because x cubed, I just found. x, its derivative is 1, so I can do the derivative of x fourth the same way. It'll be f. So practicing that formula again with x cubed and x, it's x cubed times 1 plus this guy times the derivative of f. Right? I'm always going back to that formula. So the derivative of f, x cubed, we just found-- 3x squared-- so I'll put it in. And what do we have? x cubed here, three more x cubeds here. That's a total of 4x cubed.
OK. We got another one. Big deal. What is important is-- and it's really what math is about-- is the pattern, which we can probably guess from those two examples and the one we already knew, that the derivative of x squared was 2x. So everybody sees a 2 here and a 3 here and a 4 here, coming from 2, 3, and 4 there. And everybody also sees that the power dropped by one. The derivative of x squared was an x. The derivative of x cubed involved an x squared.
Well, let's express this pattern in algebra. It's looking like the derivative of x to the n-- we hope for any n. We've got it for n equals 2, 3, 4, probably 0 and 1. And if the pattern continues, what do we think? This 4, this n shows up there, and the power drops by 1. So that'll be x to the n minus 1, the same power minus 1, one power below. So that's a highly important formula.
And actually it's important to know it, not-- right now, well, we've done two or three examples. I guess the right way for me to get this for n equals-- so we really could check 1, 2, 3, and so on. All the positive integers. We could complete the proof. We could establish the pattern. Actually, induction would be one way to do it. If we know it for, as we did here, for n equals 3, then we've got it for 4. If we know it for 4, the same product formula would get it for 5 and onwards, and would give us that answer. Good.
Even better is the fact that this formula is also true if n is a fraction. If we're doing the square root of x, you recognize the square root of x is x to the-- what's the exponent there for square root? 1/2. So I would like to know for 1/2. OK, let me take a couple of steps to get to that one.
All right. The steps I'm going to take are going to look just like this, but this was powers of x, and it'll be very handy if I can do powers of f of x. I'd like to know-- I want to find-- So here's what I'm headed for. I'd like to know the derivative of f of x to the n-th power equals what? That's what I'd like to know.
So let me do f of x. Let me do it just as I did before. Take n equals 2, f of x squared. So what's the derivative of f of x squared, like sine squared or whatever we're squaring. Cosine squared. Well, for f of x squared, all I'm doing is I'm taking f to be the same as g. I'll use the product rule. If g and f are the same, then I've got something squared. And my product rule says that the derivative-- and I just copy this rule.
Now I'm taking p is going to be f squared, right? Can I just write f squared equals-- so it's f times-- f is the same as g. Are you with me? I'm just using the rule in a very special case when the two functions are the same. The derivative of f squared is f. What do I have? f times the derivative of f, df dx. That's the first term. And then what's the second term? Notice I wrote f instead of g, because they're the same. And the second term is, again, a copy of that. So I have 2 of these. Times 2, just the way I had a 2 up there. This was the case of x squared. This is the case of f of x squared.
Let me go one more step to f cubed. What am I going to do for f cubed? The derivative of-- hold on. I have to show you what to pay attention to here. To pay attention to is-- the 2 we're familiar with. This would have been the x, that's not a big deal. But there's something new. A df dx factor is coming in. It's going to stay with us. Let me see it here. The derivative of f of x cubed. Now let's practice with this one.
OK. So now what am I going to take? How do I get f of x cubed? Well, I've got f, so I'd better take g to be f squared. Then when I multiply, I've got cubed. So g is now going to be f squared for this case. Can I take my product rule with f times f squared? My product rule of f times f squared is-- I'm doing this now with g equals f squared, just the way I did it over there at some point with one of them as a square. OK. I'm near the end of this calculation.
OK. So what do I have. If this thing is cubed, I have f times f squared. That's f cubed. And I take its derivative by the rule. So I take f times the derivative of f squared, which I just figured out as 2f df dx. That's the f dg dx. And now I have g, which is f squared, times df dx.
What are you seeing there? You're seeing-- well, again, these combine. That's what's nice about this example. Here I have one f squared df dx, and here I have two more. That's, all together, three. So the total was 3 times f squared times df dx. And let me write down what that pattern is saying. Here it will be n. Because here it was a 2. Here it's going to be 2 plus 1-- that's 3. And now if I have the n-th power, I'm expecting an n times the next lower power of f, f to the n minus 1, times what? Times this guy that's hanging around, df dx. That's my-- you could call that the power rule. The derivative of a power. This would be the power rule for just x to the n-th, and this is the derivative of a function of x to the n-th.
There's something special here that we're going to see more of. This will be, also, an example of what's coming as maybe the most important rule, the chain rule. And typical of it is that when I take this derivative, I follow that same pattern-- n, this thing, to one lower power, but then the derivative of what's inside. Can I use those words? Because I'll use it again for the chain rule. n times one lower power, times the derivative of what's inside.
And why do I want to do such a thing? Because I'd like to find out the derivative of the square root of x. OK. Can we do that? I want to use this, now. So I want to use this to find the derivative of the square root of x. OK. So that will be my function. f of x will be the square root of x. So this is a good example. That's x to the 1/2 power. What would I love to have happen? I would like this formula to continue with n equals 1/2, but no change in the formula. And that does happen.
How can I do that? OK, well, square root of x is what I'm tackling. The easy thing would be, if I square that, I'll get x, right? The square of the square root. Well, square root of x squared-- so there's f of x. I'm just going to use the fact that the square root of x squared is x. Such is mathematics. You can write down really straightforward ideas, but it had to come from somewhere.
And now what am I going to do? I'm going to take the derivative. Well, the derivative on the right side is a 1. The derivative of x is 1. What is the derivative of that left-hand side? Well, that fits my pattern. You see, here is my f of x, squared. And I had a little formula for the derivative of f of x squared. So the derivative of this is 2 times the thing to one lower power-- square root of x just to the first power-- times the derivative of what's inside, if you allow me to use those words. It's this, df dx. And that's of course what I actually wanted, the square root of x, dx.
This lecture is not going to have too many more calculations, but this is a good one to see. That's clear. I take the derivative of both sides. That's clear. This is the 2 square root of x. And now I've got what I want, as soon as I move these over to the other side. So I divide by that. Can I now just do that with an eraser, or maybe just X it out, and put it here. 1 over 2 square root of x. Am I seeing what I want for the derivative of square root of x? I hope so. I'm certainly seeing the 1/2. So the 1/2-- that's the n. It's supposed to show up here. And then what do I look for here? One lower power than 1/2, which will be x to the minus 1/2.
And is that what I have? Yes. You see the 1/2. And that square root of x, that's x to the 1/2, but it's down in the denominator. And things in the denominator-- the exponent for those, there's a minus sign. We'll come back to that. That's a crucial fact, going back to algebra. But, you know, calculus is now using all that-- I won't say stuff. All those good things that we learned in algebra, like exponents. So that was a good example.
OK. So my pattern held for n equals 1/2. And maybe I'll just say that it also would hold for cube roots, and any root, and other powers. In other words, I get this formula. This is the handy formula that we're trying to get. We got it very directly for positive whole numbers. Now I'm getting it for n equals 1 over any-- now I'm getting it for capital Nth roots, like 1/2. Then I could go on to get it for-- I could take then the n-th power of the n-th root. I could even stretch this to get up to m over n. Any fraction, I can get to. But I can't get to negative exponents yet, because those are divisions. Negative exponent is a division, and I'm going to need the quotient rule, which is right now still a big blank.
OK. Pause for a moment. We've used the product rule. I haven't explained it, though. Let me, so, explain the product rule. Where did it come from? I'm going back before the examples, and before that board full of chalk, back to that formula and just think, where did it come from? How did we find the derivative of f times g, of the product p? So we needed delta p, right? And then I'm going to divide by delta x. OK. So let me try to make-- what's the delta p when p is-- remember, p is f times g.
Thinking about f times g, maybe let's make it visual. Let's make it like a rectangle, where this side is f of x and this side is g of x. Then this area is f times g, right? The area of a rectangle. And that's our p. OK, that's sitting there at x. Now move it a little. Move x a little bit. Move x a little and figure out, how much does p change? That's our goal. We need the change in p.
If I move x by a little bit, then f changes a little, by a little amount, delta f, right? And g changes a little, by a little amount, delta g. You remember those deltas? So it's the change in f. There's a delta x in here. x is the starting point. It's the thing we move a little. When we move x a little, by delta x, f will move a little, g will move a little, and their product will move a little. And now, can you see, in the picture, where is the product? Well, this is where f moved to. This is where g moved to. The product is this, that bigger area.
So where is delta p? Where is the change between the bigger area and the smaller area? It's this. I have to figure out, what's that new area? The delta p is in here. OK, can you see what that area-- well, look, here's the way to do it. Cut it up into little three pieces. Because now they're little rectangles, and we know the area of rectangles. Right?
So help me out here. What is the area of that rectangle? Well, its base is f, and its height is delta g. So that is f times delta g. What about this one? That has height g and base delta f. So here I'm seeing a g times delta f, for that area. And what about this little corner piece? Well, its height is just delta g, its width is delta f. This is delta g times delta f. And it's going to disappear. This is like a perfect place to recognize that an expression-- that's sort of like second order. Let me use words without trying to pin them down perfectly.
Here is a zero-order, an f, a real number, times a small delta g. So that's first order. That's going to show up-- you'll see it disappear. These three pieces, remember, were the delta p. So what have I got here? I've got this piece, f delta g, and I'm always dividing by delta x. And then I have this piece, which is the g times the delta f, and I divide by the delta x. And then this piece that I'm claiming I don't have to worry much about, because I divide that by delta x. So that was the third piece.
This is it, now. The picture has led to the algebra, the formula for delta p, the change in the product divided by delta x. That's what calculus says-- OK, look at that, and then take the tricky step, the calculus step, which is let delta x get smaller and smaller and smaller, approaching 0. So what do those three terms do as delta x gets smaller?
Well, all the deltas get smaller. So what happens to this term as delta x goes to 0? As the change in x is just tiny, tiny, tiny? That term is the one that gives the delta g over delta x, in the limit when delta x goes to 0, is that one, right? And this guy is giving my g. That ratio is familiar, df dx. You see, the cool thing about splitting it into these pieces was that we got this piece by itself, which was just the f delta g. And we know what that does. It goes here. And this piece-- we know what that does.
And now, what about this dumb piece? Well, as delta x goes to 0, this would go to df dx, all right. But what would delta g do? It'll go to 0. You see, we have two little things divided by only one little thing. This ratio is sensible, it gives df dx, but this ratio is going to 0. So forget it. And now the two pieces that we have are the two pieces of the product rule. OK. Product rule sort of visually makes sense.
OK. I'm ready to go to the quotient rule. OK, so how am I going to deal, now, with a ratio of f divided by g? OK. Let's put that on a fourth board. How to deal then with the ratio of f over g.
Well, what I know is the product rule, right? So let me multiply both sides by g of x and get a product. There, that looks better. Of course the part that I don't know is in here, but just fire away. Take the derivative of both sides. OK. The derivative of the left side is df dx, of course. Now I can use the product rule. It's g of x, dq dx. That's the very, very thing I'm wanting. dq dx-- that's my big empty space. That's going to be the quotient rule.
And then the second one is q of x times dg dx. That's the product rule applied to this. Now I have it. I've got dq dx. Well, I've got to get it by itself. I want to get dq dx by itself. So I'm going to move this part over there. Let me, even, multiply both sides-- this q, of course, I recognize as f times g. This is f of x times g of x. That's what q was. Now I'm going to-- oh, was not. It was f of x over g of x. Good Lord. You would never have allowed me to go on.
OK. Good. This is came from the product rule, and now my final job is just to isolate dq dx and see what I've got. What I'll have will be the quotient rule. One good way is if I multiply both sides by g. So I multiply everything by g, so here's a g, df dx. And now this guy I'm going to bring over to the other side. When I multiply that by g, that just knocks that out. When I bring it over, it comes over with a minus sign, f dg dx. And this one got multiplied by g, so right now I'm looking at g squared, dq dx. The guy I want.
Again, just algebra. Moving stuff from one side to the other produced the minus sign. Multiplying by g, you see what happened. So what do I now finally do? I'm ready to write this formula in. I've got it there. I've got dq dx, just as soon as I divide both sides by g squared. So let me write that left-hand side. g df dx minus f dg dx, and I have to divide everything-- this g squared has got to come down here. It's a little bit messier formula but you get used to it. g squared. That's the quotient rule.
Can I say it in words? Because I actually say those words to myself every time I use it. So here are the words I say, because that's a kind of messy-looking expression. But if you just think about words-- so for me, remember we're dealing with f over g. f is the top, g at the bottom. So I say to myself, the bottom times the derivative of the top minus the top times the derivative of the bottom, divided by the bottom squared. That wasn't brilliant, but anyway, I remember it that way.
OK. so now, finally, I'm ready to go further with this pattern. I still like that pattern. We've got the quotient rule, so the two rules are now set, and I want to do one last example before stopping. And that example is going to be a quotient, of course. And it might as well be a negative power of x. So now my example-- last example for today-- my quotient is going to be 1. The f of x will be 1 and the g of x-- so this is my f. This is my g. I have a ratio of two things.
And as I've said, this is x to the minus n. Right? That's what we mean. We can think again about exponents. A negative exponent becomes positive when it's in the denominator. And we want it in the denominator so we can use this crazy quotient rule.
All right. So let me think through the quotient rule. So the derivative of this ratio, which is x to the minus n That's the q, is 1 over x to the n. The derivative is-- OK, ready for the quotient rule? Bottom times the derivative of the top-- ah, but the top's just a constant, so its derivative is 0-- minus-- remembering that minus-- the top times the derivative of the bottom.
Ha. Now we have a chance to use our pattern with a plus exponent. The derivative of the bottom is nx to the n minus 1. So it's two terms, again, but with a minus sign. And then the other thing I must remember is, divide by g squared, x to the n twice squared.
OK. That's it. Of course, I'm going to simplify it, and then I'm done. So this is 0. Gone. This is minus n, which I like. I like to see minus n come down. That's my pattern, that this exponent should come down. Minus n, and then I want to see-- oh, what else do I have here? What's the power of x? Well, here I have an x to the n-th. And here I have, twice, so can I cancel this one and just keep this one?
So I still have an x to the minus 1. I don't let him go. Actually the pattern's here. The answer is minus n minus capital N, which was the exponent, times x to one smaller power. This is x to the minus n, and then there's another x to the minus 1. The final result was that the derivative is minus nx to the minus n, minus 1. And that's the good pattern that matches here. When little n matches minus big N, that pattern is the same as that. So we now have the derivatives of powers of x as an example from the quotient rule and the product rule.
Well, I just have to say one thing. We haven't got-- We've fractions, we've got negative numbers, but we don't have a whole lot of other numbers, like pi. We don't know what is, for example, the derivative of x to the pi. Because pi isn't-- pi is positive, so we're OK in the product rule, but it's not a fraction and we haven't got it yet. What do you think it is? You're right-- it is pi x to the pi minus 1. Well, actually I never met x to the pi in my life, until just there, but I've certainly met all kinds of powers of x and this is just one more example.
OK. So that's quotient rule-- first came product rule, power rule, and then quotient rule, leading to this calculation. Now, the quotient rule I can use for other things, like sine x over cosine x. We're far along, and one more big rule will be the chain rule. OK, that's for another time. Thank you.
[NARRATOR:] This has been a production of MIT OpenCourseWare and Gilbert Strang. Funding for this video was provided by the Lord Foundation. To help OCW continue to provide free and open access to MIT courses, please make a donation at ocw.mit.edu/donate.
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To learn to read and spell words children must learn phonemes and letter correspondences. Sometimes a phoneme is represented by two letters that go together to make one sound such as /sh/. This is called a diagraph and is very common in the English language. The following lesson will help children practice learning the /sh/ sound when they see s and h together in print.
Elkin Letterboxes, letters: s, h, o, p, i, f, d, c, r, b, u, p, s, One Fish, Two Fish, Red Fish, Blue Fish by Dr. Suess, picture page
1. Introduce the lesson by explaining how some letters are placed together to make one sound. To read we must be able to tell when a sound is being made by two letters such as /sh/.
2. How many children have been told by their parents. "SSSSHHH! You are being too loud!" Me too. Now lets be the parents and make the /sh/ sound together by pushing air out our mouth with our teeth together.
3. We will practice with a tongue twister: Shelly showed Shane shells she found on the shore. Say it with me this time. Wonderful! Now say it one more time stretching out the /sh/ sound. SSSHHHelly ssshhhowed SSSHHHane ssshhhells ssshhhe found on the ssshhhore.
4. Letterbox lesson: Pass out the letters and have the students turn the letters to lower case side. Take tape and connect the s and h to make /sh/. Review and ask, "Does anyone remember what sound this makes?" ( /sh/ Excellent!) Now I will demonstrate with the word ship (sh 1st box, i 2nd box, p 3rd box)
5. Have students spell out shop, fish, and dish. Open another box for crash and brush, and as a final challenge open one more for splash.
6. On the board spell out words and have the students read aloud .
7. In groups read One Fish, Two Fish, Red Fish, Blue Fish by Dr. Suess. Have them go back and point out all /sh/ words.
8. For assessment have students circle and write the name of pictures containing /sh/ from a picture sheet. The worksheet will be corrected aloud when everyone is finished.
Reference: Reading Genie www.auburn.edu/rdggenie www.auburn.edu/rdggenie/illum/jonesbr.html
Murray, B.A. & Lesniak, T (1999). The Letterbox Lesson. The Reading Teacher, 53,644-650.
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One of the things which children find quite hard to do is to set out a question in the best format. In the Key Stage 2 tests addition problems are rarely, if ever, set out in the standard form that children learn.
This page tries to help with the addition of two 3-digit numbers. The first 10 questions are set out in the standard way, but the next ten are written across the page. When faced with questions like this it is important to re-write the sum to have the best chance of success. Of course, it is important to keep the numbers in line (units under units, tens under tens etc) and squares have been provided to help with this.
A very useful page for those who are still uncertain about how to approach these questions.
- Free Year 5 Maths Worksheets
- © 2009 Maths Blog
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Lesson 3 Section 2
HOW TO NAME OR READ A DECIMAL
Ignore the decimal point and read 038 as the whole number "Thirty-eight." The last digit, 8, falls in the thousandths place.
When we read .038 as "Point 0, 3, 8," that is "spelling" the number, which is often convenient. But its name is "Thirty-eight thousandths."
Ignore the decimal point, and read 002135 as the whole number 2,135 ("Two thousand one hundred thirty-five" Lesson 2, Question 4). The last digit 5 is in the millionths place.
This is called a mixed number. The decimal point separates the whole number 14 on the left, from the decimal fraction on the right. In a mixed number, we read the decimal point as "and."
Example 4. Write these in numerals:
a) Two hundred four thousand
b) Two hundred four thousandths
c) Two hundred and four thousandths
Example 5. Write in words: $607.08
Answer. Six hundred seven dollars and eight cents.
Save "and" for the decimal point.
Note that cents means hundredths. (Centum in Latin means 100.) 1 cent is the hundredth part of one dollar. We write 1 cent either as
$.01 or 1¢.
When we write the cent sign ¢, we do not write a decimal point.
Example 6. Write "eighty cents" using the dollar sign $ and using the cent sign ¢.
Answer. $.80 80¢
At this point, please "turn" the page and do some Problems.
Continue on to the next Section.
Please make a donation to keep TheMathPage online.
Copyright © 2012 Lawrence Spector
Questions or comments?
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- Begin with a topic the learners are interested in.
- Talk over what they want to write. Help the learner write ideas or words they may need.
- Write a rough draft. Explain to the learners that all writers use a rough draft.
- Encourage learners to proofread their work. Underline words they are not sure of. This is a good time to practice dictionary skills.
- Read over the piece of writing together. A piece of writing can always be changed, or you can add more information.
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Tests are a way for you and your teacher to measure how well you have learned the material covered by the class. Think of them as a challenge! Here are some tips for studying for tests.
- Be sure to find out ahead of time.
Study in a place that is free of distractions. Have ready all the things you will need, such as paper, pens, or a calculator.
Study at a time when you are alert and not hungry or sleepy.
Don't wait until the last minute to study! Short daily study sessions are better than one long session the night before the test.
Set a goal for each study period. If you are being tested on three chapters, set up four study sessions, one for each chapter and one for a review of the main ideas in all three chapters.
Repetition is key! Read and reread your class notes and the relevant chapters in the textbook.
While you are reviewing your notes, cover them up periodically and summarize them out loud. Pretend that you are explaining the material to someone else.
Create your own study aids.
- what material the test will cover
- what type of test it will be (multiple choice, true false, short answer, essay)
- how the test will be graded
- how much the test will count toward the final grade
Do any practice exams or study sheets provided by the teacher. These will help you focus your study session and give you confidence.
Get help from the teacher if you do not understand something.
- Make an outline from your notes of just the main ideas.
- Make a timeline of important dates or the order of events.
- Make flashcards for studying vocabulary or events and important dates.
- Make up your own quiz or test based on your notes and have a friend, parent or sibling test you.
Experts say that studying in a group can be more effective than studying alone. Students say it can be more fun, too! Here are a few tips for organizing a study group.
- It often works best to have just three to five people in a study group. That way, each person gets the time to talk and make sure she understands the material.
- Schedule a few study sessions. Whether studying alone or in a group, a few short sessions are much more useful than one long "cram" session.
- Having one person act as the leader can help a group to run smoothly. The main goal of the leader is to keep everyone focused on studying so that things don't become too social.
- Be prepared! A study group is a place to share your understanding of a subject. The other people in the group aren't there to teach you facts you should already know. The more you can offer the group, the more you'll get out of it.
Sticking to an agenda is important. Here's one plan for organizing your group time.
- First, compare your notes and review old homework. If there is something you have had trouble understanding, write down your questions about it before meeting with your study group.
- Next, drill each other on facts you need to memorize. For example, What are the four stages of a butterfly's life cycle? You might want to give each other practice quizzes.
- Lastly, take the time to discuss "why" questions. For example, Why do monarch butterflies migrate?
One way to handle "Why" questions is to make a list of the important ones you will want to review. Then divide the questions among the group. At your next meeting, have each person present a lesson about her questions.
- Read the instructions carefully. Never assume you will know what they will say! Ask the teacher if you are unsure about anything.
- Read the entire test through before starting. Notice the point value of each section. This will help you to pace yourself.
- Answer the easiest questions first, then the ones with the highest point value. You don't want to spend 20 minutes trying to figure out a two-point problem!
- Keep busy! If you get stuck on a question, come back to it later. The answer might come to you while you are working on another part of the test.
- If you aren't sure how to answer a question fully, try to answer at least part of it. You might get partial credit.
- Need to guess on a multiple-choice test? First, eliminate the answers that you know are wrong. Then take a guess. Because your first guess is most likely to be correct, you shouldn't go back and change an answer later unless you are certain you were wrong.
- On an essay test, take a moment to plan your writing. First, jot down the important points you want to make. Then number these points in the order you will cover them.
- Keep it neat! If your teacher can't read your writing, you might lose points.
- Don't waste time doing things for which you will not receive credit, such as rewriting test questions.
- Leave time at the end to look over your work. Did you answer every question? Did you proofread for errors? It is easy to make careless mistakes while taking a test.
- When the test is returned, read the teacher's comments carefully and try to learn from your mistakes.
- Save tests for later review for end-of-term tests.
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Who Wants Ice Cream?
By: Melinda Hardin
Rationale: For children to become skilled readers they must understand that correspondences appear differently in different words. Also children need to know the difference between long and short vowels. The have to understand that these correspondences are spelled and pronounced differently. In this lesson we will review the i=/i/ correspondence and introduce the correspondence i_e=/I/. The students will be introduced to the correspondence through spelling words with letterboxes and later reading them. Also to better chk their understanding of the new correspondence we will have them read pseudo words.
White board and marker
Picture of ice cream, with i_e in it
Sign with "Ivy's ice cream is icy" with another ice cream picture
Teacher letterbox and letters
Letterboxes for each student
Letters for each students: b, c, d, e, f, g, i, k, l, m, n, p, r, s, t, w
Individual copies for each student of the book Di and the Mice (Phonics Readers Long Vowels, Book 6 -- Long i). Publisher: Educational Insights (1990)
Note cards with pseudo words (such words can include: pim, fime, scrime, rin, tine)
1.Now that we have already learned all of our short vowels, we are going to move on to long vowels. To begin introduce the lesson by reviewing i=/i/. Can everyone remember what I says when it's all by itself in a word? "Icky Sticky"?. Since we know that when we see I alone in a word it says /i/. Today we are going to find out what sound we make when there is an i, a consonant, and then an e at the end of the word. (Write i_e on the board). When we see i_e in a word, the i says its name /I/ and the e is silent. Okay now we need to look at our Ice Cream poster. Whoever likes ice cream raise their hand. Great! So whenever we see i_e in our reading, we are going to say /I/ and lick our Ice Cream cones. Now let's all try it, /I/.
2.Now we are going to say this tongue twister together. ) Make sure the students can see the poster) "Ivy's ice cream is icy." Who can hear the /I/ in our tongue twister? Good. Every time we hear the /I/ in our tongue twister we are going to get our ice cream cones and act like we are licking them. Let's try: "IIIIIIIIvy'sIIIIIce cream is IIIIcy." Great job!
3.Everyone look at this word on the board. (Write the word pine on the board) Who can come up here and underline the i_e in this word? (Have one of the students come up to the board and underline the i and e). Whenever we see the i_e we need to remember that is a signal that the i is going to say its name. First let's look at the i_e, which says /I/. Add the beginning /p/ /I/ and then add the /n/‰¥Ï /p/ /I/ /n/. Pine. When we say all of these together what word do you say? Always remember that the e on the end let's us know the i says /I/. It is important to know the difference in how short I and long I are spelled.
4.Before moving on make sure they understand by asking questions. Now we are going to listen for the /I/ in some words and whenever you hear /I/ I want you to lick your ice cream cone. (Say the following slowly) Miley likes to ride her bike in limes. Scan the classroom as you say the sentence to make sure the students understand.
5.Next we are going to get out our letterboxes ad practice spelling some words. The words will consist of 3, 4, and 5 phoneme words. Each student will have out their letterboxes and then give them the letters needed. Use the teacher set of letterboxes and letters to model for the students. I will model the first word for you. If we are using 3 letterboxes, how man phonemes is our first word going to have? Three is right! Since the e signals that the i says its name, it is silent and goes on the outside of the third box. The first word I will spell is bike. I want to ride my bike. Bike. /b/, b is going in the first box. /I/, i is going in the second box and I know the e is going on the outside of the third box. /b/ I/ /k/, so k is going to go in my third box.
6.Now we are going to spell come more words with our letterboxes. We will start off with 3 boxes. Have the students spell: tip, mike, tin, fine.
7.Excellent! Now we are going to use 4 boxes, which means our words will have 4 phonemes. Have students spell: slice, bride, trip, gripe, slime, spin. Now add one more box and we will spell words with 5 phonemes. These are a little harder but y'all are great spellers so do not worry. Have students spell: twist, strike, sprite
8.Then model to the students how to read each of the words without the letterboxes. I will show you how to read this word (point to a word that you rewrite on the board). First I see the i_e so I know the i says its name. /b/ /I/ /k/. Bike. Now it is your turn to read the words. Then have the students read the words you just previously spelled.
9.Then pass out the copies of Di and the Mice. Who likes to ride bikes? Well guess what so does Di! One day Di is riding her bike until she stops to eat for a little bit, and she sees something white in the vines! What do y'all think is in the vines? Do you think Di will be scared? What do you think Di will do? Well to find out you'll have to read with your partner. Have the students pair up and help each other read the words and use the different decoding strategies they know.
10.After they are done reading have them write a message about riding their own bike. If the students do not have a bike have them tell why they do or do not.
11.Finally for assessment have each of the students come to your desk and have them read words on the note cards you prepared earlier with pseudo words on them. This will let you see whether or not each student understands the i_e correspondence.
Rebecca Neilson, "I scream for Ice cream"
to the passages index.
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Grammar Index : 2
A and B are talking to each other.
We use reciprocal pronoun when each of two or more subjects is acting in the same way towards the other.
For example :
A is talking to B.
B is talking to A.
So we say :
The action is reciprocated.
John talks to Mary and Mary talks to John.
I give you a present and you give me a present.
The dog bites the cat and the cat bites the dog.
There are only two reciprocal pronouns and they are both two words.
When we use these reciprocal pronouns :
There must be two or more people, things or groups involved (so we cannot use reciprocal pronouns with I, you [singular], he/she/it).
They must be doing the same thing.
The children can help each other in doing the home work.
Victor and Laurie were sitting next to each other.
They gave all evidence against each other.
The two of them sat facing one another.
From Reciprocal Pronoun to HOME PAGE
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How to Divide Numbers on the Number Line
You can use the number line to divide. For example, suppose you want to divide 6 by some other number. First, draw a number line that begins at 0 and ends at 6, as in the following figure.
Now, to find the answer to 6 ÷ 2, just split this number line into two equal parts, as shown in the following figure. This split (or division) occurs at 3, showing you that 6 ÷ 2 = 3.
Similarly, to divide 6 by 3, split the same number line into three equal parts, as in the following figure. This time you have two splits, so use the one closest to 0. This number line shows you that 6 ÷ 3 = 2.
But suppose you want to use the number line to divide a small number by a larger number. For example, maybe you want to know the answer to 3 ÷ 4. First draw a number line from 0 to 3. Then split it into four equal parts. Unfortunately, none of these splits has landed on a number. That’s not a mistake. You just have to add some new numbers to the number line, as you can see in the following figure.
Welcome to the world of fractions. With the number line labeled properly, you can see that the split closest to 0 is 3/4. This image tells you that 3 ÷ 4 = 3/4.
The similarity of the expression 3 ÷ 4 and the fraction 3/4 is no accident. Division and fractions are closely related. When you divide, you cut things up into equal parts, and fractions are often the result of this process.
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Stars form from dense clumps of molecular gas deep inside a cloud. The clumps shrink down until their centers become hot enough (around 10 million degrees) for hydrogen to fuse together. At that point, the energy generated by fusion pushes their outer layers outwards and halts the contraction. The delicate balance between gravity and gas pressure continues as long as there is hydrogen to fuse in the core. During this long, hydrogen-burning phase of their lives, stars fall on the main sequence of an HR diagram.
It all sounds good so far .... but several questions immediately arise:
We can make a pretty decent estimate to this question by looking at the Sun. Suppose we make a couple of simplifying assumptions:
You can figure out how long the hydrogen will last like this:
Seems like a long time, doesn't it? How does it compare to the age of the Solar System? Are we in danger of waking up tomorrow to find out that the Sun has stopped shining?
Our estimate involves several simplifications. To do the job right, one needs to build a model of a star mathematically. Most models break the star up into a series of thin spherical shells.
Within each shell, the computer keeps track of a number of variables, among which are
The goal is to come up with just the right combination of quantities in each shell; in order for the star to be in equilibrium, each shell must satisfy
Back in the old days, astronomers had to work through all the equations in all the different shells by hand; it took a LONG time, and was extremely boring. Fortunately, we can now just write a computer program to do all the dirty work, and look at the results. Some astronomers have even made it possible for you to run their programs via the Web!
We can use the Stellar Interior Construction Site to generate a model of a star just like the Sun at the time it starts to fuse hydrogen. The model lets us look at the temperature of each shell:
Q: Is the temperature at the center of the Sun high enough to run the CNO cycle? (Need a hint? Click me)Or the density of each shell:
Hey -- check out the density of the shell about halfway out to the edge of the Sun.
Q: If you could scoop out a blob of gas from that deep inside the Sun, and throw that blob into the ocean ... would it float or sink?
Okay, so one can make a model which shows the structure of a star when it starts to fuse hydrogen in its core. That's good. But you can also use stellar models to watch the star's properties evolve with time. As time goes by, the innermost regions of a star's core change from mostly hydrogen to mostly helium, which changes the rate at which energy is produced. A whole series of changes ripple outwards through the stellar model as the interior becomes more and more helium rich.
We can't see these changes within the interior of other stars directly, but we can observe the photosphere's temperature and the overall luminosity.
If you go to Siess's Computation of Isochrones web site and
Additional information Mass Tc roc etac Menv Renv/R Tenv flag 0.100 4.396E+06 5.321E+02 3.78 0.0000 0.00000 4.396E+06 0 0.130 5.490E+06 3.372E+02 1.96 0.0000 0.00000 5.490E+06 0 0.160 6.120E+06 2.484E+02 1.15 0.0000 0.00000 6.119E+06 0 0.200 6.678E+06 1.826E+02 0.49 0.0000 0.00000 6.677E+06 0 0.250 7.370E+06 1.422E+02 -0.02 0.0000 0.00000 7.369E+06 0 0.300 7.807E+06 1.133E+02 -0.41 0.0000 0.00000 7.808E+06 0 0.400 8.479E+06 7.813E+01 -0.98 0.0237 0.08784 7.851E+06 0 0.500 8.901E+06 7.153E+01 -1.16 0.2883 0.54073 4.593E+06 0 0.600 9.537E+06 7.302E+01 -1.25 0.4558 0.61232 3.803E+06 0 0.700 1.030E+07 7.523E+01 -1.35 0.6057 0.65363 3.222E+06 0 0.800 1.126E+07 7.835E+01 -1.46 0.7371 0.67965 2.835E+06 0 0.900 1.232E+07 8.219E+01 -1.56 0.8547 0.69772 2.627E+06 0 1.000 1.345E+07 8.659E+01 -1.66 0.9722 0.72340 2.302E+06 0 1.100 1.455E+07 8.963E+01 -1.75 1.0864 0.75981 1.855E+06 0 1.200 1.603E+07 9.832E+01 -1.85 1.1965 0.81750 1.246E+06 0 1.300 1.745E+07 1.026E+02 -1.96 1.2995 0.87643 7.524E+05 0 1.400 1.877E+07 1.027E+02 -2.09 1.4000 0.92522 4.121E+05 0 1.500 1.974E+07 9.869E+01 -2.23 1.5000 0.96242 1.984E+05 0 1.600 2.058E+07 9.373E+01 -2.39 1.6000 0.98761 7.253E+04 0 1.700 2.141E+07 8.955E+01 -2.55 1.7000 0.99140 5.515E+04 0 1.800 2.232E+07 8.822E+01 -2.70 1.8000 0.99068 5.390E+04 0 1.900 2.369E+07 9.350E+01 -2.84 1.9000 0.99004 5.362E+04 0 2.000 2.476E+07 5.130E+02 -1.27 2.0000 0.98780 5.242E+04 1 2.200 2.523E+07 4.656E+02 -1.41 2.2000 0.98660 5.216E+04 1 2.500 2.625E+07 3.782E+02 -1.69 2.5000 0.98610 5.109E+04 1 2.700 2.739E+07 3.086E+02 -1.97 2.7000 0.98580 5.085E+04 1 3.000 2.692E+07 4.346E+02 -1.58 3.0000 0.98420 5.056E+04 1 3.500 2.867E+07 4.214E+02 -1.72 3.5000 0.98300 5.029E+04 1 4.000 2.972E+07 2.322E+02 -2.40 4.0000 0.98460 4.947E+04 1 5.000 3.483E+07 3.636E+01 -4.50 5.0000 0.99460 1.705E+04 1 6.000 3.464E+07 2.000E+02 -2.79 6.0000 0.94480 1.825E+05 1 7.000 3.822E+07 1.860E+02 -3.01 7.0000 0.94200 1.971E+05 1The final column in this table contains a flag:
Q: What is the maximum mass of a star which can continue to fuse hydrogen for at least one billion years?
Using stellar models, one can predict the lifetime on the main sequence for stars of various masses; in other words, the length of time during which they can continue to fuse hydrogen into helium. The results may surprise you -- the most massive stars live the shortest lives:
initial mass (solar) lifetime (Myr) ------------------------------------------- 0.5 56000 1.0 12000 2.0 900 5.0 90
One can fit a very rough formula to this relationship:
-2.5 lifetime ( mass ) --------------- = ( ------------ ) solar lifetime ( solar mass )
You can use this formula to estimate the length of time that a star will remain on the main sequence.
Q: Roughly how long will a star of 10 solar masses remain on the main sequence?
Why do the most massive star die so soon? Because they use up their fuel much more rapidly than their low-mass cousins. This movie compares the evolution of a high-mass star (15 solar masses) to a low-mass (3 solar masses) star.
Q: How much more fuel does the high-mass star have at the start of its life? Q: What is the luminosity of the high-mass star? What is the luminosity of the low-mass star? Q: How much more energy does the high-mass star generate each second?
Now, if you go back to look at the HR diagram of stars in our local stellar neighborhood,
you'll see that there really aren't many stars at the high-mass end. Aha! And that's just what the stellar models predict: the high-mass stars burn through their hydrogen very quickly, so they don't stick around for long.
Now, if you look at the low-mass end of the main sequence, you also see relatively few points. Astronomers believe that low-mass stars are actually formed more frequently than stars like the Sun, and (as you've just seen) they should last a long, long time. So why are there so few observed low-mass stars?
Copyright © Michael Richmond. This work is licensed under a Creative Commons License.
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Pat looked at the washer. The washer had dials on it. It had two dials on it. There were words next to each dial. Each dial had three words next to it. The words next to one dial were Small, Medium, and Large. This dial was for the size of the load. Did Pat have a small load, a medium load, or a large load? The words next to the other dial were Cold, Warm, and Hot. Did Pat want to wash her clothes in cold water, warm water, or hot water? Pat turned one dial to Large, and the other dial to Hot. Then she pushed the Start button on the washer.
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- Equation SolverFactoring CalculatorDerivative Calculator
Point Slope Form
Point-slope refers to a method for graphing a linear equation on an x-y axis. When graphing a linear equation, the whole idea is to take pairs of x's and y's and plot them on the graph. While you could plot several points by just plugging in values of x, the point-slope form makes the whole process simpler. Point-slope form is also used to take a graph and find the equation of that particular line.
The point slope form gets its name because it uses a single point on the graph and the slope of the line. Think about it this way: You have a starting point on a map, and you are given a direction to head. You have all the information you need to draw a single line on the map.
The standard point-slope equation looks like this:
It should be noted that "y1" does not mean y multipled by 1. In this case it simply denotes a particular y value which you will plug into the equation. The variable m is the slope of the line.
You are given the point (4,3) and a slope of 2. Find the equation for this line in point slope form.
Just plug the given values into your point-slope formula above. Your point (4,3) is in the form of (x1,y1). That means where you see y1, use 3. Where you see x1, use 4. Your slope was given to you, so where you see m, use 2. Pretty simple, huh? Your final result should look like:
Your point is (-1,5). The slope is 1/2. Create the equation that describes this line in point-slope form. Try working it out on your own. The answer is: .
If that's not what you got, re-read the lesson and try again.
Point-slope form is all about having a single point and a direction (slope) and converting that between an algebraic equation and a graph. In the example above, we took a given set of point and slope and made an equation. Now let's take an equation and find out the point and slope so we can graph it.
Find the equation (in point-slope form) for the line shown in this graph:
To write the equation, we need two things: a point, and a slope. It is simple to find a point because we just need ANY point on the line. The point I've indicated, (-1,0), just happens to be the easiest one to find. Note also that it is useful to pick a point on the axis, because one of the values will be zero.
Finding the slope requires a little calculation, but it is also pretty easy. Just count the number of lines on the graph paper going in each direction of a triangle, like I've shown. Remember that slope is rise over run, or y/x. Therefore the slope of this line is 2. You could have used any triangle to figure out the slope and you would still get the same answer.
Putting it all together, our point is (-1,0) and our slope is 2. We know how to use the point-slope form, so the final answer is:
As you can see, point-slope form is nothing too complicated. It is just one method to writing an equation for a line. The other common way of doing this is the y=mx+b method. Just practice converting between a line on a graph and an equation and you'll get the hang of it in no time. And of course, if you need more help, feel free to ask the volunteers on our math help message board.
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PatrickHaller/fineweb-edu-plus
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Practice a variety of skills and standards with this cute booklet and fun way for your students to learn or review, write, recognize and read numbers and number words.
- Students read, trace and write the number and number word.
- They see a number of penguins in a sentence and say it.
- They spy the number in a sequence and circle it.
- They X-out that many ten-frame boxes or use a bingo dot marker or stamp.
- They cut and glue the set/group of penguins to the matching numbered box.
1-2-3 Count Penguins With Me
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PatrickHaller/fineweb-edu-plus
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Return to Chemistry Index
Schaumburg, Carl Von Stueben MSC
Purpose is to show what happens to the pressure inside a container of steam when
it is cooled and how the pressure affects the boiling point of a liquid.
Empty aluminum popcans and sinks or trays full of water.
Ditto cans and rubber stoppers to fit.
Filter flasks, short pieces of rubber tubing on sidearm, thermometers inserted in
stoppers to fit flasks, ring stands, rings, wire gauzes, bunsen burners, bunsen
clamps, pinch clamps, and boiling chips.
Start by having the class hold popcans in clamps. Class is directed to add
various amounts of water (1 to 10 mL) to the can. Boil, and place can in a sink full
of water. The class is told, "Be ready to discuss what happens, think of an
explanation for what happens, and tell what amount of water works best." At least
some of the cans should be crushed. Discuss which techniques worked best and what
happened inside the can. Talk about what pressure is, and how cooling the steam
affects pressure inside the can.
Sitting all by itself clamped in a ring stand on the desk, have a stoppered ditto
can which already has been filled with steam (by boiling water inside) before the
class came in. As it cools in the air it should also be crushed. A few drops of
water on the outside may be necessary to help it a bit. Have the class explain what
must have happened. With another ditto can have the class recreate what happened in
the can. (A silent lecture could be effective here.)
Working in groups, final part uses the filter flask. Add enough water so the
bulb on the thermometer is under the surface. Add a few boiling chips, stopper with
the thermometer, clamp on the ring and ring stand, and heat until enough steam has
been produced to push out all the air. TURN OFF THE BURNER, and using the pinch
clamp close off the tubing on the sidearm. "Watch the temperature!" It may go up.
If it does be ready to release extra pressure with the pinch clamp, if the
temperature goes to 104 degrees Celsius. Using the clamp as a handle, remove the
flask from the stand and cool in cold water. "Watch the temperature!" Of course it
goes down. but point out that the water is still boiling. "What is the lowest
temperature at which you can get the water to boil?"
Relate to the two previous parts. When you cool the flask filled with steam the
pressure goes down inside. "In spite of being cooled the water inside the flask
continues to boil. Why?" Discussion should lead to the concept that boiling
temperature depends on pressure. Ask, "Where in your car is boiling at different
pressures used?" The radiator. "Where in cooking is pressure used?" The pressure
cooker. "Why do people in Denver need special cooking instructions? Who will have a
harder hard boiled egg, someone boiling an egg in Denver or someone on the seashore
if they both heat the same amount of time. How does Folgers make freeze dried
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When you look in a mirror you see your own reflection, i.e. you see yourself. 'Yourself' is an example of a reflexive pronoun. Just as a mirror reflects your image, so does a reflexive pronoun reflect the subject pronoun!
Reflexive pronouns are used in two different ways:
RULE A – When the subject and object is the same thing. In this case the reflexive pronoun is needed in the understanding of the meaning of the sentence.
e.g."She looks at herself in the mirror." (She and herself is the same person)
RULE B – For extra emphasis. In this case the reflexive pronoun is not needed in the understanding of the meaning of the sentence.
e.g. "He baked the cake himself."
Choose a pronoun from the box below for each sentence. Some are object pronouns. When a reflexive pronoun fits in a sentence, decide whether it is RULE A or RULE B.
Lesson by Danica, EC Cape Town English school
- 1) She looked at in the bathroom mirror.
- 2) Did you hear about Fred and Amy? He asked to go out with him!
- 3) I taught how to speak English, I never had a teacher.
- 4) The dog had fleas and was scratching the whole day!
- 5) Nobody wanted to help them, so they cleaned the streets .
- 6) Bobby is a bit crazy. He always sits alone and talks to .
- 7) Wow! Did you write this book ?
- 8) They blame for the accident, because they didn’t pay attention to road signs.
- 9) James forgot Susan’s birthday, but she told not to worry.
- 10) We painted the house . Nobody helped us!
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After listening to a computer-read story, "Jack and the Beanstalk," the students will find out that beans were used as an exchange for Jack's cow. Jack traded his pet cow for an old man's magic beans. Were they both happy? They should be! People exchange goods because both feel they will be better off after the exchange.
- Identify that barter is trading without money.
- Explain that people voluntarily exchange goods and services because they expect to be better off after the exchange.
Do you have a pet? Would you trade something for your pet? If someone gave you money for your pet, would you trade your pet for money? Would you trade your pet for food if you were hungry? Would you trade your pet for five beans? In the story we'll hear in our lesson, that is just what happens!
- Jack and the Beanstalk: Here is a story about Jack and the Beanstalk. Be sure to emphasize the part where Jack trades his pet cow for beans.
- The Trading Game: The Trading Game is an interactive activity in which students will be assigned an item and then be given the opportunity to trade for other goods with other people. This activity will help students to understand barter and exchange.
The Trading Game
An exchange involves trading goods and services for other goods and services or for money. Barter, however, does not involve the use of money. Barter is the direct trading of goods and services for other goods and services. Voluntary exchange occurs when all participating parties expect to gain.
Students: If you want a new pair of shoes, how do you go about getting them? You have to EXCHANGE something for the shoes. Exchange means to trade something for something else. What would you trade the store clerk for the pair of shoes? [Money.] Would you give the clerk money for the shoes? [Yes.] Could you trade a hamburger for a pair of shoes? [No.]
If you wanted a pair of shoes that your sister or brother had, could you trade something with your sister or brother for the shoes? [Yes.] Can you think of something your sister or brother might want--other than money-- that you could trade for the shoes? Trading of this sort is called BARTERING. BARTERING is trading without money.
When you make a trade, both people should be satisfied after the trade. Why? [You should not have traded if you did not expect to be satisfied about it.]
Was the old man satisfied he got the cow? [Yes.] Was Jack satisfied that he got the magic beans? [Yes.] When you trade you should both be satisfied. Was Jack's mom satisfied? [No.] What did she want Jack to get in trade for the cow? [Money.]
But Jack and the old man traded the cow and beans. The old man bartered the beans for the cow.
Do you think Jack's mom was satisfied about the exchange of the cow for beans at the end of the story? [Yes.] Do you think Jack got Milky White back from the old man? [Answers may vary.]
What trade would make you satisfied? Fold a piece of paper in half. On one side of the paper draw a toy that you have that you would be willing to trade. On the other side of the paper draw something that you would like to trade for.
When you exchange one thing for another, the trade should make both people satisfied. You should not trade for something you do not want. When you trade and you don't use money, it is called barter.
Have students use The Trading Game to practice trading with others.
The Trading Game is an interactive activity in which students will be assigned an item and then be given the opportunity to trade for other goods with other people. They will be asked if they would like to trade their item for the other goods. They can decline to trade or they can "trade" their item for another object. After the trades have occurred, the students will be asked if they are satisfied with their trades; they will be told that, if they are not satisfied, they should not have made the trade in question. The students also will be asked whether their exchange was an example of barter or whether they used money in the trade.
This activity loops continuously. If students are sharing computers, give each child an opportunity to go through two to three cycles of the Trading Game before letting another student take their turn.
Note: Children tend to want to make a trade just to be trading something. Many times, after the fact, they are very upset that they traded. The lesson here is that both parties to a trade should benefit from the trade. If they don't expect to benefit, then they should not make the trade.
The objects that are assigned to the student are generated randomly, so students can play the game several times to reinforce the concepts in the lesson.
Have students bring a small item from home or provide them with items such as stickers, pencils, and candy. Give them a set amount of time to trade their items with one another. When 'trading time' is over, have students discuss their trades with the rest of the class.
“The teacher might ask what other items a person could use to barter.”
“I think this lesson is good for learning about money and all things economics.”
“I'm an English teacher in Spain. I've been looking for plays to perform in my class for weeks but all I could find was to buy. Today I found Jack and the beanstalk to download free! Then I found you and your activities to help me. Thank you very much for your free website!”
“Very nice site!”
“Wow! This was a great lesson for my 2nd graders! Thanks a lot!”
“I was surfing the web when I discovered this site. I enjoyed the lesson and will use it in my technology class. Thank you very much. I have to share this site with other teachers.”
“This lesson was great. The Trading Game was awesome for reinforcement. The students loved playing it on the interactive whiteboard. Next year, I will use it when we read Jack and the Beanstalk in our reading core.”
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PatrickHaller/fineweb-edu-plus
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For some questions on the Math IIC test, you’ll need to
translate the problem from a language you’re used to—English—into
a more useful, albeit less familiar, language. We mean the language
of math, of course, and one of your main test-taking responsibilities
is to be able to write an equation based on the information given
in a problem.
You’ll also be asked to find an expression for a certain
quantity described in a word problem. The best way to learn how
to do these things quickly and effectively is to practice. Here’s
a sample problem:
a sack of 50 marbles, there are 20 more red marbles than blue marbles.
All of the marbles in the sack are either red or blue. How many
blue marbles are in the sack?
To start with, you can write r + b =
50, where r is the number of red marbles and b the
number of blue marbles in the sack. This equation tell us that the
50 marbles in the sack consist entirely of red marbles and blue
Now that you have an initial equation, you need to decipher
what exactly the question is asking for. In this problem it is clear-cut:
How many blue marbles are in the sack? You must therefore find the
value of b.
Unfortunately, you need more information to do that. You
can create a second equation based on the knowledge that there are
20 more red marbles than blue marbles. This part of the word problem
can be written in the form of an equation as r = b +
20 (or b = r – 20).
Let’s list the two equations we have so far:
Using both of these equations, you can solve for b.
After a little manipulation, which we’ll cover in the coming sections,
you’ll find that b = 15 (and r =
35). Don’t worry about the solution for now—just focus on how we
translated the word problem into equations that lead to the solution.
That problem was easy. Here’s a harder one:
sells oranges for c cents apiece. The minimum number
of oranges that Stan will sell to an individual is r,
but the first f oranges are free (f <
r). Find an expression for the price in dollars of 35 oranges
if 35 > r.
According to the problem, we need to find an expression
(notice, not an equation) for the price in dollars of 35 oranges.
The key to a problem like this one is working step by step. First,
find out how many of the 35 oranges aren’t free of charge.
Next, find the price of those oranges.
But wait. Did you notice that the question asked for the
price of 35 oranges in dollars? The writers of
the Math IIC are a clever bunch, if a bit sneaky. They figure that
a good number of test-takers will see only the word price and
not notice what units are asked for. Be careful not to fall into
their carefully laid trap.
We know there are 100 cents per dollar, so we can easily
convert the price by dividing by 100.
Before we move to another problem, note that the variable r didn’t
appear anywhere in the answer. Egad! It is yet another attempt (and
a common one at that) by those devious test writers to lower your
score. You may come across many problems, especially word problems,
in which extraneous information is provided only to confuse you.
Just because a variable or number appears in a problem doesn’t mean
that it will be useful in finding the answer.
Here’s another problem:
needs to paint his house, which has a surface area of x square
feet. The brand of paint he buys (at a cost of p dollars
a can) comes in cans that cover y square feet each.
Gus also needs to buy ten pairs of new jeans (he is uncoordinated
and spills often). They cost d dollars a pair.
If Gus makes these purchases, what is the difference (in dollars)
between the cost of the paint and the cost of the jeans? Assume
he doesn’t buy any excess paint—that is, the required amount is
not a fraction of a can.
This word problem is long and complicated, but you need
to carry out just four steps to solve it:
Gus must buy x
/y cans of paint
to cover his house.
will cost him xp
jeans Gus buys cost 10d dollars.
the difference, in dollars, between the cost of the paint and the
cost of the jeans is xp
/y – 10d.
For the rest of this chapter, we’ll constantly be converting
word problems into equations. If you’re still uncomfortable doing
this, don’t worry. You’ll get a lot more practice in the sections
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PatrickHaller/fineweb-edu-plus
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Blueprint Building Math Activity
What you need:
- Building blocks
- Sheets of paper
- Pen or pencil
- To create the blueprints (and encourage your child to help): Take a piece of paper, and place the blocks on top of the paper. Arrange them to create a bridge, a tower, building, etc.
- Trace the shapes of your creation onto the paper. Be sure to name the shapes as you trace them.
- Then, have your child choose a blueprint and try to recreate the structure, using the shapes of the blocks, to figure out what goes where (like puzzle pieces).
- For older children: Make it a game by timing how long it takes her to complete the blueprint.
- For multiple children: Make photocopies of one of the blueprints and give each child a set of blocks. On your mark, get set, build! Who will build the block structure first?
Get more brain-building activities for your kid! Check out our Brain Building Boot Camp with Dr. Christine Ricci.
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PatrickHaller/fineweb-edu-plus
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Explore the slope of the sin curve
[25 Oct 2010]
This was an important problem for mathematicians for centuries. If something is moving so that its velocity and acceleration are forever changing, how do we measure the rate of change?
It is easy to find rate of change (or slope, or gradient) for an object moving at constant speed, or constant acceleration, but what do we do if when the speed or acceleration is not constant, as is the case for objects moving in circular or regular paths (which we can describe using the trigonometric functions)?
This article, and the 2 that follow, shed some light on this interesting problem.
First, some reminders so you can better follow what is going on.
Tangent to a curve
A tangent to a curve means the line that touches the curve at one point only.
The tangent of the curve at the point A
(For more information, see Tangents and Normals).
The slope of a curve means the slope of the tangent at a particular point.
Here is the curve y = sin x. The values of x are in radians and one complete cycle goes from 0 to 2π (or around 6.28).
Graph of sin x
y = sin x
Our aim is to explore the slope of the curve y = sin x. Clearly. the slope of the curve changes as we move left to right.
Graph of cos x
Next we have y = cos x. It has the same shape as the sine curve, but has been displaced (shifted) to the left by π/2 (or 90°).
y = cos x
Slope of Sine x
First, have a look at the interactive graph below and observe that the slope of the (red) tangent line at the point A is the same as the y-value of the point B.
Then slowly drag the point A right or left and observe the curve traced out by point B. (The point B has the same x-value as point A, and its y-value is the same as the slope of the curve at point A).
Hopefully you can see that B traces out the curve y = cos x. In other words, the slope of the graph y = sin x at any point (x,y) has value cos x. Using calculus notation, we would write this as:
See more on the differentiation of sin, cos and tan curves. (This is in the calculus section of IntMath.)
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Sticky Icky Piggy
This lesson will help children identify and understand the sound of the short vowel /i/. Students will recognize the vowel in spoken language by learning the meaningful representation of sticky icky hands. As students gains the understanding of corresponding graphemes and phonemes, students are well on their way to becoming fluent readers. Students will be reciting a tongue twister using their correspondence; they will also have further practice with this correspondence as they complete a letterbox lesson as well as read a decodable book.
Primary paper and pencils for the student
Picture of stick icky fingers with the /i/ letter.
Poster with tongue twister written on it: "Nick slipped on the slick brick". Every time you hear the s word act like you have stick icky fingers.
Class set of the book Tin Man Fix It (Phonics Reader, Educational Insight)
List of letterbox words in phoneme count order- 3(fit, sat, sit, fib) 4 (brick, bats, pink, spit,) 5- drink
Letter tiles: a, b, c, d, f, k, I, n, p, r, s, t,
Introduce the lesson by writing a lower case letter i on the board and ask the students if they know what sound the letter makes. "Does anyone know what sound this letter makes?" praise the students for trying and giving examples. "Great job, the letter i make the /i/ sound!" Explain to the students that letters make different sounds and that we need to be able to match the letters to the sounds they make, in order to become fluent readers. "Today we are going to learn how to identify the letter i and the /i/ sound in words."
2. Hold up the picture with the Icky Sticky hand gesture on it. Ask the students have they ever touched something that was sticky? "Have you ever touched icky, sticky peanut butter, glue, or gum with your hands and you try to shake it off?" Well I have and it was very icky and sticky! "Do you hear the /i/ sound in icky-sticky?" If so I want you to say /i/ and shake your icky-sticky hands." Demonstrate and explain for the students how to do the icky-sticky hand gesture and mouth move. "When you say the /i/ sound and do your icky-sticky hand gesture, your mouth should be opened and you tongue slightly lowered, and then you should shake both your hands in and upward and downward motion.
3. Have the students to tell you if they hear the /i/ sound in different words. "I want to listen closely to some words as I say them, and tell me which words have the /i/ sound in them." "Do you hear the /i/ sound in dig or dog? Milk or map? Him or her? Great job! You did hear the /i/ sound in dig, milk, and him.
4. Pass out primary paper and pencil to each student. "I want to be sure that everyone knows how to write the letter i." Demonstrate and encourage the students to write the letter i. Let students all try to write the letter i. "Start at the fence line and draw a straight tree top standing tall (have students draw line as you demonstrate on the board). Then go up a little over the tree and put a tiny round sun.
5. Begin the letterbox lesson. Pass out Letterbox sets and lower case letterbox tiles: a, b, c, d, f, k, I, n, p, r, s, t to each student. Demonstrate how to use the letterbox and letter tiles to pronounce and spell words with the students. "Now we are going to spell some words that have the /i/ sound in them. Remember that each box should only have one sound in it. I am going to spell the word "slip" watch and listen closely at what I do. S-s-s-l-l-l-i-i-i-p-p-p. It helps if you say the word very slowly to yourself. The first sound I hear is /s/, so I will put a s in the first box. Then I hear the /l/ sound, so I will put an l in the second box. Then I hear the /i/ sound that we have been learning about (demonstrate the icky-sticky hand gesture for the students while looking for the letter i) so I will put an i in the third letterbox. Finally I hear the /p/ sound, so I will put the letter p in the fourth letterbox. Now lets see can we spell these words with the /i/ sound in them." Have the students to use the Elkonin letterboxes and tiles to spell the following words [2 at, up 3pig, lip, pit, hip, fit, hut, sun, big, pin, sit, fish 4 gift]. Remember to tell the students how many boxes they will need for each word. "Now lets practice saying some words with the /i/ sound. See if you can use the steps that I used to spell slip, to spell the new words. When you are finished spelling a word, put a thumbs up in the air, and I will come by and look at your spelling." Then pass out the class set of index cards with the words at, up, pig, lip, pit, hip, fit, hut, sun, big, pin, sit, fish and gift. Have the students to read the words on each card aloud as a class.
6. Pass out the book Tin Man Fix It to each student. Do a picture walk and book talk for the students, to get them interested in reading the book. "Today we are going to read Tin Man Fix It." This book is about a tin man named Tim and his friend Jim. One day Tim and Jim were outside working in a garden. A kid named Sid skates by and knocks Tim down. Tim falls down and pieces of his tin are on the ground. Lets read and find out what happens to Tim." Have the students read the text on their own. Afterwards have students to recall words with the /i/ sound that they read in the book and write those words on the board. "Who can tell me which words have the /i/ sound on page one."
7. For the assessment, I will give each student a worksheet that has words that have the /i/ sound. Students will circle which sounds like /i/.
Sounds Like /i/!
Return to Caravans Index
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PatrickHaller/fineweb-edu-plus
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Ollie the Ostrich and Oliver the Octopus
By: Victoria Barron
Rationale: Children must understand that every letter has a sound associated with it. In order to read, children must blend words beginning with the vowel sound, then the body and coda. In this lesson , students will be learning short o. They will learn ways to remember that o=/o/, then practice by reading a decodable book.
Six boxes per student for letterbox lesson
Picture of the letter O with octopus legs coming out of it
Poster with "Ollie the Ostrich and Oliver the Octopus"
Decodable book Doc in the Fog for each student
Cards with phoneme awareness words printed: top/tip, fog/fig, lock/land, frog/free, doc/duck
Copies of worksheets for each student (url below)
1. Introduce the letter O by asking students what your mouth looks like when you say /o/. Let students make the sound.
2. Have all of the students say /o/ and feel the shape of their mouth as they say the sound. Ask, "What words have this letter in it?" Have the students feel their mouths as they say the word "top".
3. Show the students the picture of the octopus with the tongue tickler written on it. Read it aloud at a regular pace first, then slowly. The third time exaggerate the /o/ sound on each word. O-o-o-ollie the O-o-o-strich and O-o-o-liver the O-o-o-ctopus. Have all of the students say it with you. Repeat.
4. Say, Now we are going to work on recognizing the letter /o/ on words. I am going to say two words and I want you to tell me which word you hear the letter o in. Do you hear /o/ in top or tip, fog or fig, land or lock, frog or free, dock or duck? Great job!
5. Say, Since everyone did such a great job at recognizing which words have the /o/ sound we are going to practice spelling some words that have the letter /o/ in them. Everyone get your squares out and place them flat on your desk. Line up all the letter neatly so you can see them. Be sure to only put one sound in each box." Model the word strong on the board. S-t-r-o-n-g. (one phoneme in each box). The students should work individually on spelling the words. [words: 3-rock, top, job 4-frog, smog, block, stop, flop 5-strong] Say, Raise your hand once you think you have the word spelled out so I can check it. Write all the words on the board and have the students say them after they have spelled them all out.
6. Say, We will now read the book Doc in the Fog. In this book, Doc does some magic to turn tops into dolls and dolls into mops! Uh-oh, what happens when Doc messes with the fog?
7. Have the students read in pairs. Each student should read one page then let the other read the next page. Encourage the students to help each other with words.
Assessment: Have all the students complete the work sheet by saying the words to you, then coloring them and practicing writing o.
King, Michaela. Oscar the Ostrich loves Olive.
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Step 1. Questions
Put two or more simple machines together, and you have a compound machine. Even the most complex machines are examples. Look at the parts of a car, for example, and you will find levers, wheels and axles, and pulleys. When simple machines are put together the right way, they can do all sorts of things!
For this e-Journal project, you will choose at least one interesting compound machine and learn how it works. Here are some questions to guide your research.
Are you ready? Begin by researching the compound machine of your choice. You may choose from those listed in the Web links, which are found in Step 2. Or use search engines to find other compound machines. When you are ready, follow Steps 3 and 4 to write your report.
- What simple machines make up the compound machine?
- How do the simple machines combine to make the compound machine work?
- What provides power to the compound machine?
- How is an animal’s body like a compound machine?
- What questions do you have about compound machines and how they work?
Step 2. Research
Research answers for the questions you were asked in Step 1. Visit these Web sites. Take notes about them on this page, too!
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Art All Around
Kindergarten Oral Language Resources
Children will:• Learn about the concept of art.
• Access prior knowledge and build background about different kinds of art.
• Explore and apply the concept of how we can make art.
Children will:• Demonstrate an understanding of the concept of art.
• Orally use words that describe different kinds of art.
• Extend oral vocabulary by speaking about how we feel about art.
• Use key concept words [create, imagine].
Explain• Use the slideshow to review the key concept words.
• Explain that children are going to learn about art:
• How to create art.
• Things to imagine.
Model• After the host introduces the slideshow, point to the photo on screen. Ask children: What do you see in this picture? (crayons, paint, play dough).
• Ask children: What can you do with these art supplies? (draw, paint, etc.)
• Say: Today we are going to learn about art. We will talk about how to use supplies to create art. We will talk about how to use our brain to imagine art. What are the different types of art? (sculptures, paintings, drawings, etc.)
Guided Practice• Guide children through the next four slides, showing them that there are many different types of art. We can use different supplies to make different art. Always have the children describe their favorite type of art.
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 art pieces that they created. After the second game, have them discuss why things are opposites.
Close• Ask children: What are your favorite art supplies to use? Explain.
• Say: There are many different art supplies to use, and many different types of art to create. Think about what you would create using your favorite art supplies.
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If you watch the moon every night, you see its shape
appear to change. Does the moon really change shape? Of course not, but
its appearance from Earth certainly
changes. How does this work? The answer lies within the part of the moon that
receives sunlight, and the part of the moon that does not receive sunlight.
Letís look at a diagram of the Earth moon system to figure out how this works.
Sunlight approaches the Earth-moon system from the right on this diagram
(Click on the picture to start the program).
Your job is to determine which half of the moon is
receives sunlight, and which half of the Earth receives sunlight.
Move the mouse on each part of the diagram to arrange
the light/dark shades over each moon position, click to set the shadow on the
moon. (The program will tell you when you have them all correct).
Sunlight will shine on the side of the Earth (or moon) that faces the sun. We
call this day on the side of the Earth that faces the sun, and
night on the side of the Earth that does not face the sun.
Keep in mind that sunlight will illuminate the side of an object that faces it!
Click on the arrow in the corner to go to Part 2.
OK, so what does this have to do with moon phases?
Well, the moon "shines" by reflected sunlight. As the moon orbits Earth, sunlight "shines" on
different parts of the moon on the side of the moon that we can see.
We always see the same side of the moon. (Why? Because the moon only spins
once per lunar month on its own axis as it orbits the Earth, so we always
see the same side.)
The key to understanding moon phases is: although the sun always shines on the same side of the moon,
the moon is not always in the same place while orbiting Earth with respect to the
sun. That sounds confusing, so let's work through a little diagram so you can visually see
this and figure it out.
Click Activity 2 above to go to the next part of the activity.
The diagram still shows the shadows
that you correctly identified before, but in this diagram, you will need to determine what
the moon looks like to humans on Earth. It's all a matter of perspective.
The green dashed line divides the moon into two halves -
the half we can see from Earth, and the half we don't see.
Look at the moon when it is at position (a). It looks like half of the moon is light
and half is dark.
Find and click the picture that shows what the moon looks like in position (a).
If you pick the correct picture and information box will pop up telling
you about the phase. You can close the box and move on to the next phase.
Your job is to continue through all the phases, through
(h), to determine if you can figure out which moon phase matches with the
position on this diagram.
After you get match the picture for all of the phases, Try answering these
questions to see if you really understand the facts about the Earth-moon
This part puts everything in action and lets you observe
moon moving around the earth in it's orbit.
You can click on the moon and drag it with the mouse.
Click the "Start Simulation" button and the moon will move in it's orbit and the earth will spin on it's axis. (The
timing of the simulation is scaled accuratly, The earth makes a complete
rotation 29.5 times in the time it takes the moon to go through a complete cycle).
You can also click on the number buttons to jump to a certain
day in the moon's phase cycle.
Or click on the phase buttons 'First Quarter', 'New Moon', etc.
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I am particularly intrigued by what students in eighth grade are meant to understand about what it means for a number to be irrational.
Okay hypothetical eighth grader, come with me down this road. As you work through some classroom tasks, this is what you will discover:
- If you build a square with 3 things on a side, the square will have 9 things in it. 4 to a side, 16 things in it. A shortcut to how many things in the square is the side times itself. Notation for something times itself is something2.
- If you try to arrange a certain number of things into a square, you can't do it with any old number of things. only numbers like 9 and 16 and 25 will work. We call these numbers of things "perfect squares". To decide if a number is a perfect square, see if you can find something times itself that equals it. We call this function square root and use a funky symbol √ which is really a stylized r because it's a root.
- There's no reason to restrict our side lengths to discrete values. If I can transition you to thinking about area, you can see that if I build a square on a grid with a side that's 2.5, there is an area of 6.25 square units inside the square. The 2.52 shortcut still works.
- Likewise, if I tell you a square has an area of say 20.25, you can find the length of a side of that square. The square root thing again. Keep trying to square numbers until you hit on the one that gives you 20.25.
- Now you will look for the square root of two. Sure you can use your calculator. Only use the multiplication function, please. I know there's the funky symbol. Just ignore it for now please. (Or maybe I didn't tell you about the funky symbol. But someone is heard about it, or will find it, and spill the beans. (Intentional nod to the Pythagoreans.))
- No matter what, the class will quickly discover that they can ask their calculator for the square root of two. The calculator will give them a nine- or ten-digit number. If they think to square that number, the calculator will say 2. They will think they have found it.
- Nothing I do will convince you that irrational numbers are a really different kind of number.
So I try to get around this, the most extreme version of that goes like this, picking up at 3:
- No calculators. We build a square on a grid with a side that's 2 and 1/2, which I will try to give as 5/2. There is an area of 25/4 square units inside the square. You will probably write this as 6 and 1/4. Maybe you will see that (5/2)2 still works, if I can convince you to just work with improper fractions.
- I tell you a square has an area of 81/4, and you can easily find the root.
- Now you will look for a square root of two. Still no calculators. We guess 3/2, but (3/2)2 is 9/4, and that's too big. Maybe you reason that 3/2 is the same as 6/4, so 5/4 is a little bit smaller. but (5/4)2 is 25/16, and that's too small. Okay let's try (11/8)2. Still too small.
- You give up after a while. I tell you that, surprise, there is no fraction whose square root is two. The square root of two can not be expressed as a ratio. We call numbers like that irrational. You know how when we divided out fractions to express them as a decimal, and the decimals always ended up ending or repeating a pattern? Irrational numbers don't do that.
- Just trust me, kid.
8.NS.1 says "Know that numbers that are not rational..." hold it right there. Is it even possible for an eighth grader to grok that there are numbers that are not rational? For that to mean anything and not just be a memorized definition? What definition would they be able to hold onto?
|Potential Definition of Irrational Number||Potential Misconception|
|non-repeating decimal displayed by calculator||1/19 is irrational|
|anything with a √ in it||√2.25 is irrational|
|weird looking numbers like π and √2||π and √2 are the only example of irrational numbers I know|
This is something that has been breaking my brain for a while, it's just freshly breaking it this week. I know lots of really smart people, and there doesn't seem to be a right answer. But, you know, it's okay. Questions are cool, too.
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When people speak English, they don't say every word and every part of each word with the same speed, pitch, and loudness. English has patterns of stress, which means saying some sounds louder and stronger. There are two kinds of stress: stress within words and stress within sentences.
Stress within words
Each word is made up of syllables. A syllable is made of a vowel sound (a, e, i, o, u) and the consonant sounds that come with it. For example, the word "example" has 3 syllables:
ex am ple
In every word, there is one syllable that is the most stressed:
ex AM ple
In longer words, there can be more than one stressed syllable, but there's always one syllable that has the biggest stress:
mis un der STAN ding
Stress within words is something that you should learn when you are learning new words. Pay attention to how the word is being said and try to copy how loudly different parts of the word are said. Using correct stress within words makes it easier for a listener to understand what you're trying to say.
Stress within sentences
Stress within sentences is even more important than within words because it can actually change the meaning of the sentence. Here are some simple rules for how you use stress:
- Stress the word that is the topic of your sentence. If you say "I don't know who THAT is," you are suggesting that there is someone else who you do know. On the other hand, if you say, "I DON'T know who that is," you are emphasizing that you don't know it, although someone might think you do.
- When you are pointing out things that are different from what someone else said, or from what you said in the previous sentence, you should stress the parts that are different. For example, if someone said, "I love cheese" you might say "I love BEER". The word "I" is stressed because it's referring to a different person (you, not the person who said "I love cheese." The word "beer" is stressed because it's different from "cheese".
- Nouns, verbs, and adjectives are stressed more than words like "to", "of", "will", "that", "is", "about". For example, here's how a normal sentence would be stressed: "This MORNING I WOKE up at SEVEN THIRTY and was OUT of the HOUSE by EIGHT."
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Using the X and Y Intercept to Graph
You've learned one way to graph a standard form equation - by converting it to slope intercept form! Click here to review this lesson.
There is another way to graph standard form equations, and that is to find the x and y intercepts.
Before we begin, let's quickly review what standard form looks like.
What is Standard Form?
Now let's review what the term intercepts means. An intercept is where your line crosses an axis. We have an x intercept and a y intercept.
The point where the line touches the x axis is called the x intercept. The point where the line touches the y axis is called the y intercept.
Take a look at the graph below.
If we can find the points where the line crosses the x and y axis, then we would have two points and we'd be able to draw a line.
When equations are written in standard form, it is pretty easy to find the intercepts. Take a look at this diagram, as it will help you to understand the process.
Now, let's apply this. Just remember:
To find the X Intercept: Let y = 0
To find the Y Intercept: Let x = 0
Let's look at an example.
This concept can be confusing, so let's take a look at the video to explain example 1.
Ok.. now let's look at a real world problem that we can solve using intercepts.
You've done it! You are now the master of graphing linear equations. You have several techniques that you can use to graph any linear equation!
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Verbal arithmetic is a mathematic game, where letters stand in for numbers. The aim is to work out what number each letter stands for. Each letter represents a different digit, and the first digit of a multi-digit number should not be zero.
In addition, there should ideally be only a single solution, and the words should also make up a meaningful phrase - as above.
So, can you solve the problem? Answer on the next page...
In column 4, the addition of S and M has produced a carry-over into column 5. The carry-over can only be a 1, since the letters represent single digit numbers. So for instance, if you add 8 and 9, you get 17, so you carry 1 into the next column. But you can never carry more than 1. So M = 1.
In order for there to be a carry from column 4 to column 5, S + M has to come to at least 9, so S is either 8 or 9. Therefore S + M is 9 or 10, and so O is 0 or 1. But we have established that M = 1, so therefore O = 0.
If there were a carry from column 3 to column 4, then E would be 9 and N would be 0. But O = 0, so there is no carry, and S = 9.
If there were no carry from column 2 to column 3, then given that E + O = N and also that we know that O = 0, this would mean that E = N. But that is impossible. So therefore there is a carry from column 2 to column 3, and N = E + 1.
If there were no carry from column 1 to column 2, then (N + R) mod 10 = E, and given that N = E + 1, this would mean that E + 1 + R = E mod 10, so therefore R would be 9. But we know that S = 9, so therefore there must be a carry from column 1 to 2, and R = 8.
To produce a carry from column 1 to column 2, D + E = 10 + Y. Since Y cannot be 0 or 1, D + E must be at least 12. As D is at most 7, then E is at least 5. Also, N is at most 7, and N = E + 1. So therefore E is 5 or 6.
If E were 6, then to make D + E at least 12, D would have to be 7. But N = E + 1, so N would also be 7, which is impossible. Therefore E = 5 and N = 6.
To make D + E at least 12, we must have D = 7, and so Y = 2.
A word of explanation about the use of mod 10. Modular arithmetic is sometimes referred to as clock arithmetic, although a clockface actually works in mod 12; so for example if it is 8 o'clock and you add 6 hours, you end up at 2 o'clock, so (8 + 6) mod 12 = 2. In the same way, if you add 7 and 8 you get 15. But if you are performing an addition, as we are here, you would carry the 1, and leave the 5. So therefore (7 + 8) mod 10 = 5.
This puzzle was originally set in the Strand magazine in 1924, by the well known English puzzler Henry Dudeney (1857 - 1930).
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Rationale: This lesson teaches children about the long vowel correspondence i=/I//. In order to be able to read, children must recognize the different sounds vowels make because vowels are used to spell all words in our vocabulary. It is important for students to understand the phoneme and grapheme of each vowel. In this lesson, students will be able to identify the /i/ (short i) in spoken words, give it a meaningful name, and learn to spell words using the short I (/i/).
Sentence strip with “Izzie the icky sticky iguana was inside and ill.”
Tin Man Fix-it (Educational Insights, phonics reader),
Flash cards with the words: at, it, bit, did, hit, big, tin, kiss, lip, and swiss.
Letter tiles I, t, b, d, h, g, n, k, l, p, 3 s’s, w, a
1. Introduce the lesson by writing a lower case letter i on the board and ask the students if they know what sound the letter makes. "Does anyone know what sound this letter makes?"If students say correct sound and examples give students praise. "Awesome! the letter i make the /i/ sound!" Tell the students what they will be doing in today’s activity. "Today we are going to learn how to identify the letter i and the /i/ sound in words."
2. Hold up the picture with the Icky Sticky hand gesture on it. Ask the students have they ever touched something that was sticky? "Have you ever touched icky, sticky glue or gum with your hands and you try to shake it off?" Well I have and it was very icky and sticky! "Do you hear the /i/ sound in icky-sticky?" If so I want you to say /i/ and shake your icky-sticky hands." Model and explain for the students how to do the icky-sticky hand gesture and how to move your mouth the correct way to make the /i/ sound. "When you say the /i/ sound and do your icky-sticky hand gesture, your mouth should be opened and you tongue slightly lowered, and then you should shake both your hands in and upward and downward motion.
3. “Let's take a look at a tongue twister (sentence strip). Izzie the icky sticky iguana was inside a igloo and ill Now let’s all say it 3 times together. Good! Now every time we hear the sound /i/ lets stretch it out and say it loud. IIIzzie the iiiicky stiiicky iiiguana was iiiinside an iiigloo and iiiill. Good! Now let’s say it one more time, but this time lets break the /i/ sound out of the word and say it separately. /I/zzie the /i/cky st/i/cky i/guana was /i/nside an /i/gloo and/i/ll.”
4. Have the students to tell you if they hear the /i/ sound in different words. "I want to listen closely to some words as I say them, and tell me which words have the /i/ sound in them." "Do you hear the /i/ sound in big or bag? Pick or pack? Dig Stick or stack? Great job! You did hear the /i/ sound in big, pick, and stick.”
5. Pass out primary paper and pencil to each student. "I want to be sure that everyone knows how to write the letter i." Demonstrate and encourage the students to write the letter i. Let students all try to write the letter i. "Start at the fence line and draw a straight tree top standing tall (have students draw line as you demonstrate on the board). Then go up a little over the tree and put a tiny round sun.”
6. Begin the letterbox lesson. Pass out Letterbox sets and lower case letterbox tiles: I,t,b,d,h,g,n,k,l,p,3 s’s, and w to each student. Demonstrate how to use the letterbox and letter tiles to pronounce and spell words with the students. "Now we are going to spell some words that have the /i/ sound in them. Remember that each box should only have one sound in it. I am going to spell the word "hip" watch and listen closely at what I do. H-h-h-h-i-i-i-i-p-p-p. It helps if you say the word very slowly to yourself. The first sound I hear is /h/, so I will put a h in the first box. Then I hear the /i/ sound that we have been learning about (model icky sticky hand gesture) so I will put an i in the second letterbox. Finally I hear the /p/ sound, so I will put the letter p in the third letterbox. Now let’s see can we spell these words with the /i/ sound in them." Have the students use letterboxes and tiles to spell the following words [2 at, it 3bit did hit tin big kiss lip 4 Swiss]. Remember to tell the students how many boxes they will need for each word. "Now let’s practice saying some words with the /i/ sound. See if you can use the steps that I used to spell hip, to spell the new words. When you are finished spelling a word, put a thumbs up in the air, and I will come by and look at your spelling." Then pass out the class set of index cards with the words it, bit, did, hit, big, tin, kiss, lip, and swiss . Have the students read the words on each card aloud as a class.
6. Pass out the book Tin Man Fix It to each student. Do a picture walk and book talk for the students, to get them interested in reading the book. "Today we are going to read Tin Man Fix It." This book is about a tin man named Tim and his friend Jim. They were playing outside when a big kid named Sid skates by and knocks Tim down. Tim falls and breaks apart. Will Jim be able to fix Tim?" Have the students read the text on their own. Afterwards have students to recall words with the /i/ sound that they read in the book and write those words on the board. "Who can tell me which words have the /i/ sound on page one."
7. For the assessment, I will give each student a worksheet that has picture that have the /i/ sound. Students will circle which sounds like /i/ and x out pictures that do not.
Norris, Michael 'The Icky Sticky Insect':
Hollis, Caitlin 'Sticky Icky Pig':
Return to the Doorways Index
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But no one is born knowing how to set goals and develop a plan to carry them out. Reader Jane Haney suggests five steps to help your child learn how to set goals . . . and achieve them:
- At the beginning of the week, help your child identify one challengingêbut attainableêgoal. It might be turning in a book report on time. It might be getting 90% correct on a spelling test.
- Have your child write the goal on a piece of paper. Post it on the refrigerator or a bulletin board.
- Talk about how to accomplish the goal. Help your child break the goal down into smaller steps. For example, "You could read two chapters every day. Then you can spend a day writing your report and another day revising it."
- As the week progresses, ask how things are going. If problems come up, talk about possible solutions. If your child falls behind in reading, for example, a ten-minute extension of bedtime might encourage him to catch up.
- At the end of the week, help your child evaluate how well she did. Did she achieve her goal? Why or why not?
Most important, praise your child for trying. Then set a new goal for next week.
Copyright © Parent Institute
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5th Grade, Research and Inquiry Activities
2. Click on Overview and read the first paragraph, which discusses the importance of music.
3. Scroll down to the bottom of the page and click on Home to return to the main Web page.
4. Click on Songbook and click on a song title to learn more about it. Read the lyrics and listen to the song being performed.
5. You can also click on the names of the composers and performers to learn more about them.
6. After you have listened to several songs and read their lyrics, choose your favorite song. Copy the first line from the song into the space below. What does the line make you think of? How does it make you feel? Write your own song using this as the first line. You can use the same title or make up one of your own.
First line: _______________________________________________________________________
To read about other types of song lyrics, click on http://www.niehs.nih.gov/kids/music.htm.
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This one is especially for parents of children who have just started school. If your child’s school is using Jolly Phonics chances are your child has already begun to learn his or her sounds.
Jolly Phonics is a form of synthetic phonics. This means that it first teaches the letter sounds and then teaches children to “blend” sounds together to read and write words eg. cat = caat. Blending is often referred to as “sounding out”. Children are also taught to “segment” which involves breaking words up into sounds eg c/a/t. We do this when spelling words.
Your child will probably already have completed the Sounds in Set 1 and perhaps Set 2 at this stage. Here they are:
Download this free glance card and save it for when you are doing homework.
You can use it in 2 main ways:
- Randomly point to a letter and ask your child what sound it makes.
- Call out a sound and ask your child to point it out.
You now have an easy way to check your child’s sounds Just remember that it is letter sounds and not letter names that children learn in the beginning.
Be careful when pronouncing these sounds. Think of a simple 3 letter word eg sat and sing it rather than say it! It is easier to hear the constituent sounds if you do.
Here is an explanation of the sounds covered is Sets 1-2. It is always tricky to write down phonetic sounds. I hope that they make sense
“s” is a long sound as in sssssnake and not suh
“a” is a short sound as in a/nt
“t” is a short sound as in t/ap and not a harsh tuh ( the “uh” at the end in soft)
“i” is a short sound as in it
“p” is a short sound as in pig. It has a very gently “uh” sound at the end. Curl your lips in around your teeth & push them out like a little explosion. The “uh” sound is subtle rather than pronounced.
“n” is a long sound as in nnnnet and not nuh
“c” and “k” are a short sounds as in cap and kit. It has a very gently “uh” sound at the end.
“e” is a short sound as in egg
“h” is a soft, short sound and not huh. Take a deep breath and sigh to hear it :)
“r” is a long sound as in rrrrip and not ruh
“m “is a long sound as in mmmat and not muh
“d” is a soft, short sound as in dip with a quite rather than pronounced uh sound at the end.
I hope that this helps . It is so important to get it right in the beginning. If you have any further questions please feel free to email me [email protected].
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PatrickHaller/fineweb-edu-plus
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If you're asking this question, I'm sure that you have access to a periodic table of the elements somewhere (if not, there's one at this site
that you can look at) If you look on the periodic table, you will see that there is a number by each element. That number is the "atomic number" and is equal to the number of protons in the atom. If the atom is neutral (not an ion), then there are the same number of electrons as protons.
Now, for more difficult things. Imagine the atomic symbol of an element, say Helium, He. Now imagine a little square around the He. The square has four corners, and sometimes there will be numbers in those corners, like:
Each of these spots may have a number that tells you something:
Let's start with the lower left corner, where the "2" is. This is the atomic number, or the number of protons.
Now look at the upper left corner, where the "4" is. This number corresponds to the number of protons plus the number of neutrons. Use the top left to find the number of neutrons. We see that our atom has 2 protons, so we just subtract: 4 - 2 = 2 neutrons.
The upper right corner has to do with charge and number of electrons. This may be blank - just think of a blank spot meaning "0." If it is not blank, the number there is how many more protons than electrons that the atom has. This number may be positive or negative (you could have a 3- there, instead of a 3+, for example). In our atom, we have a "1+". That means there is one more proton than electron. Take the number of protons (from the upper left) and use this:
1+ means there is one more proton than electron. There are 2 protons. 2 - 1 is 1, so there is one electron.
If the number were negative (Let's say 2-), then you would say "there are two less protons than electrons" and:
2 - (-2) = 2 + 2 = 4 so there would be four electrons in this case.
Hope this helps!
(published on 10/22/2007)
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PatrickHaller/fineweb-edu-plus
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Anna put some coins on the table.
One half of them were tails up.
Anna turned over two of the coins, and then one third of them were tails up.
How many coins did Anna put on the table?
How did you use this starter? Can you suggest
how teachers could present or develop this resource? Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.
If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:
This starter has scored a mean of 3.2 out of 5 based on 121 votes.
let the number of coin be x
(x ÷ 2) - 2 = x ÷ 3
3(x ÷ 2) - 6 = x
3x ÷ 2 = x + 6
3x = 2x + 12
x = 12
There were 12 coins on the table
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PatrickHaller/fineweb-edu-plus
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“Chug Chug Chug goes the Train”
Rationale: When children are learning to read, it is important for them to place sounds with the correct letter. Some sounds contain more than one letter. When two letters are placed together to make a sound it is called a digraph. This lesson will teach the digraph ch. It will teach how it is spelled and how it is used in different words.
Materials: Elkonin boxes, letter manipulatives (a,c(2),e,h,m,r,t,u,x,ch(2), book “Chip Gets a Dog” published by Steck Vaughn Company for each child, worksheet with pictures including some pictures, such as chair, cheese, chew,etc, that have the /ch/ sound.
1) I want everyone to pretend that they are a train with a really heavy load trying to go up a hill. What is the sound it makes? Chug, Chug,Chug, Great! Does everyone hear the ch-ch-ch? We are going to focus on that sound today.
2) If you know what letters make up the /ch/ sound raise your hand. Great, you are exactly right c & h. Is there /ch/ in chain? Yes. How about car? No.
3) We are going to practice the /ch/ sound. Repeat these words back to me. Church (repeat), chew (repeat), chore (repeat), ranch (repeat). Do you hear /ch/ in corn or charm? Hatch or hat? Great! Everyone is “catching” on nicely!
4) We are going to practice spelling words by sounding out the words and placing each individual sound in their own box. On the board I will draw some boxes and we are going to put each sound of a single word in them. Example: Teacher will model by spelling church in three boxes. Children will then spell chex in three boxes, charm in three boxes, chug on three boxes, match in three boxes.
5) Children will be asked randomly to read aloud individually from their books “Chip Gets a Dog.” Every time they hear the /ch/ sound they will snap their finger once.
6) After they have identified all the /ch/ sound words, we will write them down on the board. We will practice saying them and making sentences from them.
7) I will assess the students by giving them a worksheet. On the sheet will be pictures of recognizable items. If an item has the /ch/ sound, they write ch beside the picture.
Murray, Bruce A., Lesinak, Theresa, Teaching Reading, The letterbox lesson: A hands-on approach for teaching decoding. Vol. 52, no. 6, Copyrights 1999 International Reading Association 644-650.
Click here to return to
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Exercises for Lesson 5
- Learn the next 5 expressions in Pre-Lesson 1.
- Using the sentence ["Ɣä̲n a thï̲n"] as the one frame sentence, write the following sentences in Nuer substituting the
different nouns for [Ɣä̲n].
- Is there milk? I want milk.
- Is there water? He wants water.
- Is Jɔk present? She wants Jɔk.
- Is my mother here? My father wants my mother.
- Is there money? Your brother wants money.
- Use the following frames and substitute the correct word in the following sentences.
||Bɛl a thï̲n.
- Do you want my mother? My mother is here. No, I want your father.
- Do you want this? No, I want this.
- Do you want money? There's money here. Yes, I want money.
- Do you want tin? There's tin here. Yes, I want tin.
- Do you want your sister? Your sister is here. No, I want my brother.
- How do you say the following:
- Hello. It is you, my sister.
It is good peace? You are present?
It is good.
What do you want?
- I want to talk with you.
I want a tin can.
- It is you my mother. Is your body at peace?
Where is my brother? Is he at-house?
I want him now.
- Your brother is here. He is sleeping.
Go. Call him
- Where is the money? My friend wants it now.
Is it here? It was with your sister yesterday.
- Translate in writing:
- Ram ɛmɔ ɛ ŋa? Ɛ nyimaar pa̲ny. Go̲o̲rɛ ni̲ ŋu̲ tä̲ä̲mɛ? Ku̲a̲cä̲ jɛ. Go̲o̲rɛ ji̲.
- Ɛ ɤä̲n Jɔk. Gua̲a̲r a ni̲?
Gu̲u̲r a luaak. Tɔ̲ɔ̲cɛ.
Wër, cɔl ɛ. Ɣä̲n göörä̲ jɛ.
- Mä̲ä̲dä̲ a ni̲? Jɛn a duɛ̲ɛ̲l?
Ɣëc, jɛn a bëëni̲ tä̲ä̲mɛ. Jɛn a luaak.
- Where is the milk?
There's the milk. Do you want the milk?
- Is the milk here? My mother wants the milk.
Where are they?
- Write these sentences:
- Do you want my brother? He's eating now.
- Do you want my mother? She's cooking now.
- Do you want my uncle? He's sleeping.
- Do you want my father? He's working now.
- Where is the tin? It is at the house.
- Where is the money? It is with him.
- Where is the water? It is here.
- Where is the money? There it is the money.
- Is there milk? Yes, there's the milk.
- What are you doing?
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PatrickHaller/fineweb-edu-plus
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/u/ says Uhhhhh?
Rationale: Letter name knowledge is a very strong predictor in beginning reading achievement. Students need to learn letter names and their sounds to be good readers. Short vowels are very difficult for children to learn because several short vowel phonemes sound very similar. In this lesson, the children will learn the short u, u=/u/. The students will learn ways to remember u and have practice identifying written and spoken words containing u=/u/.
Materials: - Picture of the caveman
Letter Manipulative: u, p, b, t, c, f, n, s, a, e ,k, z, z
-Primary Paper and pencils for each student
-Notecards with words from letter box
-Copies of the book Bud the Sub
1.Introduce the u=/u/ with the picture of the caveman and explain how to find it in words. "Today we are going to find the letter u in words that we hear, see, and even say! The letter u makes the /u/ sound. Watch how my mouth moves when I say the letter u. Turn to your neighbor and watch their mouth as they make the /u/ sound. This is like the sound we make when we don't know what to do. When we say the /u/ sound everyone put their hands up and look confused as you say Uhhhhh just like the caveman in the picture.
2.To practice recognizing the letter u in written text, the teacher will write two words on the board. One will have the short u vowel and the other will not (like sub and bad) Ask students to help you find the word with the /u/ sound. The teacher is going to ask aloud to the class "Do I hear /u/ in su-u-u-u-b or ba-a-a-d?” (Allow students to try to answer) Then say, I hear the uhhh /u/ sound in sub, not bad.” Do a few more of these kind of words and tell them to put their hands up and look confused like the caveman when they hear the /u/ sound.
3."Now, let's practice saying a tongue teaser together. "Ursella was unable to put up her ugly umbrella." Say it together several times. "This time lets stretch out the /u/ sound and act confused each time you hear /u/. "Uuuursella was uuuunable to put uuuup her uuuugly uuuumbrella .” Great job!
4. Draw the letterboxes on the board to use during this part of the lesson. Give each student a letterbox and letter tiles. "We are going to practice spelling words with the /u/ sound. Look at the board and see how there are three spaces for three mouth moves. Right now, I am going to spell the word fuzz. The first box is for the first sound in fuzz, the /f/. Remember how the /u/ sound makes the sound the caveman is? The /u/ goes in the second box. The last box is for the last sound, /zz/.” Now, students practice with the following words: (2) - up (3)- tub, cut, fun, sat, ten. (4)-stuck.” Do the words on the board, so students can check their answers. Remember to count the sounds with the number of boxes.
5. Have the letterbox words written on note cards. Show students the model word. "We are going to read the word tub. Let's start with the /u/, now let's add the /t/ , this gives us the sound /tu/. Its time to add the last sound /b/ , which makes/tub/. Now, let's say the whole word- tub." Continue doing this with all the words from the letterbox.
6.The students will read Bud and the Sub. The teacher will give a book talk before pairing students up: "This book is about a sub named Bud. He is a small sub, but one day he goes out and a tug boat is in trouble! Can Bud help the tug?”
Assessment: Students will be given a page with pictures of words that have the /u/ sound and some that do not. Students should circle the pictures with the /u/ sound. Have the children write the names of the pictures under each one after they find the /u/ sounds.
Bud the Sub. Educational Insights, 1990.
Dobbin, Samantha http://www.auburn.edu/academic/education/reading_genie/adventures/dobbinbr.htm
Fuzz and the Buzz. Educational Insights, 1990.
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PatrickHaller/fineweb-edu-plus
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You know the feeling, you walk into a store to make a quick purchase, maybe it's a candy bar or a can of soda pop. You pick something up for 75 cents. Then, just to the side you notice a small ad for a similar product that reads, 'New larger size, only 95 cents!' Now what? Do you go with your original item or switch? Which is the better deal? Is bigger always better?
In this lesson, to help you compare prices, you'll learn how to figure out the price per unit of an item to help you compare prices. You'll investigate what other factors might be considered besides just price per unit - 'The Best Deal' might not be what you actually want to purchase! You will also create a price per unit problem for others to solve.
The key to comparing prices is to break the cost down to a price per unit. For example, a 20 ounce bottle of soda pop may cost $0.95 and a 12 ounce bottle of soda pop may cost $0.75. To determine the better deal, you want to compare the price per unit (in this case, the price of one ounce of soda pop). To find this, divide the price by the number of units.
For the 20 ounce bottle, you divide $0.95 by 20. This equals $0.0475 per ounce of soda pop. In this lesson we will round to the nearest penny, so the answer would be rounded to $0.05 per ounce of soda pop.
For the 12 ounce bottle, you divide $0.75 by 12. This equals $0.0625 or $0.06 per ounce of soda pop. Which one is the better deal?
Your teacher may have other examples to help you learn this process. Can you think of your own example?
Now that you know how it's done, practice comparing prices by taking the Best Deal Challenge. You may want to use a calculator to help you, although some problems can be solved using mental math. Look at this short story (to precede through the interactive story use the right arrow key on your keyboard). Are there ever times when you would choose to not take the best deal?
The next time you go to a grocery store, take along a calculator to determine the price per unit of some items you or your family might purchase. Some grocery stores already have this information posted for you (you may want to check to see if they are right!). Bring this information back to your class; discuss it with others to explain how determining price per unit influenced your shopping decisions. Where else could you apply what you learned in this lesson?
Now that you've completed the Best Deal Challenge and know how to determine price per unit, it's your turn to create a price problem. Use The Best Deal worksheet or simply take a blank sheet of paper. Fold the worksheet over to the dashed line (or fold a paper in half) so it covers the answers. On the front cover of the sheet, either draw or write a problem like the one you've just completed. On the inside, reveal the correct answer and list the correct price per unit of each item. After your teacher has checked your work, share your problem with classmates for additional practice.
1. If possible, take a class field trip to a store for more practice, or bring in items to create a class store.
2. For a project idea, create a multimedia project similar to the Best Deal Challenge. One slide or card could show a problem, and the choices could be linked to the answers.
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PatrickHaller/fineweb-edu-plus
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How to Solve Inequalities
In this page we are going to discuss about solving inequalities concept . Math problems contain <,>,<= and >= are
called How to Solve Inequalities
of inequalities are a set of two or more inequalities with the same variables. An
inequality says that two values are not equal. a ? b says that a is not equal to b for example,
* a < b says that a is less than b.
* a > b says that a is greater than b.
* a ? b means that a is less than or equal to b.
* a ? b means that a is greater than or equal to b.
Solving algebra inequalities
Below are the examples on solving algebra inequalities - How to Solve Inequalities
Solve for4(x+1) <2x+3
Step 1: It can be written as 4x+4<2x+3. (Subtract 2x on both the sides)
Step 2: 4x+4-2x<2x-2x+3.
Step 3:2x+4<3 (subtract 4 on both the sides)
Step 4: 2x+4-4<3-4.
Step 5: 2x<-1 .so x= -1/2.
Solve for (4x+2) (10-20x)>=0
Step 1: It can be written as (4x+2)>=0, (10-20x)>=0.
Step 2: Now we need to solve x
Step 3: So 4x>=-2, 10-20x>=0.
Step 4: 4x>=-2,-20x>=-10.
Step 5: x>= -2/4, x>=-10/20.
Solve for 9x-72 >0.
Step 1: Here also we need to solve x.
Step 2: So, 9x >72.
Step 3: Now we need to divide using 9 on both the sides. How to Solve Inequalities
Step 4: When we divide we get x>8.
Solving inequalities word problems
Below are the examples on solving inequalities word problems -
Suppose a bangle cost 19a earrings14.Write an inequality to find how many earrings you
can buy along with one bangle if you have $65to spend.
Step 1: the earrings cost & 14 each .so the total cost will be 14*#of earrings(x).
Step 2: Cost of 1 bangle + (14 #of earrings) must be $65.
Step 3: So it can be written as 19+14x to 65
Step 4:14x 65-19
Step 5: so the equation is 14x 46.
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PatrickHaller/fineweb-edu-plus
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Multiplication With Jungle Joe
Joe had some sense that he should build a house in order to survive. "I think I'll make it out of leaves", thought Joe.
He started gathering leaves, until he picked up a big pile of leaves, and there was something else in it besides the leaves. A warm, furry creature jumped out.
"Hi, I'm Saerita the Sloth!"
"Hi, my name is Joe. I'm a mad scientist on vacation. You don't look like a sloth, you look demented."
"That's because I'm a cross between a sloth and some unknown animal. Interesting place for vacation. What are you doing?"
"I'm trying to make a house out of leaves, because I'm lost and I want to go home."
"I know how you can get home. Use your multiplication skills... You do know how to multiply, right?"
"Sorry, I never past the 3rd grade."
"I'll teach you how! That's one of the first steps of getting out of the jungle!"...
How To Do Multiplication
1. Look at the problem. For example- 376 x 9. You are trying to find out how much there is in 9 groups of 376
2. Line your numbers of as shown.
3. Start at the first number and in 376 and multiply it by 9. Then, do the same with every number in 376, going right to left. If you have a number bigger than 10, you carry it to the next place and then add it to the number it is above, just like when you carry numbers in addition. For example, 9 x 6 = 54, so you would put the 5 over the 7 in 376. The 4 would go below the 9.
4. Repeat with every number. For example, 7 x 9= 63. You would add 5 to 63 which is 68. Then, carry the 6 over the 3 and put the 8 by the 4.
5. Lastly you would multiply 9 x 3= 27. You would add 6 to that, and the answer is 33. Because this is the last number you have to multiply, you don't carry the number, you just put it in your answer.
6. To Finish of the problem, put a comma in for every 3 numbers. So, there would be a comma in between the two 3. Your final answer is 3,384.
You Rock At Multiplication!
Didn't Get it? Feel free to go to the practice page.
If you don't understand the words on this page go to the dictionary page!
Dictionary with Dick
Introduction: This page will teach
you about advanced multiplication, with Saerita the Sloth
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PatrickHaller/fineweb-edu-plus
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It is helpful to have an understanding of the mean, median and the mode prior to beginning work with Stem and Leaf Plots.
What is A Stem and Leaf Plot Diagram?
Data can be shown in a variety of ways including graphs, charts and tables. A Stem and Leaf Plot is a type of graph that is similar to a histogram but shows more information. The Stem-and-Leaf Plot summarizes the shape of a set of data (the distribution) and provides extra detail regarding individual values. The data is arranged by place value. The digits in the largest place are referred to as the stem and the digits in the smallest place are referred to as the leaf (leaves). The leaves are displayed to the right of the stem. Stem and Leaf Plots are great organizers for large amounts of information.
What Are They Used For?
They are usually used when there are large amounts of numbers to analyze. Series of scores on sports teams, series of temperatures or rainfall over a period of time, series of classroom test scores are examples of when Stem and Leaf Plots could be used.
What Does a Stem and Leaf Look Like?
|Test Scores Out Of 100|
|9||2 2 6 8|
|7||2 4 6 8 8 9|
|6||1 4 4 7 8|
|5||0 0 2 8 8|
What does this Stem and Leaf Plot Show?
The Stem shows the 'tens' and the leaf. At a glance, one can see that 4 students got a mark in the 90's on their test out of 100. Two students received the same mark of 92. No marks were received below 50. No mark of 100 was received. When you count the total amount of leaves, you know how many students took the test. The information is nicely organized when a Stem and Leaf Plot is used. Stem and Leaf Plots provide an 'at a glance' tool for specific information in large sets of data, otherwise one would have a long list of marks to sift through and analyze.
More Than One Set of Data?
To compare two sets of data, you can use a 'back to back' Stem and Leaf Plot. For instance, if you wanted to compare the scores of two sports teams, you would use the following Stem and Leaf Plot:
|0 3 7 9||3||2 2|
|2 8||4||3 5 5|
|1 3 9 7||5||4 6 8 8 9|
The tens column is now in the middle and the ones column is to the right and left of the stem column. You can see that the sharks had more games with a higher score than the Tigers. The Sharks only had 2 games with a score in of 32. The Tigers had 4 games, a 30, a 33, a 37 and a 39. You can also see that the Sharks had the highest score of all - a 59, compared to the Tigers with a 57.
Stem and Leaf Plots enable you to find medians, determine totals, and determine the modes.
Try your own Stem and Leaf Plot with the following temperatures for June. Determine the median for the temperatures.
77 80 82 68 65 59 61
57 50 62 61 70 69 64
67 70 62 65 65 73 76
87 80 82 83 79 79 71
|5||0 7 9|
|6||1 1 2 2 4 5 5 5 7 8 9|
|7||0 0 1 3 6 7 7 9 9|
|8||0 0 0 2 2 3 7|
Begin with the lowest temperature.
The lowest temperature of the month was 50. Enter the 5 in the tens column and a 0 in the ones column. What's the next lowest temperature? It's 57, enter a 7 in the ones column, next is 59, enter a 9 in the ones column.
Now, find all of the temperatures that were in the 60's, 70's and 80's.
Enter the rest of the temperatures sequentially until your Stem and Leaf Plot contains all of the data. It should look like the one on the left.
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PatrickHaller/fineweb-edu-plus
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Students should begin learning to read through an explicit phonics
lesson. They need to learn the correspondence between letters and
phonemes. Vowels are the most difficult for students to learn because
there is not a one to one correspondence between the letter and its
phoneme. This lesson is designed to help students learn short a.
Class set of A Cat Nap
poster for tongue twister
Letterbox for teacher
Individual letterboxes for students
Letters: a, b, c, d, g, h, k, l, m, n, p, t, v
List of words for Letterbox Lesson
List of words for assessment
Today we are going to talk about the letter a. When we say the letter
a, we hear /a/. Can everyone say /a/? Lets say it together: /a/.
Exactly. It sounds like when you scream on a roller coaster:
/a/a/a/a/a/a/a/. Do you make that sound when you ride a roller coaster?
Lets all say it together: /a/a/a/a/a/a/a/a/a/a/a/a/a/! Great Job!
2. Tongue Twister:
Ally the alligator asks for an apple.
I am going to read the tongue twister on the poster. Now I want
everyone to read it together. Great. Now, lets say it one more time.
This time, lets really find the /a/ sound. Stretch out the /a/ when you
hear it. Good!
3. Letterbox Lesson:
What is the letter we have been working with today? Right, a. What
sound does a make? /a/. Now we are going to practice spelling and
reading words with our /a/ sound. Take out your letterboxes and the
letters a, b, c, d, g, h, k, l, m, n, p, t, v and line them up on the
I am going to spell the word hat on my letterbox on the overhead. I
start with /s/, oh that is an s; /a/ /a/, oh that is the /a/ so I am
going to put an a; /t/ /t/ that is a t. There it is /s/ /a/ /t/: sat.
Now I am going to say a word and you have to spell the word and put it
on your letterbox. When you have the word spelled, raise your hand and
I will come check it.
Once all of the words are spelled, I will write the words they spelled
on the board and the students will read them.
4. A Cat Nap:
In this story, Tab the cat loves to nap in weird places. Also, his
owner Sam loves to play baseball. What do you think will happen when
Tab falls asleep in another one of his weird places? You can read this
story either by yourself or with a partner.
5. Writing Workshop
When you finish reading about Tab, write a story about your pet, a
family member’s pet, or your friends pet. Tell me about something silly
the pet did or something fun you did with the pet.
While the students are working on their writing workshop I will call
them over to my desk one at a time to read me the words off of a
prepared list. There will be a combination of words from the letterbox
lesson and pseudo words.
Checklist for Teachers:
Can the students identify /a/ in written and spoken words?
Can the students spell the word lists correctly using the letterboxes?
Can the students decode the /a/ sound in their pseudo test?
Liles, Sarah Frances
Return to the
Letterbox Word List:
Assessment: /a/ word list
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PatrickHaller/fineweb-edu-plus
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“Creaky Door e”
lesson will help beginning readers to learn to spell and
read words. They will learn to recognize e = /e/ in written and
words. They will learn a meaningful representation and practice
and reading words with e = /e/ using a letterbox lesson. Also,
read along with the class and finally be assessed.
Class set and teacher copy of “Red Gets Fed”
Letterboxes: set of 3, 4, 5 for each student and teacher
Letterbox letters for each student and teacher: b, d, e, f, h, l, n, p, r, s, t, t, w
Overhead Projector (for teacher to model letterbox lesson)
Chart with tongue twister: Everybody saw Eddie and the Eskimo enter the elevator on the elephant.
Primary writing paper and pencils
Worksheet (pictures of two choices, which one has the e = /e/ sound in it: egg or bowl, bed or door, elephant or horse, elf or sleigh)
Picture of a door opening
erase markers and dry erase board
1. Begin by showing the students the letter e on the overhead projector. Can anyone tell me what letter this is? Does anyone know what sound this letter makes? Very good! This letter sounds like a squeaky door. Now let’s look at this picture of an old door opening (place on overhead) and imagine the sound it makes while opening. Model the sound for the students while stretching the e = /e/ sound out. Have the class repeat it after me.
2. Show the students the chart with the tongue twister on it. I am going to say this sentence out loud (stretching out the e sound), and then when I’m done I want everyone to follow along and say the sentence with me. When we hear the special e sound, we are going to act like we’re opening an old door with our hands. Can everyone show me how you open a door? Great job! Let’s practice, remember to listen for the e = /e/ sound. Tongue Twister: Everybody saw Eddie and the Eskimo enter the elevator on the elephant.
3. Next, I am going to say some words and I want each of you to listen for the special e sound in the words. I will read both words and then call on good listeners who raise their hands to tell me which word has the special sound in it.
Words: Bed or Floor
Blue or Red
Car or Best
Head or Hair
Raise your hand if you can tell me a word that has the e sound in it. I will write the word on the board and we will say it as a class together.
4. We are now going to use our letterboxes
to practice spelling words with the e sound.
Everyone take out their letter boxes and all the lower case letters.
Watch me as I show an example of how to use our letter boxes. I have placed three boxes on the over head, so
that there are going to be three sounds in my word. This also means
that our mouths
are only going to move three times to say this word. Here is the first
see I hear /b/ first, what letter makes that sound? b. So b
goes in the first letter box. Next I hear the e sound so the
goes in my
Last, I hear d what letter makes that sound? d. Good job!
I want you to use
the letters you
have in front of you to spell the following words. Everyone open their
three squares. The words are ten,
web, pen, red (I will say a sentence with each word
and place the word on the
overhead for everyone to check their spellings after giving
time after each word to spell). Next let’s try our four letter words:
test, help, sent. Last let’s try a big word with five
blend. Great job everyone on all of your spellings!
5. I am going to show you some of
the words that we spelled out in the boxes. I now want to see if you
them to me. (Model the first one.) We are going to start with the e sound. Then we are going to add the r
sound. Now we have re. Finally let’s add the d sound. That spells red. I am going to
put some other words
up here one at a time and I want you to read them for me.
6. Introduce decodable text: “Red Gets Fed.” Have you ever had a pet that liked to beg to eat and get fed lots and lots? Well in this book, Red the dog begs everyone in his family for food. Let's read to see if he gets fed. Have the children break up into groups to read “Red Gets Fed”. The students will take turns reading to each other while I walk around and listen to them read. Watch each child in the room read a page and take notes as they read. If I don’t get around to every child reading since the book is so short, I may have to go around to those I didn’t hear read individually to note their ability.
7. Finally, we are going to write a message about our pet named red. I want you to make up a sentence about this imaginary pet. Remember (model on overhead), this is how we write our e. They can use inventive spelling to write the words.
Assessment: As I go around hearing and noting miscues of each student reading, I will be able to check each child’s reading level by anecdotal notes that I will collaborate throughout the semester to check reading progress. The students will be given a worksheet with pictures on it, some containing the e = /e/ sound in them. The goal will be to circle the picture that contains this sound. After they have circled the picture they will write the word of the picture under it to practice writing the lowercase e. After they have written the word on paper, they will then spell the words into their individual letterboxes.
Cushman, Sheila. Red Gets Fed. Educational Insights: Carson, CA. 1990.
DeNamur, Whitni. /e/ Says the Old Door.
Murray, Bruce. http://www.auburn.edu/rdggenie/letbox.html
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PatrickHaller/fineweb-edu-plus
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What is OpenGL?
In this lesson, you will learn what OpenGL is and how it enables you to program in 3D.
What exactly is OpenGL? It's a way to draw stuff in 3D. It can also be used for 2D drawing, but this site doesn't focus on that. There are better tools for straight 2D drawing, such as SDL and Allegro.
The graphics card is where the 3D computation happens. The purpose of OpenGL is to communicate with the graphics card about your 3D scene.
So why not talk to the graphics card directly? Each graphics card is a little different. In a sense, they all speak different "languages". To talk to them all, you can either learn all of their languages, or find a "translator" that knows all of their languages and talk to the translator, so that you only have to know one language. OpenGL serves as a "translator" for graphics cards.
Next is "Part 0: Getting OpenGL Set Up".
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PatrickHaller/fineweb-edu-plus
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We use many different techniques to graph lines, but one of the most efficient and straightforward, when given the equation of the line, is graphing lines using intercepts. If we are not given a table of values, the easiest two points to find are usually the x- and y-intercepts. Graphing lines using intercepts is not the only method, we can also graph using the slope and the y-intercept.
Whenever you're asked to graph a line, you have a choice of what method you want to use.
Some people like to graph lines by making an X-Y table. That's where you choose X values, substitute them in one by one and find the corresponding Y values. Use those as points and connect them.
Another method you guys might like to use is the slope intercept method. That's where you put your equation into Y equals MX plus B form. Your first doc was at B that's at the Y intercept. From there you count your slope and make another point and you connect them. Be sure to use a ruler.
The method I really want you guys to practice a little bit more and what you're going to see in your homework is this method 3. Finding and connecting the X and Y intercepts.
The way to find X intercept is to substitute Y equals 0. The way to find the Y intercept is to substitute in X equals 0. It doesn't matter what form the equation is in when you start doing that process.
What you're going to end up with is two different points on the two different axes and all you need to do is connect them using a ruler.
So if you guys get used to using all three of these methods you'll get better at being able to tell which method is the best and the most efficient for any given problem.
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PatrickHaller/fineweb-edu-plus
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Ever wanted to know how to multiply other than using a calculator? Well we have put together a brilliant trick that is simple to learn and works every time!
We are going to use lines to calculate 21 X 32
First we look at the left part of the sum, 21.
The first digit, 2 needs to be represented in line format. How? Well we draw two lines diagonally, like so:
If it was 31 then there would have been three lines.
Ok, so now we need to draw a line for the 1 of 21:
So now we have the 21 part of the sum sorted out.
Next we concentrate on the 32 part of the sum.
Not surprisingly we need to draw lines in the opposite direction to the way 21 was drawn.
Let’s look at the 3 of 31:
And finally we add the lines for the 2 of 32:
Right, so we have all the work done that is necessary to calculate the answer to 21 X 32. But how do we know what to do next? Easy. Break the diagram above into three sections, the first section is the left part of the diagram, the 2nd section is the top and bottom intersection and the third is the right intersection. The diagram below should clarify this for you:
Looking at part one circled above, you can see 6 red dots. These dots are there when one line crosses over another one. You can see that there are 6 red dots, this makes up the first part of the answer.
Looking at section 2 there are four red dots at the top section and three red dots at the bottom section. Add them together totalling 7. This makes up the second part of our answer.
Finally, part three. There are two red dots cutting the intersection. The third part of the answer is two.
Putting all these answers together to get 672.
So our answer 21 X 32 = 672
So how did you find it?
This method will also work for larger numbers too. Try 123 X 321 and see how you fair.
So what about when the sum gets bigger? How do we tackle it?
Well let’s take an example of 42 X 37, and having drawn in all the lines we should have an image something like this:
Looking at part one on the left, how many red dots are there?
I count 12.
Part two, how many red lines do you see? I count 34 (don’t worry, this won’t make it any more difficult).
And finally, part three. How many red dots? 14.
so, put the numbers together, in order and you get 12, 34, 14
But, this isn’t the answer yet. We need to have only single digits in each part and to do this you add the tens part to the left hand side. The tens part, for example would be the three of 34 or the 1 of 14.
So to make these numbers be on their own its easier to work from the right to left.
Move the 1 of the 14 to the left, adding the 1 to 34 giving 35. In this movement we have just got our last digit in the answer, 4.
So now our sum looks like this:
12, 35, 4
Next, move the three of 35 across to the left, and adding it to the 12, giving:
15, 5, 4
And finally, notice that we cannot add the 1 of 15 to anything on the left hand side, so we know we have reached the end of the calculation. All we need to do now is remove the commas and we have our answer.
So 42 X 37 = 1554
And that’s how you multiply numbers using lines!
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PatrickHaller/fineweb-edu-plus
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Teach how to write the word names for numbers zero through ten with this easy to follow worksheet.
Practice number words with your class with this fun worksheet. Show the number words on the board or a chart with the number next to it. Practice reading and saying the words out loud. Use this sheet to help write the number words independently.
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PatrickHaller/fineweb-edu-plus
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|A wedge is
a simple machine shaped like an inclined plane. A wedge
is actually like a moving inclined plane. An easy way to
see how a wedge works is to think of it as an inclined
plane standing on its narrow end. A fairly weak force,
applied to the wide end of a wedge whose narrow end is
being pushed into something, will send a strong force
pushing out at the sides. An example would be to take a
wedge of steel and bang it into the end of a log, the log
will split open. We can use the wedge action to cut and
shape ice and wood sculptures, clay or whatever.
A wedge may seem like a simple tool. But the wedge is very important while doing work, crafts, or at play. Yes, even play! A shovel is acting as a wedge while you're shoveling the sand or snow that you're playing in. I think you'll agree that it's a lot easier to move an object using a wedge than if it were moved by only your hands.
TRY THIS EXPERIMENT
To see how a wedge works, hold the point of a nail on top of a piece of thick cardboard. Press the nail down against the cardboard. The point enters the cardboard first and makes a path for the larger part of the nail to enter and separate the paper.
ON YOUR OWN
Make a list of different wedges you have around your home or in your classroom.
Wedge - You can use a wedge to split a block of wood, by driving it into the wood with a hammer.
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The Old Creaky Door
Rationale: This lesson will help beginning readers to learn to spell and read words. They will learn to recognize e=/e/ in written and spoken words. They will learn a meaningful representation and practice spelling and reading words with e=/e/ using a letterbox lesson. Also, they will read a new book.
Letterboxes, set of 3, 4, and 5 for each student and teacher
Letterbox letters for each student and teacher: (p,e,n,r,d,b,t,l,l,m,s,f)
Picture of creaky door
Poster with tongue twister: Everybody saw Eddie and the Eskimo enter the elevator on the elephant.
Book Red Gets Fed for each student
Worksheet with pictures for assessment (pictures of two choices, which picture do you hear e=/e/? (egg or bowl, bed or door, elephant or horse, elf or sleigh)
1. First, I will show the students the letter E on the overhead projector. I will use the upper and lower case E from my set of letterbox tiles. "Can anyone tell me what letter this is?" "That's correct, it is the letter E." "Who can tell me what sound it makes?" "Wow, you guys are so smart!" Now I will place the picture of the creaky door on the overhead. "The e=/e/ makes the sound /e/ like you are opening a creaky door." I will then stretch out the E sound to sound like an old creaking door. "Now I want everyone to open their old creaky door with me, ready?"
2. Next, I will show the tongue twister on the overhead projector. "I am going to read this silly sentence to you and then I want you to read it after me." I will read the sentence stretching out the /e/ to sound like a creaky door. "Now it's your turn to repeat after me: Everybody saw Eddie and the Eskimo enter the elevator on the elephant.
3. Now, I want you to pay really close attention because I am going to ask you some questions. "I am going to read two words to you and I want you to be listening for the creaky door /e/. After I read the words, I want you to raise your hand and tell me what word you heard the creaky door in."
Rest or Run
Window or Bed
Red or Gold
Head or Nose
4. Hand out letterbox tiles and have students turn them over to the lowercase side. Now I want everyone watch me as I model how to use our letterboxes. For this word, I am going to need three letterboxes. That means there are three sounds in my word. This also means that our mouths are only going to move three times when we say this word. The word is…bed. The b says /b/ so we need to put the letter b in our first letterbox. The second sound is /e/ so we need to put the letter e in the second letterbox. The last sound is /d/ so we need to put the letter d in the last letterbox.
Now it is your turn. The students will being by reading each word and then spelling it.
Words: (3) pen, red, ten, bad (4), smell, left, bark, best (5) spend, slept. The students will use their letterboxes and letter tiles to spell the words. I will walk around the room and monitor the students and help them if needed.
5. I will now have students read words off the overhead projector. I will show a list of words that they spelled in step 3. If a child cannot read a word, I will use body-coda blending to facilitate reading.
6. Next, I will introduce the decodable book: Red Gets Fed. Have any of you ever had a pet that like to beg for his food? Well in this book, Red the dog begs everyone for food. Now lets read the book and find out if Red ever gets fed. The students will break up into groups and read the book. They will take turns reading to each other as I walk around the room and listen.
7. Finally, we are going to write a message about our pet dog named Red. I want each of you to make up a sentence about Red. Remember, this is how we write our /e/. Students may use invented spelling when writing.
As I go around hearing and noting miscues of each student reading, I will be able to check each child's reading level by anecdotal notes that will collaborate throughout the semester to check reading progress. Each student will be given a worksheet with pictures on it, some containing the /e/ sound in them. The goal will be to circle the picture that contains the /e/ sound. Under the picture, they will write the word of the picture.
B.A., and Lesniak, T. (1999) The Letterbox Lesson: A
hands on approach for teaching decoding. The
J Lloyd. (2005). Teach
Decoding: Why and How.
M.Fred's Red Elephants. http://www.auburn.edu/academic/education/reading_genie/constr/lowerybr.html
Cushman, S. (1990). Red Gets Fed. Phonics
Short Vowels. Carson, California: Educational Insights
Return to Encounters index.
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By a student of grade 3.You need:
- white drawing sheets
- tempera paint
Do a step by step guide on the blackboard to make this drawing:
1. Put the sheet in the width for you.
2. Draw a wavy line on 2/3 of the bottom.
3. Place a dot in the middle on the top of the sheet.
4. Draw lines with a ruler from the bottom and sides of the sheet to the dot.
5. Divide the strips in squares.
6. Draw houses and trees on the horizon line.
After this the students can finish their artwork independently. Paint the squares all different and use different patterns. Stpale or paste the artwork on a coloured background.
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Learn the Months
Learning the months needs lots of repetition, so be sure to practice them often. In addition to watching The Month’s Chant video, here are some activity ideas for the home or classroom.
Jump the Months
Type and print a flashcard for each month. Include a picture that represents something that happens during that month, for example a holiday, celebration or a change in the season. If possible, laminate them so they will last longer. Spread the flashcards on the floor and have students help you put them in the correct order. Next, stand in a line next to January and jump to February, March, etc. Listen to The Months Chant and jump to each month in order.
Next, mix up the cards so that students have to jump back and forth to the next month.
If you have a large class, have two students come to the front of the class to jump while the other students help them.
Months Clapping Game
This game works great for 2 to 6 students, if your class is larger than that, split them into smaller groups. Have students sit in a circle. Each student puts their left hand palm up and their right hand palm down resting on the hand of the student next to them. Start by saying “January” and clapping the hand of the student to your right. That student will say the next month as they clap the hand of the student next to them. Continue around the circle saying all of the months of the year in order. Repeat several times.
To add some challenge to the game, every time a student says “December”, the next student should try to move their hand before it can be clapped. If the student moves their hand before the student who said “December” can clap it, the student who said “December” is out and the circle gets smaller. Start from January again. If the student who says “December” is able to clap the hand of the next student, that next student is out. Keep playing until there is only one student left.
You can use this quick and easy game to practice any sequential vocabulary such as the letters of the alphabet, days of the week and counting.
Make a Calendar
What better way to practice the months than to make a calendar of the upcoming year? Include special events, holidays and birthdays for each month. When is the last day of school? The first day? How about the 100th day of school? You can have students draw pictures to represent things that happen during each month. Hang it on the wall and use it to talk about the days, months and holidays.
Do you have other teaching ideas for learning the months of the year? Share them below in the comments!
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To spice up weekly spelling lessons introduce some action by using Response Paddles. Here are three whiteboard spelling activities that keep students engaged and learning:
- Create a worksheet with one sentence for each spelling word. Leave a blank space for the word. For example: We walked _____ the park on the way to my aunt’s house. Hand out the worksheet.
- Read the first sentence aloud and ask for a volunteer to name the spelling word that belongs in the blank.
- Give the students three possible spellings of the missing word. Example: a) though b) thru c) through. (Prepare an overhead transparency ahead of time with the choices or write them on the chalkboard as you do the activity.)
- Have students write the correct spelling of the word on their Response Paddles and hold them up.
- Show students the correct response.
- Students who responded correctly get one point. Students who made the wrong choice should erase and write the correct word.
- When all students have written the correct spelling of the missing word, go on to the next sentence.
- Create a reward system for high point-getters, such as earning free time or one pass on a future spelling test.
- Use Response Paddles on pre-test day.
- Say each spelling word and ask students to write the word on their Paddles.
- Ask students to hold up their Paddles after writing the word.
- Show the correct spelling of word. Tell students who have misspelled the word to write it correctly on a separate piece of paper. This sheet serves as the list of words that will require extra study.
- Continue through the list. At the end of the pre-test, ask students to let you know how many words they added to their list for future study. This gives you a tally of words missed for each student.
Whiteboard Spelling Bee:
- Use words from all previous spelling tests in an all-class Whiteboard Spelling Bee.
- With students in their seats, say a spelling word.
- Give students 30 seconds to write the word on their Response Paddles.
- Have them hold up their Paddles.
- Students who misspell the word are asked to move and stand to one side of the classroom.
- Say the second word. All students — including those against the wall — have 30 seconds to spell the word.
- If a student in the group against the wall spells the word correctly, he/she can take his/her seat.
- Students at the wall who misspelled the word remain and are joined by the students in their seats who misspelled the second word.
- As the number of seated players shrinks to less than half the class, you can focus the game on eliminating only the seated players.
- Continue until one student remains seated.
To print a copy of these instructions, open this PDF file:Spice up Spelling with Paddles.
And let us know how you use Response Paddles to spice up spelling in your classes.
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In this continuation, we’re basically going to go through a bunch of ways to invert functions.
Log is how you invert exponentiation.
Before I get into that, let me talk about a log. First off, every log has a “base.” Symbolically speaking, has base a. The most common base is e, which is denoted “ln” for natural log. Also common is base-10.
Here’s the math of how a log works:
Let’s go through what we’re saying here. The operation you’re doing is “log base a.” We’re telling you “log base a equals y.” What that means is this: if you raise a to y, you’ll get x.
If you think about it, this explains how the log inverts the exponent.
Let’s revisit the phrase above: “if you raise a to y, you’ll get x.” You could also say that as “y is the power to which you must raise a to get x.”
So, now say we have . Now we just rephrase the above as “? is the power to which you must raise a to get . Now, to what power do we have to raise a in order to get ? Obviously, we need to raise it to x. So, the answer is x:
as long as x is real. Correspondingly,
as long as x is positive.
Because we’ve shown it to be true for the general case of base-a logs, it must also be true for any particular base. And this is how you can nicely simplify exponential equations.
Here’s an example:
You can’t solve that with simple algebra. BUT, you know that is simply equal to x! So, we can simplify to:
This could be restated now as “ten raised to the something gets me 23.” There are nice mathematical ways to do this, but don’t worry about it now. In this case, it’s okay to just use the “log” key on your calculator. Usually, if something is just written “log” it refers to base-10. Don’t feel too bad about it. Your grandparents used a slide rule, and their grandparents used a chart.
Now, what would you have done if you were dealing with, say, ? You’d have to use base-2, which is probably not a key on your calculator. Fortunately, there are some simple conversion rules:
3) (where r is any real number)
There is also one restriction to remember: the log of 1 always equals zero. Think about why: When you take the log of 1, you’re asking “what do I have to raise this number to in order to get 1.” The way to do this is to raise to 0. Thus, the log of 1 (for any base!) is always 0.
If you have a log whose base is between 0 and 1, you get a flipped curve. Try to figure out why.
The Natural Log
As I said in the last section, we won’t yet delve into why e is important. But, it is part of a special class of logs called “natural logs” which get their own notation: “ln.”
From what we learned earlier, the following should be clear:
for real x.
for positive x.
And, = 1.
Lastly, they give a very important formula called the change of base formula.
Unfortunately, they give you a particular case, rather than the general case. The way the phrase it might lead you to suspect it’s a quality only of natural logs, and not of logs in general. Here’s the general version:
You can actually deduce this from the above laws of logarithms. See if you can figure out it. If you do, free cookie! If not, it’s in the book :)
Just because they’ve got it there, here’s the version for natural log:
Same deal as before, only now it’s with base-e.
Lastly, I wanna give you some thoughts on logs:
First off, logs tend to be something you skim because they seem a bit confusing. Bad nerd! Bad! Logs are going to come up again and again, and you will use every single rule I listed up there. Much like trig, it’s a subject even smart kids tend to gloss over and fail to understand at a fundamental level.
So, here’s what you need to do: Work a bunch of practice problems until all the log laws are second nature to you. Then, check out graphs of various log functions to get a sense of them. In terms of modeling, an important thing about a log is that it grows extremely slowly. Think about the function y = . For y to equal a giant number, like a trillion, x only has to equal , which is about 40.
Exponential equations rise extremely fast. So, logs rise extremely slowly.
Next subsection: The Dreaded Inverse Trig Functions
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A flat ()
is a sign placed in front of a natural note which lowers the pitch
a half step (1 fret). A lower case B (b) is used to indicate a
flat sign in text documents. There is a half step between E-F
and B-C naturally, so that Fb is the same note as E, and Cb is
the same as B. For now think of these notes by there natural names
only (E and B).
A flat remains in effect for the entire measure, or until it
is canceled by a natural sign ().
Once you cross into the next measure the flat is canceled out.
Flats, sharps and natural signs that temporarily change the pitch
of a note are known as accidentals.
* Note that a courtesy
accidental in parenthesis is often used in the next measure
after a flat of the same letter name is used. This is not necessary
but is often done to avoid confusion.
Q. Hey cyberfret dude... how do I go down
1 fret from an open string (e.g. E down to Eb)?
A. First you have to have a basic understanding
of how the guitar is tuned (see basic tuning) You can't go down
1 fret from and open string, but you can go down 1 fret from the
same note played on a different string. For example when you tune
the 1st string on the guitar, you will play the 5th fret on the
2nd string. The first string open and the 5th fret on the second
string are both E. I you want to play and E flat, just move down
1 fret from the E on the 2nd string.
In the following exercise play the first 2 notes
(A and Ab) with you 4th finger. For all other notes use 1 finger
per fret (1st finger=1st fret, 2nd finger=2nd fret etc...) Be
sure to name the notes to yourself as you play.
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How does gravity work in space?
Yes. When objects are in orbit around each other, there is a strong pull of gravity between them. For example, we commonly say that the Moon is in orbit around the Earth. However, the Moon pulls back on the Earth as well. This changes the Earth a little. One way we see this happening is the ocean tides.
The amount of gravity between two objects depends on the masses of the objects, and also the distance between them. When you have two very large objects like the Moon and the Earth, different parts of them are pulled differently due to distance. The part of the Earth closest to the moon is pulled most. If there are oceans there, they will bulge out. The middle of the Earth is not pulled as strongly towards the moon, but it still is pulled more than the water on the far surface of the Earth. The far side of the Earth is pulled least, making another bulge on the far side of the Earth. As the Earth rotates underneath these bulges, we experience two high tides per day.
Is there gravity in space?
What is an orbit?
What travels in an orbit?
What is gravity?
What is in space?
What is mass?
Why do mass and distance affect gravity?
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Have you ever heard the expression, "solid as a rock"? As it turns out, rocks are not entirely solid. Rocks actually have tiny pockets of air inside them. This is obvious when you look at a piece of volcanic rock (often called basalt), which is full of visible holes. But dense rocks, such as granite, have tiny air pockets inside them, too. These pockets of air are just much smaller.
If you picked up one volcanic rock as well as one granite rock of the same size, you would notice they don't weigh the same. The granite is heavier than the volcanic rock. The many large holes of air in the latter make it less dense—and more porous—than the granite, which also makes it lighter. Something that has more holes in it is more porous. So "porosity" is one characteristic that can help tell you what kind of rock you have.
Rocks—and most other objects, for that matter—are made up of particles of varying sizes that are packed together. In between the particles are spaces that are filled with gas, air or liquid. Particles' shapes and sizes affect how they aggregate, including how tightly they can pack together, which affects a rock's porosity—a property that is the ratio of the volume of a rock's empty spaces to its total volume.
In general, larger particles cannot pack together as well as smaller particles can, which means that packing larger particles together leaves more space for air to fill between the particles. You can imagine this if you have one cup full of marbles and another cup full of sand. You'll be able to see many more spaces between the marbles than between the grains of sand.
• Three clear plastic cups
• Measuring cup
• Rocks that can be sorted into one of three size groups (ideally all of the same type of rock, such as granite)
• Screen (optional)
• Make sure that the rocks are sorted into three different groups by size. The greater the difference in size between the rocks is, the easier it'll be to interpret your results. There should be enough of each group of rocks to completely fill a plastic cup.
• Fill each clear plastic cup to the top with one of the groups of rocks. How much space do you see between the rocks in the different cups?
• Fill the measuring cup with one cup of water.
• Pour the water into one of the cups of rocks, filling the cup to the top.
• How much water is left in the measuring cup? Subtracting the amount left in the measuring cup from one cup will tell you how much volume the air between the rocks took up. How much volume did the air take up?
• To each of the two other cups of rocks, again measure one cup of water, fill each cup of rocks with water, and determine how much volume the air took up.
• How much air did the cup with the largest rocks have compared with the cup with the smallest rocks? How did the volume of air in those cups compare with the volume of air in the cup with the medium-size rocks?
• Extra: You can calculate the porosity of each of the cups of different size rocks you used in this activity. To do this, divide the volume of air taken up by each cup of rocks by the total volume of water the cup could hold (without rocks in it). For example, if the air took up one half cup and the cup could hold one cup total, the porosity would be 50 percent. What is the porosity of each of the cups of the different-size rocks?
• Extra: Soil is a mixture of rocks, minerals and organic matter. Porosity is also a property of soil. Try the same activity using different types of soil: clay, loam, sandy, silty, potting soil, compost, etcetera, but put a screen on top of the cup to keep organic matter from floating out as you pour the water into the cup. Do different types of soils have different porosities?
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Rationale: Children should be instructed and exposed to phoneme awareness in order to have a good understanding of the spoken and written language. In this lesson students can associate sound with letters for spelling and this will enable them to spell words. When students accomplish isolating certain sounds they will be able to recognize which letters make up certain sounds. The focus of this lesson is to help the children identify sh=/sh/.
Materials: Primary paper and pencil; chart with a large sh and “Sherrie works at the shoe shine shop.” and a word list with fish, ship, dish, rainbow, ocean, and water; baby doll; Rainbow Fish by: Marcus Pfister; crayons; and a picture page with: a shoe, ship, dog, fish, pencil, and dish (This will be hand-drawn or created from clip-art.)
1. Introduce the lesson by explaining that letters and combined to create the words we speak, read, and write. How many of you have a baby brother or sister? Has you mom ever said, “Ssshhh, don’t wake the baby.” Well, that /sh/ sound is used in a lot of words and today you are going to learn how to recognize and spell it.
2. “Let’s pretend that this is my baby (hold and rock baby doll while talking). She is sleeping so we have to be very quiet (hold finger to mouth and make the /sh/ sound). Can you all practice making that sound with me? Great job! (Point to the letter combination sh on the chart.) These are the letters that we use to make the /sh/ sound.
3. “Now let’s try a tongue twister. Sherrie works at the shoe shine shop(follow words on a written chart with your finger each time). Can you repeat that with me? Nice! Let’s say it one more time, but this time hold out the ssshhh sound because the baby is still sleeping and we don’t want to wake her. Ssshhherrie works at the ssshhhoe ssshhhine ssshhhop. You are doing a great job.”
4. (Hand out primary paper and pencil). Let’s practice writing the letters that make the /sh/ sound. The first letter in the /sh/ sound is s. To make the letter s we will start just below the roof and make a little c so that it sits on the fence line. Then, go down the sidewalk and make a curve the opposite way. (Model writing the letter s.) Okay, now we need to make the other letter in the /sh/ sound and it is an h. To write the letter h you start just below the roof again and make a straight line all the way to the sidewalk. Then, place you pencil on that line where the fence line is. Bring your pencil out and down to the sidewalk to make a hump. (Model writing the letter h.) That is excellent work. (Place sticker on work). Now I would like you to repeat that combination of letters 4 more times.
5. I will have students practice by reading the word list on the chart. Then the students will read Rainbow Fish . At the end of each page, I will ask them to raise their hands if the recognize a word that has sh in it.
6. For their assessment I will distribute a picture page with a shoe, ship, dog, fish, pencil, and dish (I will draw the pictures for the picture page). I will ask the students to write the name of the object on the line under the picture. Then I will have them color the pictures that have the name with a /sh/ sound.
Reference: Murray, Bruce
(1998). Lessons for Learning to Read (pg. 21)
“Where’s Waldo?” by: Rebecca Crissey
Click here to return to Insights
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Although you can’t get inside your students’ heads and shake up their brains, there are some activities that you can do to make their brains more alert and to help improve learning. Vigorous physical activity gets the blood flowing and releases stress. According to Eric Jensen (BRAIN-BASED LEARNING), children need to “stand up and stretch” every 20 minutes. I think most teachers could use “brain breaks” as well! It’s also important to build cross-lateral exercises into your day. Cross-lateral movements are those in which arms and legs cross over from one side of the body to the other. The left side of the brain controls the right side of the body, and the right side of the brain controls the left side. Both sides are forced to communicate when arms and legs cross over. This “unsticks” the brain and energizes learning.
You can use these activities to start your day, between activities, or whenever your students appear bored or restless. And it certainly wouldn’t hurt to try them before, during, or after testing! They are simple, inexpensive, and might even create some smiles!
Try out one at a time and see how your class responds. Write those they like on a poster or put them on an index card and store them in a “brain break” can. After several weeks, children can choose their favorite exercises and lead the class.
Hint! Most of these are a lot more fun if you do them to some catchy music with a strong beat.
Cross the Midline
Stand with arms at sides. Touch right hand to left knee. Stand with arms at sides and touch left hand to right knee. Count or sing as you do this.
Hint! Put a piece of painter’s tape down the middle of children’s bodies so they can be aware of crossing the midline.
Stand with arms at sides. Bend and touch right elbow to left knee as you raise your leg. Stand and then touch left elbow to right knee.
Feet spread apart and arms extended. Bend over at waist and tap right hand to left foot. Back up and then bend and tap left hand to right foot.
Bend left knee and put foot behind right leg. Reach back around with right hand and touch left foot. Reverse and put right foot behind your left leg as you touch it with your left hand.
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5th Grade Oral Language Resources
Students will:• Learn about the concept of hot air balloons.
• Access prior knowledge and build background about hot air balloons.
• Explore and apply the concept of hot air balloons and how they fly.
Students will:• Demonstrate an understanding of the concept of hot air balloons and how they fly.
• Orally use words that describe the characteristics of hot air balloons.
• Extend oral vocabulary by speaking about hot air balloons and how they fly.
• Use key concept words [helium, hot• air; curvature, atmosphere, altitude, hover, propel, aloft].
Explain• Use the slideshow to review the key concept words.
• Explain that students are going to learn about:
• Hot air balloons.
• The history of hot air balloons.
• Characteristics of hot air balloons and how they fly.
Model• After the host introduces the slideshow, point to the photo on screen. Ask students: What do you see in this photo? (hot• air balloons). How many? (25). Have you ever been in a hot• air balloon? (answers will vary).
• Ask students: How are hot• air balloons an unreliable source of transporation? (They work with the wind. You can't take them to everyday places like school. They take a long time to get to another place.)
• Say: In this activity, we're going to learn about hot air balloons and how they fly. Where would you like to take a hot• air balloon to? (answers will vary).
Guided Practice• Guide students through the next three slides, showing them how hot• air balloons were invented and how they fly. Always have the students describe the benefits of hot• air balloons.
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 students to talk about additional things that they have seen float or sink. After the second game, have them discuss any experiences they have had with taking a ride through the sky.
Close• Ask students: Would you like to fly in a hot air balloon? Why or why not?
• Summarize for students that hot• air balloons are a very fun mode of transportation. Encourage them to think about what it would have been like to see the first hot• air balloon.
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Free computer Tutorials
Microsoft Excel 2007 to 2013
Combining Arithmetic Operators
The basic operators you've just met can be combined to make more complex calculations. For example, you can add to cells together, and multiply by a third one. Like this:
= A1 + A2 * A3
= A1 + A2 - A3
And even this:
=SUM(A1:A9) * B1
In the above formula, we're asking Excel to add up the numbers in the cells A1 to A9, and then multiply the answer by B1. You'll get some practise with combining the operators shortly. But there's something you need to be aware of called Operator Precedence.
Some of the operators you have just met are calculated before others.
This is known as Operator Precedence. As an example, try this:
=(A1 + A2) * A3
Hit the enter key on your keyboard, and you'll see an answer of 150.
The thing to pay attention to here is the brackets. When you place
brackets around cell references, you section these cells off. Excel
will then work out the answer to your formula inside of the brackets,
A1 + A2 in our formula. Once it has the answer to whatever is inside
of your round brackets, it will move on and calculate the rest of your
formula. For us, this was multiply by 3. So Excel is doing this:
So why did Excel give you two different answers? The reason it did so is because of operator precedence. Excel sees multiplication as more important than adding up, so it does that first. Without the brackets, our formula is this:
A1 + A2 * A3
You and I may work out the answer to that formula from left to right. So we'll add A1 + A2, and THEN multiply by A3. But because Excel sees multiplication as more important, it will do the calculation this way:
We have 50 in cell A2, and in cell A3 we have the number 2. When you multiply 50 by 2 you get 100. Add the 25 in cell A1 and the answer is 125.
When we used the brackets, we forced Excel to do the addition first:
(A1 + A2) * A3
Add the 25 in cell A1 to the 50 in cell A2 and your get 75. Now multiply by the 2 in cell A3 and you 150.
One answer is not more correct than the other. But because of operator precedence it meant that the multiplication got done first, then the addition. We had to used round brackets to tell Excel what we wanted doing first. Here's another example of operator precedence.
Substitute the asterisk symbol from your formula above with the division symbol. So instead of this:
= (A1 + A2) * A3
the formula will be this:
= (A1 + A2) / A3
When you hit the enter key on your keyboard, you should get an answer
With the brackets
Without the brackets
Just like multiplication, division is seen as more important than addition. So this will get done first. Without the brackets, Excel will first divide A2 by A3. When it has the answer, it will then add the A1. We used the round brackets to force Excel to calculate things differently. Hence the two different answers. One final example.
Change you formula in cell A5 to this:
= (A1 * A2) / A3
Hit the enter key, and you should get an answer of 625.
Again remove the brackets, and hit the enter key. You'll still have an answer of 625. That's because Excel treats multiplication the same as division: they have equal importance. When this happens, Excel will work out the answer from left to right.
Addition and subtraction are also seen as equal to each other. Try this formula in cell A5:
= A1 + A2 - A3
Now put some round brackets in. Try this first:
= (A1 + A2) - A3
And then see what happens when you try this:
= A1 + (A2 - A3)
Was there any difference? There shouldn't have been. You should have the same answer.
So keep Operator Precedence in mind - all sums are not treated equally!
To give you some practice with combination formulas, have a go at constructing
the more complex Budget spreadsheet in the link below.
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Rationale: When children are learning to read, it is very important they learn to recognize phonemes. Phonemes are the smallest units of sound. Recognizing phonemes helps children to connect letters and phonemes, seeing that letters stand for phonemes. Short vowels are very hard for children to learn because the mouth shape and sound are different. This lesson will help a child identify the phoneme /a/ (short a). A child will learn to recognize /a/ in spoken words by learning a meaningful representation and a letter symbol, and they will practice finding /a/ in words.
Materials: primary paper, pencil, chart with "Adam asked for a cat, an alligator, and a piece of apple pie" written on it, drawing paper and crayon, picture page (drawn by teacher) with bat, cab, ham, hand, bag, dog, ax, rat, pen, frog, pig, the book A Cat Nap (Educational Insights), class set of cards with a on one side and ? on the other.
1. Introduce the lesson by explaining there is a secret code in writing. Learning what letters stand for is the tricky part-as the mouth moves, we make sounds as we say words. Today we are going to focus on the mouth move /a/. When we first begin, it may seem /a/ is hidden in words, but as we continue you will be able to find /a/ in many words.
2. Ask students: Have you ever hit you head and started crying? You say /a/ when you cry. That sound is the sound we are looking for in words. Now pretend you have really hit you head hard and are really crying, stretch it out /a/. I'll pretend I have been hit by a bat, bba-a-a-at. There I cried the /a/ sound, when I said bat.
3. Now, let's try a tongue twister (on chart). "Adam asked for a cat, a alligator, and a piece of apple pie." Everybody say it together. Let's try to say it three times fast. Now say it again, and this time stretch the /a/ at the beginning of the words. " Aaadam aaasked for a cat, a aaaligator, and a piece of aaapple pie." Try it again, and this time let's break /a/ off each word: "/a/ dam /a/ sked for a cat, a /a/ lligator, and a piece of /a/ pple pie." Great Job.
4. (Have students take out primary paper and pencil). We can use the letter a to spell /a/. Let's write it. Start just below the fence, curve up until you touch the fence, go towards the left and draw a curve down to the sidewalk, curve over, and back up to where you started on the fence, without lifting your pencil, draw straight down to the sidewalk. (Model each instruction given). I want to see everybody's a. After I put a sticker on it, I want you to make seven more just like it. When you see "a" all by itself in a word, that's the signal to say /a/.
5. Ask the students these questions and call on them to answer and tell how they knew the answer. Do you hear /a/ in cat or dog? Cab or car? Bad or fear? Rag or clothe? Ham or turkey? Hand or foot? (Pass out a/? card to each student). Say: Let's see if you can spot the mouth move /a/ in some words. Show me "a" if you hear /a/ and ? if you don't. (Give words one by one). Last, stand, fan, big, apple, band, paper, phone, dig, capital, nag, at, game
6. Read A Cat's Nap and talk about the story. Read it again, and have students raise their hands when they hear words with /a/. List their words on the board. Then have each student draw an apple and write a message about it using invented spelling. Display their work.
7. For assessment, give each student a picture page and help students name each picture. Have each student circle the pictures whose name have /a/.
Eldredge, J. Lloyd, Developing Phonemic Awareness. Teach Decoding in Holistic Classrooms. New Jersey: Prentice-Hall, 1995. Pages 50-70.
Reading Genie Website: http://www.auburn.edu/rdggenie (Elucidations-lessons designs from Spring 2002).
Click here to return to Inroads.
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PatrickHaller/fineweb-edu-plus
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Then I got wise, had everyone move to the carpet, and we pulled out the unifix cubes.
Start out by building the base number-26. The first thing we were asked to do was add one more. Students had to specify that we were not adding another 'long' of 10 cubes, but just one single cube.
When we add one more cube and recount the total, we see that we have 27. To do the next one, we have to take away the extra cube first so we are back at the original number.
Now on to the 10s. Once again, we started with the base number- 26. Then my students had to explain why we were adding a 'long' instead of just a 'cube'.
Student- Mrs. Delk, we have to use a long because it has ten. A cube is just one.
Go back to the base number and try 10 less.
I know this might not seem like the hardest lesson, but believe me when I say my students were stumped for a good long while! I can tell we are going to have to have plenty of practice!
** Practice for home- I know you might not have unifix cubes at home ( I know I sure don't!) so try using dimes and pennies. Students can work on making money totals as well as adding and subtracting 10s and 1s.**
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Courtesy G. Lumis
This strong mainstay of the tree begins as a tender stem from which leaves begin to sprout. The trunk is the body of the tree, which not only supports the crown, but in addition internally channels sap and tree food from one part of the tree to another.
A tree grows taller by adding new growth at the tip. In the spring, a new shoot starts to grow at the very tip of the tree. This is called the leader. Its length indicates how much a tree has grow over the course of a year. New shoots grow out sideways from the base of the leader. Each end of each branch has a similar growth of shoots. By summers' end, buds form on the new shoots, and from these buds will develop next year's shoots.
The girth of a tree develops in quite a different way. Between the bark and the wood is a thin soft layer called the cambium. Each year this cambium produces a new layer of wood. You cannot see these layers as they are hidden by the bark. However, the age of cut trees may be determined by counting these layers- called annual growth rings - on the stump.
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PatrickHaller/fineweb-edu-plus
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The Science of Airplane Flight
Return to Physics Index
Charles Watson William H Brown School
54 N Hermitage Street
Chicago IL 60612
After this experience the student should:
1. Be able to define lift, drag, ailerons, rudder.
2. Be able to make a sketch showing the forces which act on an airplane in flight.
3. Be able to explain Bernoulli's principle.
4. Be able to explain how angle of attack is used to increase lift.
5. Be able to identify the control surfaces of an airplane.
6. Be able to explain the movement of air around an airfoil.
Patterns, styrofoam meat trays, scissors, razor blades, sand paper, glue, clay,
paper clips, tooth picks.
Throw a ball into the air a few times then ask:
l. Why does the ball come down?
2. Why is an airplane able to stay in the air?
3 What are the forces acting on an airplane that allows it to stay in the air?
Have students fan themselves with paper, and identify the forces that acted upon
the paper. (thrust, drag).
Have the students hold a piece of notebook paper on the bottom corners. Placing
the paper to their mouths and blow upon it. Then ask:
l. What happens to the paper?
2. Explain your answer.
Have students cut out and put together a puzzle of a plane and compare it with
the labeled model on overhead projector.
Have students make gliders and test fly them. Then ask:
1. Why did the gliders fly?
2. Why did some of the gliders not fly?
Convection box demonstration, use two small juice cans with the ends cut out,
a candle, and a cardboard or wooden box. Use to show up and down drafts.
Pop cans demonstration: have students blow between two pop cans an ask:
1. What happened when you blew between the two pop cans?
Have students build styrofoam airplanes and test fly them and discuss the
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PatrickHaller/fineweb-edu-plus
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Inverse Functions Study Guide
In this lesson, we introduce inverse trigonometric functions. With these, we are able to find the angles of right triangles whose sides are known.
When we plug an angle θ into a trigonometric function like sine, out comes a ratio r of lengths. The inverse sine (written either sin–l or arcsin) is a function that does the exact opposite. If you plug in a ratio r of sides, out will come the corresponding angle θ.
For example, sin(30°) = , so sin–l() = 30°. Similarly, sin(90°) = 1, so sin–l(l) = 90°. In general, if sin(θ) = r, then sin–l(r) = θ.
Said another way, sin–l(r) = the angle θ for which sin(θ) = r.
The one difficulty that arises is that several angles can have the same ratio, for example, sin(45°) = and sin(l35°) = . What should sin–l be? It cannot output two things. To avoid this problem, it has been decided that only angles –90° ≤ θ ≤ 90° can come out of the sin–l function. Because –90° ≤ 45° ≤ 90° (and 135° is not), we have sin–l = 45°. It might help to see the graph of y = sin(x) on and y = sin–l(x) Figure 14.1.
Notice that the second graph is related to the first by reversing the roles of x and y. In general, the inverse function is found in this way, by reversing the x- and y-axes—in other words, "flipping" the graph about the line y = x.
There are also inverse functions to cosine and tangent. The inverse to cos(θ) = r is cos–l(r) = θ), where the angle θ must be 0° ≤ θ ≤ 180° or 0 ≤ θ ≤ π. The inverse to tan(θ) = r is tan–l(r) = 0, where the angle θ must be –90° < θ < 90° or .
cos–l = 60° = because cos(60°) = and 0 ≤ 60° ≤ 180°
Combining Functions with Inverses
We can plug an inverse trigonometric function into a regular function like tan. This asks, "What is the tangent of the angle whose sine is ?" We have already dealt with such questions before, although now we use new notation.
Remember that sin–1 is the angle θ with sin(θ) = . Although we don't know what θ is exactly, we can draw a right triangle with angle θ, as in Figure 14.2.
The opposite side divided by the hypotenuse must be . The easiest lengths to choose are O = 2 and H = 5. Using the Pythagorean theorem, the adjacent side is A = √25 – 4 = √21. Thus,
tan–1(4) = θ, where tan(θ) = 4
The angle θ is sketched in Figure 14.3.
We choose O = 4 and A = 1 so that . The hypotenuse H = √16 + 1 = √17 is found by the Pythagorean theorem. Thus,
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STRATEGIES TO BECOME A BETTER READER
Here are important reading strategies students can use before, during and after reading:
Predict what the book is about from the title. Set a purpose for reading. Ex. I am going to read this book because I want to learn more about animals. Take a picture walk through the book. Ask, What is happening in the pictures?
Visualize - make a movie in your head just like
you do when listening to a story.
Question - think about the story, asking yourself
who, what, when, where, why, how.
· Clarify - understand new words - figure out words using print strategies
o Use finger to point under each word to keep track of where you are reading
o Use beginning sounds to figure out words
o Use ending sounds to figure out words
o Use pictures on the page to help figure out a word
o Use word chunks (group of letters in a pattern like _ack, _ight)
o Look for a smaller word within the word
o Read to the end of the
sentence. Sometimes the word that
sentence or passage to increase understanding
Make predictions - "What happens next?"
· Make connections
o What other story is like this one? (Text to Text Connection)
o Have you felt the same away as a character in the story? Did something similar happen to you? (Text to Self Connection)
o Does it help you think about something in real life not directly connected to you? (Text to World Connection)
· React - What did you think of the story?
o How did it make you
o What was most important
in the story? One way to do this is to think:
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Rationale: To become effective readers and spellers, students must master the alphabetic principle, which states that letters stand for phonemes and spellings map out phonemes. Students must learn to recognize phonemes in order to match them to letters. One phoneme students have trouble with is /p/ because of its relation to /b/. Students often confuse the letters p and b as well as the sounds. This lesson will help students isolate /p/ in spoken words as well as recognize the letter p in written words.
Materials: 1) a fake feather for each student and teacher, 2) primary paper and pencil, 3) sentence strip with "Pam the panda wears a pink parka with purple pants", 4) Dr. Seuss' Hop on Pop, drawing paper and crayons, a die cut of the letter p for every student.
Procedures: 1. Begin the lesson by telling students that letters really stand for sounds that we say. When we say certain sounds our mouth may move in a particular way that can help us identify that sound. Today we are going to learn about how our mouth moves when we say /p/. This sound can come at the beginning, end, or middle of a word, and we are going to work on recognizing in when we hear it.
2. Tell students that the /p/ sound is like the sound an old car makes when it is put-putting down the rode. When we say this sound, our lips come together and we let out a little breath of air. We're going to watch for our lips coming together when we're trying to find this sound in words. Everyone make the noise of our old car put-putting down the road. I'll do it first p-p-p-put, p-p-p-putting down the road. Watch to see if I make that sound in another word: p-p-p-ast. Did my lips come together and did I let out a breath? Yes I did, right at the beginning, very good!
3. Now we're going to try a tongue twister using the sound. Students will hold feather in front of their mouth so that it will move when they say /p/. Teacher models first. "Pam the panda wears a pink parka with purple pants." Let's all say it together once. Now let's say it again and draw out the /p/ like we did before. "P-p-pam the p-p-panda wears a p-p-pink p-p-parka with p-p-purp-p-ple p-p-pants." Good job! (Praise students if they caught the second /p/ in purple and model and correct if not.) Now we're just going to break off the /p/ sound at the beginning. "/p/ am the /p/ anda wears a /p/ ink /p/ arka with /p/ ur /p/ le /p/ ants." Very nice!
4. Tell students to take out their primary writing paper and pencils. Then write the letter p on the board and tell the students that we use that letter to spell /p/. Draw imaginary paper on the board and model how to write it while explaining. First we make a circle, starting at the second floor and going to the first floor. Next we draw a line on the left side of our circle all the way from the second floor down the basement. I want everyone to practice writing a p and let me come around to check it. After I have seen your letter, practice writing it ten more times on that row. Remember that when we see the letter p in a word, we know that we're going to say /p/.
5. Give individual students a chance to say whether they hear /p/ in the following words and how they know: Do you hear /p/ in pan or ran? Sap or sam? Glass or cup? Viper or snake? Now tell students that you are going to ask them questions and the answers are words that have /p/ in them. What do we call a fruit that is ready to be eaten? Ripe. What do we call a farm animal that goes oink and wallows in the mud? Pig. What do we look at to give us directions? Map. In those words, did your lips come together and let out a breath of air? Yes, so all those words have the /p/ sound in them. If they are not recognizing the sounds immediately, use the feathers again.
6. Read Hop on Pop. Tell students to hold up their letter p when they hear the /p/ sound. Then tell students to draw a picture of something that has that sound in it and write a sentence about it.
7. For assessment, have a worksheet with pictures of words that have and do not have /p/ in them. Have students circle the pictures that represent a word with the /p/ sound.
Questions? Email me at [email protected]
Click here to return to Challenges
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PatrickHaller/fineweb-edu-plus
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Rationale: For students to learn to read, they must first recognize what each correspondence says. It is important that students learn vowel correspondences first. Learning letters and their correspondences will lead to successful decoding, reading fluency, and reading comprehension. For this lesson, students will learn to recognize the letter u and the correspondence u=/u/.
*primary paper and pencil for each student
*letter boxes (Elkonin Boxes)
*plastic letters (one set for each child) h, u, n, t, l, c, b, o, k, j, p, s, r, g, c, h, i
*poster with tongue twister printed on it -Tongue twister: Uncle Ugh was upset because he was unable to put his umbrella up.
*Copy of the book Bud the Sub one for each student
*Which word has /u/ in it worksheet (attached).
*9 large pieces of cardstock with the following words written on them: (4) hunt, lunch, block, junk, plus (5) strung, crunch, crust, blink
(1)To engage the students, talk about how the alphabet is our "code" for spoken language. Explain to the students that we will be learning all about the code and the sound for the letter u. Example: Today students, we will be learning the all about the code for the letter u. Talk with the students about how whenever you say u's sound, /u/ your mouth is open about half way and your tongue stays behind your bottom teeth. Have the students say this with you. Example: I want you all to try this with me. Let's say /u/ all together on the count of three. These are some words that have /u/ in them. Model reading the words scrub, tub, truck, and grunt. Teacher should put emphasis on the /u/ sounds in the words.
(2)Students will repeat the tongue twister with me and act as if they are punching themselves in the stomach whenever they hear or say the /u/. Uncle Ugh was upset because he was unable to put his umbrella up.
(3)Pass out the primary paper and pencils to everyone. Explain to the students that we will be learning how to write the "code" for the letter u. (The students should already know the names for the lines on the primary paper, however they may need a review). Example: Students, to write a u on our paper, we are going to start at the fence dip down to the sidewalk and come back up to the fence. Then on the right side of your dip, start at the fence and drop all the way down to the sidewalk again. As the teacher is verbally explaining this, s/he should also be modeling on the board where a primary line should be drawn. After everyone has done it together, have the students try it themselves by finishing out the line with u's.
(4)Next, we will be learning to spell and read some words that have the /u/sound in them. At this point the teacher needs to take up the primary paper and pencils and distribute the letter boxes and the letters to the students. Teacher will model how to spell and read the words crunch, strung, and scrub. Example: Boys and girls, this is how I would spell the word crunch. Since it has 5 sounds, we need 5 letter boxes. In the first letter box I would put a c for /c/. In the second LB, I would put the r for /r/. In the third LB, I would put u for /u/. In the fourth LB I would put the n for /n/. Finally in the last letter box, I would put both c and h for /ch/. Students will spell each of the words listed in the materials list in their letter boxes one at a time with the teacher coming around to make sure that they are correctly spelled. The letter boxes and the letters should be taken away while the students attempt to read the words that the teacher will be holding in the front of the room (these are the cardstocks that have the /u/ words written on them). Students will choral read the words making the punching gesture to their stomachs.
(5) The teacher then needs to take up the letter boxes and the letters and distribute the copies of Bud the Sub. Teacher does a book talk. Example: Bud the sub has a boss named Gus. Gus guides Bud into a tug on accident. Uh oh! What will happen to Bud? You'll have to read to find out. Students will read the book with a partner. Again the teacher will be walking around making sure that everyone is on task. As a review, the teacher will have the students coral read the book and then talk about all the words that have /u/ in them.
(6) Finally, as a review the teacher will talk about what the students learned in today's lesson. Example: I like the way that everyone participated in the lesson today. We talked about u=/u/. What is our gesture for u=/u/? (Students should remember the punching gesture to the stomach). For independent practice and the assessment for this lesson, students will complete a worksheet that has them draw a line from the picture to the word.
Amy Crump Uh...Did I Do That? http://www.auburn.edu/academic/education/reading_genie/persp/crumpbr.html
Vowels: Bud the Sub (1990). Carson, CA (USA) St. Albans, Herts (UK):
to Navigations Index
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