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a) Have students hang the mass over the side of a desk and let the toy walk. Resist the temptation to stop the toy when it gets to the edge! Why doesn't it fall off? How does it "know" when to stop?
b) Remove the mass from the front of the toy. Place the toy on the board. Raise the board to an angle that just causes the toy to walk down the ramp. Use the angle of the ramp and the mass of the toy to calculate how much weight would have to be attached to the string to get it to move forward.
Why does the toy walk?
For the toy to move, you must apply a force that is at least as great as the frictional force trying to stop it. The weight of the mass pulls along the string and provides the force that results in the toy's motion. The string pulls diagonally, though, and only the horizontal component of the force makes the toy move forward.
As the toy gets closer to the edge, the angle of the pull changes. The component of force pulling forward gets relatively shorter, and the component pulling down gets relatively longer.
At the edge of the table, there is no component of force pulling the toy forward, so it stops!
Calculating the pulling mass
When the toy stands on the ramp, the force that causes its motion comes from its weight. The weight vector, however, acts perpendicular to the table top, not the ramp. So again we break the vector into its components. The vector that is parallel to the ramp is responsible for the forward motion of the toy. The triangles created by the ramp and table and by the toy and ramp are similar, and the angles indicated are congruent.
Measure the angle between the board and the ramp as indicated in the drawing above.
Get the mass of the toy. Find the mass of a small paper clip. You are now ready to find the number of paper clips necessary to pull the toy forward. The force required to overcome friction for forward motion can be calculated in the following way:
sin ø = Force pulling /Force toy weight
Force toy weight(sin ø) = Force pulling
Weight of the toy: 0.021kg x 10m/s2 *= 0.21N
Weight of one paper clip: 0.00043kg x 10m/s2 = 0.0043N
To find the force necessary to overcome friction (the Force pulling ), use 0.21N (sin 4o) = 0.015N
0.015N necessary to pull/.0043N per paper clip = 3.4 or 4 paper clips needed to move the toy forward
Attach the four paper clips to the toy, place on a level surface, and check to see if (with an initial push) it continues moving. The toy should move at least until the angle between the string and the toy is reduced to less than 4o.
(* 10m/s2 used for simplicity)
Heidi Strahm Black
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PatrickHaller/fineweb-edu-plus
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Help Your Child Explore Science
Do Science in Your Home
Parents can teach best by asking open-ended questions and taking time to encourage answers.
Observing: Invite young eyes and fingers to notice small details.
- “What shapes do you see in that spider web?”
- “Does the crust on this bread feel different from the crust on that one?”
Classifying: Put things in groups based on their characteristics.
- “Let’s sort the socks by color.”
- “Can you think of a way to divide your toys according to a pattern?”
Predicting: Put ideas about how the world works into words and test them.
- “How long will an ice cube last sitting on the counter?”
- “Will it last longer on another surface?”
Quantifying: Encourage children to quantify the world around them.
- “Who is the shortest person in the family? By how much?”
- “How many steps big is your room? The living room?”
The skills of science can and should be practiced everywhere. But it’s clear from research that children’s minds grow best when the environment is rich and varied. Use open-ended dialogue with your children as you explore the neighborhood, the grocery store, the park, or the local fire station. Field trips need not be long, expensive, or elaborate to help young minds turn to science.
Science is all around us!
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PatrickHaller/fineweb-edu-plus
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Most of the lines you will be graphing will much more complex than simple vertical and horizontal lines. There are many ways to go about graphing these, but we will only work with the two most common methods: plotting points and slope-intercept form.
Graphing lines by plotting points is pretty simple. Just find two or more points - any (x,y) points - on the line and connect the dots.
Although you really only need two points to make a line, finding a third one is often a good idea. If all three points lie in a straight line, you can feel confident that you didn't make a mistake. If the third point doesn’t fit your line, check your work and try again.
Let's start with a simple example:
To find three points on this line, pick any values you want for one variable, plug them into the equation, then solve for the other variable.
Since y is already isolated in this equation, it would be a good idea to start by picking values for x. This will give you a value for x and one for y; an (x, y) point!
Here’s a tip: in the beginning, go easy on yourself and pick nice and simple values for x, like -1, 0, and 1.
|Pick an x value||Plug into y = 2x + 1||Solve for y||(x, y)|
Now that we have our three points, we can plot these on a coordinate grid and connect.
Look Out: although you can graph a line by only plotting two points, it is always a good idea to do at least three. If all three lie in a straight line, you can feel pretty confident that your answer is correct.
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PatrickHaller/fineweb-edu-plus
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Putting on a Play
4th Grade Oral Language Resources
Students will:• Learn about putting on play.
• Access prior knowledge and build background about the significance of putting on a play.
• Explore and apply the concept of putting on a play.
Students will:• Demonstrate an understanding of putting on a play.
• Orally use words that describe the people in a play.
• Extend oral vocabulary by speaking about how to put on a play.
• Use key concept words [play, actors, actresses, narrator, director, role, audition, cast; rehearse, nervousness, playwright].
Explain• Use the slideshow to review the key concept words.
• Explain that students are going to learn about putting on a play:
• What is a play.
• Who is involved in a play.
• How does a play work.
• The purpose of a play.
Model• After the host introduces the slideshow, point to the photo on screen. Ask students: What do you see in this photo? (billboards, lights, ads, etc.) What are the ads about? (plays).
• Ask students: What play do you want to see? (answers will vary).
• Say: A play is a story written to be acted out on stage. There are many people who are involved in a play. Many people go to see plays because of the people in them or because of the story. Have you ever seen or been in a school play? (answers will vary).
Guided Practice• Guide students through the next three slides, showing them the different people involved in a play. Always have the students discuss what the people are doing.
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 their favorite actors and actresses. After the second game, have them discuss the hardest and easiest emotion to show.
Close• Ask students: How are plays different from movies? Explain.
• Summarize for students that plays are great a form of entertainment, just like movies. Both plays and movies involve lots of people, props, and stage settings. However, plays are different from movies since people are acting live and sometimes there is only one set for all the scenes, whereas in the movies, scenes happen in many different places. Encourage them to think about whether they like plays or movies.
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PatrickHaller/fineweb-edu-plus
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This maths worksheet for year 2 children looks at pairs of numbers which make 20. Before doing this children should be confident with, and know by heart, all pairs of numbers which make 10. Once they know these, pairs that make 20 becomes easy; just one of each pair is ten more e.g. 6 and 4: 16 and 4. Being able to work quickly with mental arithmetic is one of the keys to success in school as so much of the maths lesson today is carried out orally and children gain or lose confidence very quickly when answering in front of a whole class.
- Free Year 2 Maths Worksheets
- © 2009 Maths Blog
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PatrickHaller/fineweb-edu-plus
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Write the Sight Words: "When"
When is a good time to help your child learn "when"? This worksheet will help your child improve his reading skills while giving him valuable practice writing. To learn the sight word "when" he will have to trace the different letters in the word and use it in a sentence. After he finishes this worksheet he will have completed a sentence and practiced his handwriting. Learning sight words like "when" will help improve his reading skills.
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PatrickHaller/fineweb-edu-plus
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Adding Pennies, Nickels and Dimes
Main Subject Area: Mathematics
Duration of Lesson: 45 minutes
Additional Subject Area Standard(s):
Large paper coins Pocket Chart (for large paper coins)
Number chart (1-100)
Mint tins (one for each student) 10 pennies, 5 nickels, 5 dimes (real or plastic) for each tin
Price strips (strips of paper with product pictures and prices on them)
Coins Used in Lesson:
Grade Level(s): K-2
- If I went to the store and wanted to buy all these items what do I need to know about them before I can pay? (price of each item)
- Why? (So, you'll know how much money you'll need)
- To do what? (To pay the cashier)
2. Introduce the activity by stating, "Today you'll be adding pennies, nickels and dimes so that you will be able to purchase things you need."
3. Start a discussion about the uses of money:
- What do we use money for in our daily lives?
- What kind of things can you buy with money?
- I can think of some times when I don't actually buy something, but I'm paying for a machine or person to do something for me. Can anyone think of one of these types of purchases? (arcade games, movie, riding public transportation, etc.)
4. Explain that today you'll to be discussing how to use coins to buy certain items. Review coin names and values with class. Which coin is worth the most in value? The least?
5. Hold up one of the grocery items and tell the class that at the grocery store this item cost 47 cents.
- What coins could we use to make 47 cents? (pennies, nickels and dimes) Why?
- What coin would we start with to count out the price of this product? (a dime) Why? (It's worth the most of these three coins, and when we are trying to figure out change, we are always going to start by counting the most valuable coin we can use) - If we start with a dime, what are we going to be counting by (10s)
6. Start counting together by placing the large paper coins in the pocket chart for all students to see.
- If I put in one dime, how much money do I have? (10 cents) If I add another dime, how much money do I have now? (20 cents) If I add another one? (30 cents)And another? (40 cents)
- Should I add another dime? Use the number chart to show the students your goal (47) and how much money you currently have. Why should we or should we not add another dime?
- How much more change do we need to get to 47 cents? (7 cents) What coins do we have that are less than 7 cents? Which is the larger of the 2 coins that are less than 7 cents? If I add a nickel to the 40 cents we already have how much money will I have? Add the nickel to the pocket.
- If I add another nickel is that too much or too little money? So, what coin should we use to get to 47 cents? How many pennies should we add to get from 45 cents to 47 cents? Add 2 pennies to the pocket.
7. As a class count the value of all the coins (10, 20, 30, 40, 45, 46, 47 cents)
8. Gauge the class' comprehension and ask some volunteers to demonstrate how to add coins to find the value of a second product.
9. Have the students work independently to figure out the prices of 2 more items with the change in their tins. Review the rules for using the coins before distributing them.
10. Have your students work in partnersand give each pair 2 price sheets (a strip of paper with a picture of a grocery item and a corresponding price and area for the student to write). One student will count and lay out the coins on the sheet, and their partner will check their work. When the student partner has checked the work, go around to verify the pair's work.
11. Once the work has been verified, the first partner will trace the coins onto the strip and write the value of the coin inside each circle.
12. While the tracing is going on, the second partner can begin to count out the coins for the second product.
13. Repeat the verification and tracing process for this second strip.
14. Allow some of the students to share their work with the class.
15. Review with the class what they worked on today.
Assessment / Evaluation:
Differentiated Learning Options:
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PatrickHaller/fineweb-edu-plus
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Kindergarten Research and Inquiry Resources
• Children will use the computer to do research and inquiry on friends.
• Children will learn more about how friends are alike and different.
• Children will categorize pictures of friends doing things that are the same and things that are different.
• Have children look again at the Website. Give each student two note cards. On one card have them draw a picture of one thing they like to do with their friends. On the other card, have the children draw a picture of things they do that their friends do not do.
• Have children create a new game they can play with their friends. Brainstorm ideas as a class, then make up the rules to the new game and learn to play it as a class.
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PatrickHaller/fineweb-edu-plus
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Sent in by:
Henry of Bakersfield, CA
Catch this ZOOMsci out of the corner of your eye!
- different colored paper
- different colored markers
- big piece of butcher paper or a page of newspaper
- When you see something out of the corner of your eye, that's called peripheral vision.
- To find out how well you can see something moving, or color, shape and detail with your peripheral vision, cut out a different shape from each different color of paper. The ZOOMers used a square, a circle and a triangle.
- Write a different letter of the alphabet on each shape.
- Stand on a piece of butcher paper or newspaper and have a friend draw a semi-circle about arm's length away from your feet.
- Look straight ahead while your friend holds a shape and walks around the outside of the semi-circle she drew.
- Tell her when you first notice anything moving, what shape she has, what color it is and what letter (detail) is on it. Be sure to keep looking straight ahead!
- Ask another friend to write "motion," "color," "detail" or "shape" at those spots on the semi circle where you first saw those things.
- Now switch roles and use a different colored marker to mark the semi-circle for each friend.
- Compare your results. Did you see the same things at the same points on the semi-circle? Did you see each thing in the same order? Did some people see something first but see others last? How good is your peripheral vision? Is it better when you're in a bright room or a dark room? Come up with some ideas to test, and be sure to send your results to ZOOM.
Ready for the sci scoop? The back of your eye is called the retina. The retina has special cells called rods and cones that catch light. You can find rods all over your eye, but most of the cones are in the center. Both rods and cones help you see, but only cones help you see color. When a shape is out to the side, and you look straight ahead, you can only use the corner of your eye-your peripheral vision-to see it. This part of your eye doesn't have very many cones. That's why you can see motion there, but not color. When a shape is closer to the center your vision, you see it with the part of your eye that has more cones, so you can see color. You can also tell what shape it is. When a shape is in front of you, you use the center of your eye to see it, which is packed with cones. That's why it is easier to tell what letter is on the shape.
Keturah, age 10 of Springfield, MO wrote:
I saw better than my sister, Hannah, and she cheated. although I made the cards. I got all of them on one spot bcause I made them.
Anj, age 10 of Toronto, ON wrote:
It dissapeared when it was down I tried too close my right eye and look at the O and the X did dissapear.
Caprice, age 10 of Milwaukee, WI wrote:
I could see the letters, shapes and color at the same time.
Christina, age 11 of Chicago, IL wrote:
I could see almost where my ears are! But then I've practiced a lot. My friends and I did it and used 3 lettered words like "mom" or "the". We had a lot of fun.
Ameya, age 8 of Scottsboro, AL wrote:
I tried the the Peripheral Vision thing it worked. And I found out something not only you can do it with your right eye shut you can also do it with your Left eye shut. The circle is on the left side of the paper when your right eye is shut, right. So the circle has to be on the right side of the paper then you can shut your left eye.
Gracie, age 13 of Opelousas, LA wrote:
Two of my friends and I did it for a science fair project and it was pretty fun, but I don't think we did everything right. If we did do it right, then I had the best peripheral vision.
Samantha & Isaac of Freeport, ME wrote:
It dissiperd with any shapes, letters and small words like: was, hi bye mostley three letter words work the best!
Samantha, age 12 of N. Tonawanda, NY wrote:
I did the same thing and I put a circle on one piece of paper, a square on another and a star on another. The same thing happened on all of them. The shapes disappered at the same disstances when I did it. I was wondering what would happen if you did it with your right eye instead of your left eye. Instead of putting the x on the right put it on the left. So I did it and I got the same results as the left eye. I wonder if it would be different if someone else did it. I wonder if it matters if it makes a difference if you are young, old, wear glasses or have contacks. Will it make a differen then?
Devin, age 12 of Ft.Walton Beach, FL wrote:
I did this for my school science project. I saw the different things easily.
Annie of San Antonio, TX wrote:
You could see the color first then the shape then the letter. It was neat how one came after the other. Some people saw the shape before the color or thought green was blue from the corner of their eye. It was fun to play with your vision.
Rachel, age 12 of Mansfield, MA wrote:
Three of my friends and I tried this experiment. It was interesting, because we each had a different point on the semi-circle where we saw motion, color, or shape. We learned a lot about the retina and peripheral vision.
Mindy, age 13 of Lake Oswego, OR wrote:
When my dad did it, he could not do it with out looking to the side. Maybe thats beacause he has glasses. Me and my mom did OK, but not great. It may be because that we don't have glasses, but we do not have 50/50 vision. My sister with no eye problems at all did great! I think it depnds on if you have 50/50 vision or not.
Mary & Nicholas of Livonia, MI wrote:
We saw the movement and color first and then the shape and then the letter when it was in front of us. We also tried it with a person on each side with different shapes and colors and letters. We found that it's easier if the shape is at the height of your eye and not your shoulder! It was also hard to keep staring forward and not look at the paper.
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PatrickHaller/fineweb-edu-plus
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Taking your pulse is a way to measure your heart rate. When you take your pulse, you are feeling the force of blood as it’s pumped from your heart into your body. You may be asked to take your pulse regularly. Or you may just need to take it when you exercise or when you feel something is wrong.
With your first 2 fingers, press lightly on the inside of your wrist, just below the base of the thumb. You should not be pressing on a bone.
The beats you feel are your pulse. If you can’t find your pulse, try moving your fingers slightly to a new spot.
Count the beats you feel in your wrist as you watch the second hand on a clock. You may be told to count the beats for 6 seconds, then multiply that number by 10. Or you may be told to count for a full minute.
The number you get is your pulse measurement. It is measured in beats per minute (bpm). A normal pulse is between 60 and 100 beats per minute. The beats should be regular (evenly spaced).
Write down your pulse each time you take it. You may be asked to bring your results with you each time you visit the doctor.
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PatrickHaller/fineweb-edu-plus
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What Bees Do at Home
This story is designed to be used with Leader Resource 2, Beehive Poster in Activity 3.
What Do Bees Do at Home?
How do you think bees get into their hives? (Point to the opening in the hive on the poster.)
That's right; the hive has an opening so the bees can go in and out. Last week we talked about doors to our homes that we use to go in and out. The bees' home has a door, also.
Some homes have a room or rooms. Beehives have chambers. Someone made the homes we live in and the beehive had to be made, too. Some people build their own homes; some live in homes that have been made by other people, whose job it is to make homes. The bees make the beehive themselves by producing wax and building honeycombs.
What are some of the things people do in their homes?
(You will probably get most of the desired responses: “eat,” “sleep,” “be safe,” “stay away from rain/snow/cold/heat.” If not, you can ask leading questions. As participants offer responses, describe the bee version of each human activity they suggest.)
Do you eat at home? Bees eat at home, too. Do bees eat with spoons, forks or other utensils? No. Can you show me how you think bees eat?
They eat pollen, nectar, and honey. Some of the worker bees have the job of leaving the hive to find pollen and nectar. After finding it, they store it in sacs on their legs and fly back to the hive, where they share it with all the other bees.
Have you ever gathered vegetables from a garden or picked berries from a bush? Let’s all pretend we are gathering food. (Stand up and pretend to pick vegetables or berries.)
Does someone in your home leave to gather food? Some people farm the land for their food. Others work at other jobs to earn money or goods that they trade for food. No matter how the food is collected, people and bees come home to share their food with their families, communities, or colonies. A colony is what you call a hive of bees. Some colonies have 60, 000 bees! That's a lot of bees to feed!
Bees rest and sleep in their hive, much as you do at home. How do you think bees sleep? (Allow participants to show you how they think a bee might sleep.)
Worker bees take care of the young bees and old bees in their hive. People sometimes take care of children and elderly family members in our homes, too.
We need our homes for protection. Beehives give bees protection from rain and storms. The hive protects the bees when it is too cold or too hot outside.
We use our homes to store the things we need to live: like food and clothing. Bees don't need clothes, but the hive keeps their food, like honey, close by, so they can reach it when they need it.
Within the hive, bees have special jobs to do. The drones are male bees that fertilize some of the eggs. There are not too many drones in a hive. Each hive has more drones than queens because there is only one queen in each hive. The queen's job is to lay the eggs and she can lay thousands of eggs a day! The queen also spends time with the worker bees, which help take care of her.
Most of the bees in a hive are worker bees. These are female bees and they do all of the other jobs in the hive. Worker bees feed and take care of the eggs and baby bees. They build the hive. They add on to the hive when it needs to grow, by producing the wax to build the walls of the hive. They keep the hive cool or warm, as needed. They protect the hive from invaders. They leave the hive to search for pollen and nectar from plants, bushes, and trees and bring it back to the hive as food for everyone. They are always working to keep the hive healthy. That’s why people talk about being “as busy as a bee!”
In our homes, we have jobs to do, too. Some people clean and repair the home. Some take care of the young. Some people bring home food and some cook. Our homes provide for many of our basic needs, just like the beehive does for the bees. Bees in a colony also work together to make their beehive a nice place to live.
This work is made possible by the generosity of individual donors and congregations. Please consider making a donation today.
Last updated on Friday, May 17, 2013.
- Session Overview
- Session Plan
- Entire Session (Paper-Saving Version)
- Entire Session
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PatrickHaller/fineweb-edu-plus
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The next most important part of a computer, after memory, is the processor. A processor changes the values in memory as instructed by instructions stored in memory. An instruction is a group of bits (loop values) in memory that tell the processor to do something. A group of instructions that instruct the processor to do some task is called a program.
The simple kind of processor described in this book has only one type of instruction, but that instruction is sufficient to do anything, as will be seen. The instruction is 'copy' (and 'go to'). Each instruction simply copies some bits of data from somewhere in one latch in memory to somewhere else in another latch in memory. The instruction indicates:1. which latch to copy data (data is bit (loop) values) from
2. which latch to copy data to
3. which bits to change in the copied-to latch
4. how much to rotate the 'from' data before copying some of its bits to the 'to' data latch
5. which latches to get the next instruction from.
In the computer considered here, the number of address bits is the same as the number of data bits.
The explanation of the following example will not be clear at first, but just read through it. Then reread it. It will be clear later.
Consider a four-address-bit, four-data-bit memory with the values (in loops) below:
latch bit address values 0000 0100 address of instruction 0001 0001 value of a 0010 0001 not 0 = 1 0011 0000 not 1 = 0 instruction_1 0100 0001 from address 0101 1000 to address 0110 0001 'to' bits to change 0111 1000 instr.addr.and rot.amount instruction_2 1000 0010 from address 1001 0001 to address 1010 0001 'to' bits to change 1011 1100 instr.addr.and rot.amount instruction_3 1100 0000 from address 1101 0000 to address 1110 0000 'to' bits to change 1111 1100 instr.addr.and rot.amount
Only the 1's and 0's are part of the program. The rest is just comments for a person. The latch addresses are just where the program is stored. The bit values are the program.
'Instr.addr.and rot.amount' is short for 'next instruction's address and rotate amount.'
Latch 0000 holds the value 0100 so that the first instruction is in latches 0100, 0101, 0110, and 0111, and is labeled 'instruction_1' in the program. Latch 0000 is special and always holds the address of the next instruction to be executed.
The first word of instruction_1 is in latch 0100 and is 0001. That means that data (bit values) is copied from latch 0001 in memory.
The second word of instuction_1 is in latch 0101 and is 1000 and indicates that the data will be copied to latch 1000.
The third word of instruction_1 is in latch 0110 and is 0001 and indicates that only the rightmost bit, and not the three leftmost bits, of latch 1000 will be changed because only the rightmost bit of 0001 is 1.
The rightmost two bits of latch 0111 are 00 and indicate that the data in latch 0001 will not be rotated at all when data is copied to latch 1000.
The leftmost two bits of latch 0111 are 10 and indicate that the next instruction will be in latches 1000, 1001, 1010, and 1011. That is, instruction_2 will be executed next.
After instruction_1 is executed, the memory has the following bit values.latch bit address values 0000 1000 <-----| address of instruction 0001 0001 ---| | value of a 0010 0001 | | not 0 = 1 0011 0000 | | not 1 = 0 instruction_1 0100 0001 | | from address 0101 1000 | | to address 0110 0001 | | 'to' bits to change 0111 1000 ---+--| instr.addr.and rot.amount instruction_2 1000 0011 <--| from address 1001 0001 to address 1010 0001 'to' bits to change 1011 1100 instr.addr.and rot.amount instruction_3 1100 0000 from address 1101 0000 to address 1110 0000 'to' bits to change 1111 1100 instr.addr.and rot.amount
The underlined loop values (bits) were copied to when instruction_1 was executed. The italics show from where data was copied. The arrows show how data was copied. The rightmost bit of latch 0001 has been copied to the rightmost bit of latch 1000. Also, all bits of latch 0111 (that is, 1000) have been copied to latch 0000 indicating that the next instruction will be in latches 1000, 1001, 1010, and 1011 (instruction_2). That is, after the first instruction, instruction_1, is executed, latch 0000 has value 1000.
The leftmost two bits of latch 0000 are 10, so the instruction executed next is instruction_2, in latches 1000, 1001, 1010, and 1011.
1. Latch 1000 holds 0011, so data is copied from latch 0011.
2. Latch 1001 holds 0001, so data is copied to latch 0001.
3. Latch 1010 holds 0001, so only the rightmost bit of the 'to latch,' latch 0001, is copied to.
4. Latch 1011 holds 1100. The rightmost two bits of 1100 are 00 so the data copied from is not rotated at all. The leftmost two bits of 1100 are 11, so the next instruction to be executed will be in latches 1100, 1101, 1110, and 1111 (instruction_3).
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Example: Solving for a variable Example of solving for a variable
Example: Solving for a variable
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- We are told that the formula for finding the perimeter of a
- rectangle is P is equal to 2l plus 2w, where P is the
- perimeter, l is the length, and w is the width.
- And just to visualize what they're saying, and you might
- already be familiar with this, let me draw a rectangle.
- That looks like a rectangle.
- And if this side's length is l, then this side's length is
- also going to be l.
- And if this width is w, then this width up here is w.
- And the perimeter is just how, what is the distance if you
- were to go around this rectangle?
- And so, that distance is going to be this w plus this l, plus
- this w-- or that width-- plus this length.
- And if you have 1 w and you add it to another w, that's
- going to give you 2 w's.
- So that's 2 w's.
- And then if you have 1 l, and then you have another l,
- that's going to give you, if you add them together, that's
- going to give you 2 l's.
- So the perimeter is going to be 2 l's plus 2 w's.
- They just wrote it in a different order than
- the way I wrote it.
- But the same thing, so hopefully that makes sense.
- Now, their question is, rewrite the formula so that it
- solves for width.
- So the formula, the way it's written now, it says P is
- equal to something.
- They want us to write it so it's, this w, right here, they
- want it to be w is equal to a bunch of stuff with l's and
- P's in it, and maybe some numbers there.
- So let's think about how we can do this.
- So they tell us that P is equal to 2 times l,
- plus 2 times w.
- We want to solve for w.
- Well, a good starting point might be to get rid of the l
- on this side of the equation.
- And to get rid of it on that side of the equation, we could
- subtract the 2l from both sides of the equation.
- So let's do it this way.
- So you subtract 2l over here.
- Minus 2l.
- You're also going to have to do that on the left-hand side.
- So you're going to have minus 2l.
- We're doing it on both sides of the equation.
- And remember, an equation says P is equal to that, so if you
- do anything to that, you have to do it to P.
- So if you subtract 2l from this, you're going to have to
- subtract 2l from P in order for the equality
- to keep being true.
- So the left-hand side is going to be P minus 2l, and then
- that is going to be equal to-- well, 2l minus 2l, the whole
- reason why we subtracted 2l is because these are going to
- cancel out.
- So these cancel out, and you're just
- left with a 2w here.
- You're just left with a 2w.
- We're almost there.
- We've almost solved for w.
- To finish it up, we just have to divide both sides of this
- equation by 2.
- And the whole reason why I'm dividing both sides of this
- equation by 2 is to get rid of this 2 coefficient, this 2
- that's multiplying w.
- So if you divide both sides of this equation by 2, once
- again, if you do something to one side of the equation, you
- do it to the other side.
- The whole reason why I divided the right-hand side by 2 is 2
- times anything divided by 2 is just going to be that
- anything, so this is going to be a w.
- And then we have our left-hand side.
- So we're done.
- If we flip these two sides, we have our w will be equal to
- this thing over here-- equals P minus 2l, all
- of that over 2.
- Now, this is the correct answer.
- There's other ways to write it, though.
- You might want to rewrite this, so let me square this
- off, because this is completely the correct answer.
- This is the correct answer, but there's other ways that
- you might have been able to get this answer, other
- expressions for this answer.
- You might have also, you know, another completely legitimate
- way to do this problem-- let me write it this way-- so our
- original problem is P is equal to 2l plus 2w-- is on this
- right-hand side, what if we factor out a 2?
- So let me make this clear.
- You have a 2 here, and you have a 2 here.
- So you could imagine undistributing the 2.
- So we would get P is equal to 2 times l plus w.
- This is an equally legitimate way to do this problem.
- Now, we can divide both sides of this equation by 2, so that
- we get rid of this 2 on the right-hand side.
- So if you divide both sides of this equation by 2, these 2's
- are going to cancel out-- 2 times anything divided by 2 is
- just going to be the anything-- is
- equal to P over 2.
- So let me just rewrite this over here.
- Let me just rewrite this.
- So we will get P over 2 is going to be equal to l plus w.
- And then if we want to solve for w, we just subtract l from
- both sides.
- And sometimes, you know, you could write it in a separate
- line like this.
- Sometimes you could just write it like this.
- You could say, I'm going to subtract an l on that side.
- If I do it on that side, I have to do it
- on this side, too.
- That's the same thing as adding a negative l.
- And so the right-hand side, you're just left with a w.
- And then the left-hand side, you're going to have, it could
- be a negative l plus P over 2, or you could just change the
- order, and you can write this as P over 2 minus l.
- And this is also an equally legitimate answer.
- And you're probably saying, hey Sal, wait.
- These things look different.
- P minus 2l over 2, that looks different than P
- over 2 minus l.
- And they're not.
- Think about this.
- We could rewrite this as P-- let me do this with the same
- colors-- this over here is the same thing as P over 2
- minus 2l over 2.
- If I have a minus b and they're both being divided by
- 2, I can just separate-- you can imagine I'm distributing
- the division by 2 right over here.
- And over here, 2 times l divided by 2,
- that's just an l.
- So this is going to be equal to P over 2 minus l, which is
- the exact same thing as this right there.
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For a lot of teachers songs are something they only use to give their students a break. However, there's a whole lot more to using songs in the classroom than just taking a pot of correction fluid to the words and creating a cloze gap fill.
In our Song Worksheet Section we have already got a nice collection for you to use for teaching various grammar and vocab items, now it’s time to review creative ways we can use to work with songs in the classroom.
From Abba to Bob Marley there's much more you can do than just play songs in the classroom on a Friday afternoon as a wind down to the weekend: Grammar practice, vocabulary, a change in pace, listening skills, lead-ins to discussions, teaching culture or ethics/values, and much more; the list is almost endless:
With evocative titles they can be used for brainstorming vocabulary. Students can make up a story given the keywords from the song.
Amend the song
Insert wrong words into the song. This can be used with synonyms or antonyms. You could make two versions changing different words in each so that students can check with a partner.
Add extra words into the song
Students must listen and strike out the extra words.
Ordering the song
Cut up the song into manageable chunks and students can reorder as they listen.
Students order pictures representing the song.
Split sentences in two so students must match up the first and second half of sentences.
Using the text of the song
Give the students true or false sentences from the text of the song.
Students find synonyms and antonyms in the song to words given on a handout.
Students select 9 keywords from a selection of about 20 on the board and insert them into a 3 by 3 grid. When students listen to the song they tick the words off until they have 3 in a row and then a full house.
Using keywords the students retell the story of the song in a narrative.
Expand the song
Students can write an extra verse for the song.
Students can compose a verse perhaps using keywords from an original verse and then compare it with the original.
Students can write a letter from or to the singer or a character in the song.
Rhyming words can be extracted from the song.
Weak forms, contractions and unstressed words are commonplace in song lyrics.
Make out a survey for students to rate the song from 1-10. You can include questions like: Does this song make you feel happy? Does it make you feel sentimental? How would you rate the lyrics? How would you rate the tune? Will it be successful? Would you buy it? would you want to listen again? Is it suitable for background music? etc.
You need at least 20 questions. Students answer the question while or after they listen. Next they can write up a review of the song. If you have the facilities you may get them to do different songs or as a homework exercise they can do it at home with a favourite song in English or their mother tongue.
Structures (especially modals and conditionals) and tenses are often repeated in the song. Blank these out as reinforcement of the grammar.
Transfer lyrics from direct to reported speech.
'Ain't' and 'gonna' and other colloquial words which are often neglected in lessons frequently come up in songs.
Blank out all the verbs, adjectives, rhyming words, etc.
Give students a chance to predict the missing words before they actually listen.
Students must choose from a multiple choice which could be used for synonyms or confusing words.
Give the students the missing words in a jumble on the whiteboard.
All the words are blanked out so that students put the song together starting from nothing.
Music without lyrics
Play a piece of music and students write down any words that come into their heads and explain this to the group afterwards. Students draw as they listen and afterwards explain their picture.
Games to play
In pairs students listen for words ending in '-ing', rhyming words, adjectives etc
Play charades using song titles.
Students can act out the story of the song. You need a suitable song and give them time to prepare for this. e.g. 'Don't you want me?' by The Human League.
Are you using any other creative ways of teaching English through songs? Please tell us!
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I really love all your articles, they are amazing!!!
There is another way to work with songs, Cut up the song into manageable chunks, put them on a table and put your students around the table, when they listen to the song they have to take the piece they listened to, the students with more pieces is the winner!!!
I tried another way with my pupils and it worked pretty well (lower intermediate): I blanked out some words and illustrated them with pictures I found on the internet. First they had to make suggestions for the missing words thanks to what the pictures evoked, then we checked by listening to the song. the weak point is that it takes a lot of time searching for the pictures
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Rationale: In order for children to
read and spell they must first understand that letters represent phonemes.
Then once they understand how to recognize phonemes they can learn correspondences.
This lesson will help children become aware that the letter h represents
the phoneme /h/, which is a correspondence. By the end of this lesson
hopefully students will be able to identify the letter h and be
able to recognize the /h/ sound in spoken words.
Materials: primary paper, pencil, poster
with "Harry the hungry, hungry hippo is happily eating ham", book
Horton Hatches an Egg, laminated index card with a popsicle stick glued
on it and the card has the letter h on the front of it, picture page with
pictures of a hippo, baby, hotdog, hammer, apple, head, hat, bear, hand
1. Explain that all letters stand for a mouth movement of sound, which is a phoneme. Today we are going to learn that the letter h makes the /h/ sound. Sometimes when we laugh really hard we can make the sound ha, ha, ha. Do you hear the /h/ sound? Let's see what kind of mouth movement we will make to get the /h/ sound. Everyone make the laughing sound ha, ha, ha. What kind of mouth movement did you make? I felt my jaw move down. Now let's try putting our hand in front of our mouth and see what happens. I felt air coming out of my mouth and blowing onto my hand.
2. Now I am going to read a fun tongue twister (on the chart). Let's all put our listening ears on while I read. "Harry the hungry, hungry hippo is happily eating ham." Did you hear the /h/ sound in any of those words. Now let's all try saying this tongue twister together and listen for the /h/ sound. Very good boys and girls!
3. Now let”s try and stretch out the /h/ sound at the beginning of the words. "Hhhharry the hhhungry, hhhungry hhhippo is hhhappily eating hhham." Great job once again class.
4. Now we are going to try and write the letter h. Everyone take out your primary writing paper and a pencil, but place your pencil flat on your desk. First I would like for you to watch me demonstrate how to write the letter h and then you may try. We are going to start and the very top of the road and draw and line straight down to the bottom of the road. Then we are going to curve up to the middle of the road (the dotted line) and then come back down to the bottom again. Now you may try. I will come around and check to see that everyone is making the correct letter h. Let's try and make at least one row of h's. If you need help just raise your hand. Remember that when you see the letter h in a word it makes the /h/ sound.
5. (Pass out laminated index cards with the letter h on it) "Now class I am going to name some words and some of them may have the /h/ sound and some of them may not. If you hear the /h/ sound then hold up your index card. If you do not then keep your index card flat on your desk. Do you hear /h/ in hat or cage? Street or hum? Bag or ham? Fish or hunt?" After each question say each word slowly one at a time so the students can have time to raise their card or not.
6. Now we are going to read a story called Horton Hatches an Egg. I am going to read the title again and if you hear the /h/ sound touch your nose. (read the title again slowly) Now as I read the story if you hear the /h/ sound again touch your nose. Listen carefully. Now let's reread the book and I will write down the words that have the /h/ sound on the board. When I see you touch your nose then I will know to write down a word. (say the word each time before and after writing it on the board)
7. Assessment: Pass out the picture page with pictures of a hippo, baby, hotdog, hammer, apple, head, hat, bear, and hand. Have the students circle each picture that begins with the /h/ sound. Remind them that each picture should begin with the letter h and the /h/ sound. For early finishers have them draw some more pictures of words that begins with the /h/ sound on the back of their picture page.
Eldredge J. Lloyd. Developing Phoneme Awareness. Teaching decodiing in Holistic Classrooms. New Jersey. Prentice-Hall, 1995. Pp. 50-70.
Click here to return to Openings.
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Students need to be able to recognize letters and
sounds that those letters make in order to read and understand words.
lesson focuses on short a (a = /a/). Students will learn to recognize a
that a = /a/.
book: “A Cat Nap” (Phonics Readers)
sentence strip with “Anna asks for apples”
large bold letters
- Explain that our mouth makes different
formations or movements in order to make different sounds
- have students say /a/ a few times so
that they become familiar with the movement their mouth makes when
saying short a (a = /a/)
- Display the sentence strip and read
“Anna asks for apples” for them, then have them read it with you
- Have students say the sentence
stretching out the /a/. “Aaaannaaa aaaasks for aaaapples.”
- Have students identify what words they
here /a/ in. Do you hear /a/ in mat or mit? Bat or bug? Strap or stuck?
Pass or hut? Etc.
- Pass out pencils and primary paper.
Now teach the students to make an “a”. “Start at the fence, circle down
to the sidewalk, come back up and touch the fence, and move straight
back down to the side walk.” Have them practice this a few times.
- Read the
book “A Cat Nap”. After reading the book once read it again but this
time stop at the end of each sentence and have the students identify
the words they heard that have the a = /a/ sound in them.
- For further assessment have the
students identify different objects in the classroom that have the a =
/a/ sound in their name.
Click here to return to Inventions
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Why Do Objects Float in Orbit?
A spacecraft could go so far from Earth that a person would feel very little gravity. But this is not why things float on the International Space Station. The space station orbits Earth at about 200 to 250 miles high. At that height, Earth’s gravity is still very strong. In fact, a person who weighs 100 pounds on the ground would weigh 90 pounds there.
So why do astronauts float in space? The answer is that they are in free fall. Gravity pulls all objects the same way, even if they are different sizes. If you drop a hammer and a feather on Earth, the hammer will fall faster. But that is not because gravity pulls them differently. Air makes the feather fall more slowly. If there were no air, they would fall together at the same speed. Some amusement parks have free-fall rides. On those rides, a cabin falls along a tall tower. If you let go of a ball at the start of the fall, you and the ball would fall together. The ball would appear to float in front of you! That is what happens in a spacecraft. The spacecraft, its crew and everything aboard are all falling around Earth. Since they are all falling together, the crew and objects appear to float.
How Can Spacecraft Fall Around Earth?
What does it mean to “fall around Earth”? Earth’s gravity pulls objects toward the surface. Gravity pulls on the space station, too. As a result, it is falling toward Earth’s surface. The station also is moving very fast. It moves so fast it matches the way Earth’s surface curves. If you throw a baseball, gravity will cause it to curve down. It will hit the ground soon.
A spacecraft in orbit moves at the right speed so that the curve of its fall matches the curve of Earth. For the space station, that speed is 17,500 miles per hour. The spacecraft keeps falling toward the ground but never hits it. Instead, it falls around the planet. The moon stays in orbit around Earth for this same reason. The moon also is falling around Earth.
from Nasa: What is Microgravity ?, first picture via physics.uiowa, second one Nasa
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Basic Math | Basic-2 Math | Prealgebra | Workbooks | Glossary | Standards | Site Map | Help
Greater Than One ThousandYou made it to one thousand pretty quickly. Good work. You have the basics down. Counting and naming numbers uses the same patterns again and again. One of the great things in math is that it is predictable. It's a little boring if you need to count to ten thousand (10,000) by ones, but it is done the same way over and over again. Always remember that once you hit a "9" and switch to a "0", the value in the column to the left will increase by one. That's the big rule of counting by ones.
So what about numbers greater than one thousand (1,000). Math likes to keep its notation and symbols nice and neat. You will soon see patterns developing. Let's look at the nice round numbers first...
1 - One
10 - Ten
100 - One hundred
1,000 - One thousand
10,000 - Ten thousand
100,000 - One hundred thousand
1,000,000 - One million
10,000,000 - Ten million
100,000,000 - One hundred million
1,000,000,000 - One billion
With so many patterns, let's start with the ONE-TEN-HUNDRED pattern. Numbers are organized by tens. Our entire number system works that way and when you learn more about the metric system, you will learn even more about tens.
Guess what the next number in the above series is. If all of the numbers move from one to ten to one hundred, what next even value would come after one billion? Tick tock tick tock.. Ten billion. Ten billion is a one with ten zeroes after it. The next number would be. One hundred billion. We'll stop there.
Do you see another pattern in that list? Take a look at the commas (,). They come after every three places. The commas make it easier to read large numbers such as millions and billions. Also, whenever you see one of those commas, you know you are reaching a new level of counting. Starting with hundreds you move to thousands, then millions, then billions. Trillions and quadrillions come next, but you won't use them often. Not all countries use commas. European countries use dots between each of the three numbers. It's a little different, but you'll see the same pattern.
Looking at the WordsWe're not going to drag this out. Writing out numbers is a long process that is tedious. You will just need to practice, practice, and practice. You already know the basics and you will just add even larger numbers to the words now.
3 - Three
23 - Twenty-three
423 - Four hundred twenty-three (you could already do this)
1,423 - One thousand four hundred twenty-three (1 and 423)
7,423 - Seven thousand four hundred twenty-three (7 and 423)
37,423 - Thirty-seven thousand four hundred twenty-three (37 and 423)
637,423 - Six hundred thirty-seven thousand four hundred twenty-three (637 and 423)
5,637,423 - Five million six hundred thirty-seven thousand four hundred twenty-three (5 and 637 and 423)
Ugh. It gets a little long writing it out. You get the idea. Right? (1) Counting and naming starts over again after every comma. (2) Numbers between one (1) and ninety-nine (99) often use a dash between the numbers. (3) No commas when you write it out with words.
Once again, practice is the way to learn about naming numbers. When you move forward in math, no one is going to ask you to write out the full names of 15 digit numbers. That's why we have digits in the first place. It makes writing numbers a lot easier.
* The custom search only looks at Rader's sites.
Go for site help or a list of mathematics topics at the site map!
©copyright 2004-2013 Andrew Rader Studios, All rights reserved.
Current Page: NumberNut.com | Basic Math | Counting to Numbers Larger than One Thousand
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Group Activity Cards
Use groups of 3.
Materials: String, index cards, protractor
| Turn, Turn, Turn
Collect at least seven different objects from the classroom. Place them as shown in the figure below. Write the name of each object on an index card. Shuffle the cards and place them face down in a pile. Cut two pieces of string that are about a foot longer than the radius of the circle you made.
One group member selects a card and then stands at the center of the circle. The other two group members stand just outside the circle, beside the point indicated by the X.
The group member in the center of the circle holds one end of both strings. Each of the other group members holds one of the other ends. The group member at the center reads the name of the object on the card, and one of the other group members walks counterclockwise around the circle to stand beside that object. Discuss the angle formed by the string. Is it right, acute, or obtuse? Estimate the measure of the angle formed. Later, use the string and a protractor to check your estimates.
Continue in the same manner, taking turns standing at the center.
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Fill a bag with many objects of various shapes. Have the children take turns picking out an object from the bag. They decide if the object is square or not. If the object isn't a square, see if they can identify what shape it is.
Put different colored shapes made out of construction paper on the floor. Have the children name the shapes as they step on them.
SHAPE STICK PUPPETS
Have children cut out circle, square, triangle, and rectangle. Have them draw faces on each one. Tape the shapes to popsicle sticks. Write the names of each shape on the back.
HIDE AND SEEK SHAPES
Cut various shapes out of paper. Hide the shapes around the room. Let the children search for them. As they find them, see if they can identify the shape of each one they find.
FOOD EXPERIENCES WITH SHAPES
EGG IN A CIRCLE
Tear a hole in the center of a piece of bread. Place in a skillet that has been coated with butter. Put a egg in the hole and fry. Have the children look at the bread and tell you what shape they see.
Give each child a piece of toast. Let them identify the shape. Have them each take a bite. Ask them if all the shapes now look the same.
TRIANGLE CHEESE AND CRACKERS
Serve the children triangle shape crackers and cheese. Have them identify the shapes before they eat them.
RECTANGLE GRAHAM CRACKERS
Give each child a rectangle graham cracker. Let the children spread peanut butter on them.
ASSORTED SHAPED CRACKERS
Serve crackers in various shapes. See if the children can sort them into circle, squares, rectangles and triangles before eating them.
Every know and then make plans to have a shape day with your children. Ask the children to bring in circular objects to display on a round table. Or ask them to wear clothes that contain circular designs.
Cut various shapes out of different colors and patterns of contact paper. Let the children peel the backs off the shapes and use them to create designs on pieces of paper.
Fill a laundry basket with familiar items that have defininte shapes, such as a ball, softball, wooden block, a book, a plastic egg, a cookie cutter, a box, a postcard, a scarf, and a cake pan. Let the children look through the items and sort them by their shapes.
Fill the pages of a magnetic page photo album with a variety of construction paper shapes in different colors and sizes. Set out the book along with a washable felt tip marker. Show the children how to use the marker on the plastic pages to trace the shapes. Clean the pages with a damp cloth after each child's turn.
SHAPE PEG BOARD
Set a piece of peg board on a table. Use a felt tip marker to draw lines between the holes in the board to make large shape outlines. Let the children follow the outlines and insert golf tees in the holes to make the shapes.
SPENCE MAKES CIRCLES BY CHRISTA CHEVALIER
BOXES! BOXES! BY LEONARD EVERETT FISHER
TRIANGLES & SQUARES BY TANA HOBAN
SHAPES BY JOHN REISS
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Center of Mass Introduction to the center of mass
Center of Mass
⇐ 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.
- I will now do a presentation on the center of mass.
- And the center mass, hopefully, is something that
- will be a little bit intuitive to you, and it actually has
- some very neat applications.
- So in very simple terms, the center of mass is a point.
- Let me draw an object.
- Let's say that this is my object.
- Let's say it's a ruler.
- This ruler, it exists, so it has some mass.
- And my question to you is what is the center mass?
- And you say, Sal, well, in order to know figure out the
- center mass, you have to tell me what the center of mass is.
- And what I tell you is the center mass is a point, and it
- actually doesn't have to even be a point in the object.
- I'll do an example soon where it won't be.
- But it's a point.
- And at that point, for dealing with this object as a whole or
- the mass of the object as a whole, we can pretend that the
- entire mass exists at that point.
- And what do I mean by saying that?
- Well, let's say that the center of mass is here.
- And I'll tell you why I picked this point.
- Because that is pretty close to where the center
- of mass will be.
- If the center of mass is there, and let's say the mass
- of this entire ruler is, I don't know, 10 kilograms. This
- ruler, if a force is applied at the center of mass, let's
- say 10 Newtons, so the mass of the whole ruler is 10
- kilograms. If a force is applied at the center of mass,
- this ruler will accelerate the same exact way as would a
- point mass.
- Let's say that we just had a little dot, but that little
- dot had the same mass, 10 kilograms, and we were to push
- on that dot with 10 Newtons.
- In either case, in the case of the ruler, we would accelerate
- upwards at what?
- Force divided by mass, so we would accelerate upwards at 1
- meter per second squared.
- And in this case of this point mass, we would
- accelerate that point.
- When I say point mass, I'm just saying something really,
- really small, but it has a mass of 10 kilograms, so it's
- much smaller, but it has the same mass as this ruler.
- This would also accelerate upwards with a magnitude of 1
- meters per second squared.
- So why is this useful to us?
- Well, sometimes we have some really crazy objects and we
- want to figure out exactly what it does.
- If we know its center of mass first, we can know how that
- object will behave without having to worry about the
- shape of that object.
- And I'll give you a really easy way of realizing where
- the center of mass is.
- If the object has a uniform distribution-- when I say
- that, it means, for simple purposes, if it's made out of
- the same thing and that thing that it's made out of, its
- density, doesn't really change throughout the object, the
- center of mass will be the object's geometric center.
- So in this case, this ruler's almost a
- one-dimensional object.
- We just went halfway.
- The distance from here to here and the distance from here to
- here are the same.
- This is the center of mass.
- If we had a two-dimensional object, let's say we had this
- triangle and we want to figure out its center of mass, it'll
- be the center in two dimensions.
- So it'll be something like that.
- Now, if I had another situation, let's say I have
- this square.
- I don't know if that's big enough for you to see.
- I need to draw it a little thicker.
- Let's say I have this square, but let's say that half of
- this square is made from lead.
- And let's say the other half of the square is made from
- something lighter than lead.
- It's made of styrofoam.
- That is lighter than lead.
- So in this situation, the center of mass isn't going to
- be the geographic center.
- I don't know how much denser lead is than styrofoam, but
- the center of mass is going to be someplace closer to the
- right because this object does not have a uniform density.
- It'll actually depend on how much denser the lead is than
- the styrofoam, which I don't know.
- But hopefully, that gives you a little intuition of what the
- center of mass is.
- And now I'll tell you something a little more
- Every problem we have done so far, we actually made the
- simplifying assumption that the force acts on
- the center of mass.
- So if I have an object, let's say the object that
- looks like a horse.
- Let's say that object.
- If this is the object's center of mass, I don't know where
- the horse's center of mass normally is, but let's say a
- horse's center of mass is here.
- If I apply a force directly on that center of mass, then the
- object will move in the direction of that force with
- the appropriate acceleration.
- We could divide the force by the mass of the entire horse
- and we would figure out the
- acceleration in that direction.
- But now I will throw in a twist. And actually, every
- problem we did, all of these Newton's Law's problems, we
- assumed that the force acted at the center of mass.
- But something more interesting happens if the force acts away
- from the center of mass.
- Let me actually take that ruler example.
- I don't know why I even drew the horse.
- If I have this ruler again and this is the center of mass, as
- we said, any force that we act on the center of mass, the
- whole object will move in the direction of the force.
- It'll be shifted by the force, essentially.
- Now, this is what's interesting.
- If that's the center of mass and if I were to apply a force
- someplace else away from the center of mass, let' say I
- apply a force here, I want you to think about for a second
- what will probably happen to the object.
- Well, it turns out that the object will rotate.
- And so think about if we're on the space shuttle or we're in
- deep space or something, and if I have a ruler, and if I
- just push at one end of the ruler, what's going to happen?
- Am I just going to push the whole ruler or is the whole
- ruler is going to rotate?
- And hopefully, your intuition is correct.
- The whole ruler will rotate around the center of mass.
- And in general, if you were to throw a monkey wrench at
- someone, and I don't recommend that you do, but if you did,
- and while the monkey wrench is spinning in the air, it's
- spinning around its center of mass.
- Same for a knife.
- If you're a knife catcher, that's something you should
- think about, that the object, when it's free, when it's not
- fixed to any point, it rotates around its center of mass, and
- that's very interesting.
- So you can actually throw random objects, and that point
- at which it rotates around, that's the
- object's center of mass.
- That's an experiment that you should do in an open field
- around no one else.
- Now, with all of this, and I'll actually in the next
- video tell you what this is.
- When you have a force that causes rotational motion as
- opposed to a shifting motion, that's torque, but we'll do
- that in the next video.
- But now I'll show you just a cool example of how the center
- of mass is relevant in everyday applications, like
- high jumping.
- So in general, let's say that this is a bar.
- This is a side view of a bar, and this is the
- thing holding the bar.
- And a guy wants to jump over the bar.
- His center of mass is-- most people's center of mass is
- around their gut.
- I think evolutionarily that's why our gut is there, because
- it's close to our center of mass.
- So there's two ways to jump.
- You could just jump straight over the bar, like a hurdle
- jump, in which case your center of mass would have to
- cross over the bar.
- And we could figure out this mass, and we can figure out
- how much energy and how much force is required to propel a
- mass that high because we know projectile motion and we know
- all of Newton's laws.
- But what you see a lot in the Olympics is people doing a
- very strange type of jump, where, when they're going over
- the bar, they look something like this.
- Their backs are arched over the bar.
- Not a good picture.
- But what happens when someone arches their back over
- the bar like this?
- I hope you get the point.
- This is the bar right here.
- Well, it's interesting.
- If you took the average of this person's density and
- figured out his geometric center and all of that, the
- center of mass in this situation, if someone jumps
- like that, actually travels below the bar.
- Because the person arches their back so much, if you
- took the average of the total mass of where the person is,
- their center of mass actually goes below the bar.
- And because of that, you can clear a bar without having
- your center of mass go as high as the bar and so you need
- less force to do it.
- Or another way to say it, with the same force, you could
- clear a higher bar.
- Hopefully, I didn't confuse you, but that's exactly why
- these high jumpers arch their back, so that their center of
- mass is actually below the bar and they don't have to exert
- as much force.
- Anyway, hopefully you found that to be a vaguely useful
- introduction to the center of mass, and I'll see you in the
- next video on torque.
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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Where Food Comes From
Kindergarten Oral Language Resources
Children will:• Learn about the concept of how food gets to the market.
• Access prior knowledge and build background about farmers and markets.
• Explore and apply the concept of how food gets to the market.
Children will:• Demonstrate an understanding of the concept of how food gets to the market.
• Orally use words that describe food, farmers, and markets.
• Extend oral vocabulary by speaking about food, farmers, and markets.
• Use key concept words [farmer, market].
Explain• Use the slideshow to review the key concept words.
• Explain that children are going to learn about how food gets to the market:
• How food gets from a farm to a market.
• How food is grown on a farm by farmers
• What food is grown by farmers.
Model• After the host introduces the slideshow, point to the photo on screen. Ask children: What do you see in this picture? (fruit, vegetables)
• Ask children: How did these fruits and vegetables grow? (answers may vary).
• Say: Today we are going to learn about food, farmers, and markets. Many foods that we eat are grown on a farm and then sold in markets. What do you buy when you go to the market? (answers will vary).
Guided Practice• Guide children through the next four slides, showing them that food is grown on farms by farmers. Always have the children describe what they would like to grow.
Apply• Play the games that follow. Have them discuss with their partner the different topics that appear during the Talk About It feature.
• After the first game, ask children to talk about other fruits and vegetables grown on a farm. After the second game, have them discuss the difference between fruit and vegetables. Then have them give examples of each.
Close• Ask children: What are your favorite fruits and vegetables? Explain.
• Say: We would not be able to eat fruit and vegetables without a farmer growing them. Think about how you would thank a farmer if you saw one today.
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PatrickHaller/fineweb-edu-plus
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Science Main Index
There are about 10,000 different species of crab. The crab is native to all of the world's oceans. There are also freshwater crabs, and even some crabs that live on land. Crabs have a large, hard shell. Extending from the front of its shell are the eyes, mouth and two pairs of antennae. The crab has 5 pairs of legs extending from the side of its shell. The first pair of legs have claws or pincers used to catch and hold food. The other pairs of legs are used for walking. Most crabs don't swim, they use their legs to walk. However, some crabs such as the Blue Crab can use their legs as paddles to swim. Play the following videos to learn more about the crab.
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PatrickHaller/fineweb-edu-plus
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Demonstration of Day and Night
YOU WILL NEED
Globe Small Lego or Stick Figure
Blue Tack or Sellotape
1) In a darkened room, shine the torch onto the globe. Which side is in the light? Which side is in darkness? Why?
2) Spin the globe very slowly anticlockwise (when looking down from the North Pole). How fast does the real Earth turn? How do we know this? Where is it light now? Where is it night?
Find Britain - stick the small figure onto the British Isles. Imagine you are that small figure. Is it day or night? Which direction would the Sun be?
Turn the globe a little - now what time is it for our little person? Is the Sun high or low in the sky? Do you think it is about to get dark?
Pupils who find this concept easy may like to use two or three figures in different parts of the world. Turn the globe very slowly, who goes to bed first? Who has the shortest day?
Back to Earth Contents page>
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PatrickHaller/fineweb-edu-plus
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Step1. Introducing new words (10- 15 minutes)
a. Teacher presents a picture of a farm with farmers, workers, animals and children picking fruits. She attaches it on one side of the board. Teacher points to each picture and says sentences appropriate to those pictures. (Several times appropriate to the new w words)
B. students look and listen
C. each time, the teacher writes a new word on the board
D. students answer the teachers questions about the picture
E. teacher reads new words written on the board and the class repeat them, then individually read the words.
f. teacher points to a picture and class say the appropriate word.
g. teacher may ask a student to come up and point to the pictures and say sentences about them.
h. students take a short vocabulary quiz teacher writes 6 of new words followed by 5 cloze sentences to be completed by students in 1-2 minutes. Five students say the complete sentences individually.
Step 2. reading(about 10 minutes)
a. pre- reading activity: Teacher attaches a picture (of a monkey on top of a tall coconut tree picking ripe coconuts) on the board. She draws students attention to it. she says sentences about the picture and asks several questions about it.
b. Teacher asks the class to have a short look at paragraph one and one student reads the paragraph aloud. Teacher asks the following questions:
T: Are monkeys clever animals? S: yes, They are clever.
T: How do you know? S: They can learn many things.
T: Are they farm hands? S: yes, They are farm hands in same
T: Do they help farmers? S: yes, They help farmers.
C. They same procedure is followed by the teacher and the students for all five paragraphs of the passage.
D. One student reads the whole passage aloud.
E. Teacher asks one or two or three students give a short summary of the passage in several sentences.
F. Students can ask their questions and problems on the passage.
Assignment: For the following session, students must be prepared to read
Pages 20-24 and answer the teachers questions orally.
Step3. structure(about 15 minutes)
On board structure--------------as adjective as
a. Teacher attaches some pictures on the board( 2 boys of the same height , two hens of the same weight, 2 girls of the same age , two planes of the same speed…..)
b. Teacher points to each pair of pictures and says sentences about them.
T: look at these two boys Ahmad and Amir.Ahmad is 150cm tall and Amir is also 150 cm tall. T: look at these two hens. This hen is 5 kilos and that hen is also 5 kilos, and so on . in this way the teacher compares each two pictures.
c. students look and listen
d. Teacher starts from the first pair of pictures and says sentences using as adjective as
T: Ahmad is 150cm tall. Amir is 150cm tall. So we can say : Ahmad is as tall as Amir.
T: This hen is as fat as that hen.
T: This flower is as beautiful as that hen.
Teacher says sentences like the above all the pictures.
e. Teacher asks the class questions about the pictures.
T: Is Amir as tall as Ahmad. S. yes, Amir is as tall as Ahmad.
T: Is this brown plane as fast as the red plane is as fast as the red plane.
Teacher may ask individuals to answer her questions.
D. Teacher writes the rule on the board.
Noun + be( am / is / are / was / were ) + as + noun
E. Teacher may write several sentences obeying this rule .
( depending on the time of the class ).
F. Teacher writes 2 sentences using the same rule to be changed by the adjectives and nouns (pronounces) given.
On board Bob is as young as his friend.
1. fat 2. fast 3. clever
4. thin 5. good 6. tall
Parvin is as clever as Maryam.
1. I 2.he 3.we
4.she 5. you 6.They 7. my sister
Step 4 . Structure
On board structure 2 → adjective er + than……..
a. Teacher attaches some pairs of pictures on one side of the board(2 trees one taller than the other , two women one younger than the other , two cars one newer than the other…..)
b. Teacher points to each pair of pictures one by one and says sentences about them.
T:look at these two trees. The first tree is 7 meter tall and the second tree is 4.5 meters tall. Look at pair and Zahra. Zahra is 30 years old and Pari is 25 years old. In this way.
She compares each two pictures.
C. Students look and listen.
d. Teacher again starts from the first pair of pictures and says sentences using adjective er than structure
T: The first tree is 7 meters tall and the second tree is 4.5 tall.
T: so, the first tree is taller than the second tree.
T: Zahra is 30 and pari is 25.
T: Zahra is older than pari .or pari is younger than Zahra.
Teacher says sentences like the above about all pictures.
C. Teacher asks students questions about the same pictures.
T: Is the first tree taller than the second tree?
S: yes the first tree is taller than the second tree?
T: Is the red pencil longer than the blue pencil?
S: yes, the red pencil is longer than the blue pencil.
Teacher may ask individuals to answer the questions.
d. Teacher writes the rule on the board
. N+ be+ adjective+ er + than+ noun
e. Teacher may write some sentences obeying this rule.
f. Teacher writes two sentences using the above rule to be changed by the given adjectives or nouns. on board
My house is larger than your house.
1.new 2. big 3. cheap 4. small 5. old 6. clean
On board- His bicycle is faster than your bicycle.
1. his car 2. her watch 3. my car 4. our watches 5. motor cycle 6. our watches
g. Teacher wants students to say sentences about objects them selves friends, their families….. using this structure.
Assignment: for the next session , students must be prepared to do the exercises(writing 1,2,3)in class.
[+] نوشته شده توسط محمد الهي
[ دوشنبه پانزدهم فروردین 1390 ] [ 11:19 ] [ گروه زبان ]
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PatrickHaller/fineweb-edu-plus
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Solving equations with radicals, no matter what power, involves isolating the radical on one side of the equation and then raising both sides of the equation to the power of the radical. When solving radicals, the final step is to isolate the variable. If there are more than one radical, we isolate and remove one root, then isolate and remove the other root.finally, we solve the remaining equation for the variable.
Solving equations with a radical. So there's always a couple of steps that we have to do when we're solving equations with radicals, and those are always going to be pretty much the same thing.
First thing we want to do is isolate our radicals. So get the square roots or cube root or whatever it is by itself.
Second we need to get rid of the root and so we're going to take each side to a power. If it has a square root, we want to square both sides, if we have a cube root we want to square both sides so on and so forth. Okay? And the we just want to solve it out.
And lastly we always have to check our answers to make sure they work. So behind me I have a pretty straight forward example and we're going to solve this out, okay? So first thing we want to get our square root by itself. What we have to do is add 3 to both sides. Square root of x is equal to 5. In order to get rid of the square root we need to square. We square one side, we have to square the other to keep it balanced and so we end up with x is equal to 25, okay?
Common mistake is that when we square things people want to put plus or minus. You square something it always turns out positive okay. So it's just that one positive number giving us x25 then we need to check make sure it works. Plug in 25. Square root 25 is 5 minus 3 is 2, okay?
So by going through our steps, isolate our square root, take it to the appropriate power, solve and check. We're able to solve any equation with a radical.
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PatrickHaller/fineweb-edu-plus
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BEFORE READINGRead the title and look at the cover together. "What do you think the story will be about?"
Flip through the pages of the book and discuss together: "What do you think might happen next?"
Praise your child for attempting to make a prediction. "Great idea! I can tell you used the pictures (or other clues) to help you guess what might happen next!"
Comment on how interested you are to learn what does happen in the story. "I'm excited to see if any of our guesses were right! Let's read to find out!"
READING TO YOUR CHILD:
sure your child can see the pictures easily. Use plenty of expression,
reading in a natural speaking voice. Encourage your child to predict
what might happen next as the story develops. As you read, point to
each word, sliding your finger along the text.
READING WITH YOUR CHILD:
reading the story to your child at a speed your child is comfortable
with. As you read, your child will begin to pick up the pattern of the
story and read with you. Encourage your child to point to each word,
sliding a finger from word to word. When your child comes to a
difficult word, ask: "Look
at the picture. What word would make sense?" "Look at the beginning
letter of the word. What word would make sense that begins with that
sound?" "Try reading that whole sentence again. See if you can think
of a word that makes sense."
WHEN YOUR CHILD IS READING:
child may need you to introduce the pattern of the story by reading
aloud initially. Once your child feels comfortable reading, enjoy
listening to the story being read.
Talk about the story: "Were
there surprises?" "What did you like best about the characters or the
happenings or the ending?" Did the story remind you of any other story
or of things that have happened to you?"
Ask your child to retell the story in his/her own words.
Page was last updated on: Wednesday, June 6, 2012
Page has been viewed 79 times since 9-01-2004
Copyright © 2004, Warwick. All rights reserved.
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PatrickHaller/fineweb-edu-plus
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WHY? letters, sounds, math facts, contractions, antonyms, etc.
WHAT? spatula, poster board, markers
HOW? Cut 3 ½” circles out of poster board. Write uppercase letters on one side and lowercase letters on the other. Place the circles on the floor or a table. Children name the letter on one side, and then flip it over to self-check. Hint! Craft foam and corrugated cardboard also make good flippers.
Write words on one side and glue matching pictures on the back.
Write children’s names on one side and glue their picture on back.
Put pictures on one side and initial consonants or vowels on back.
Put sets, number words, or math facts on one side and the answer on the reverse side.
Write antonyms on opposite sides.
Write two words on the front and the contraction on the back.
Use the Downloads button in the menu to get a Flippers pattern.
WHY? numerals, phonics, math facts, words, shapes, colors
WHAT? 5” x 8” index cards
HOW? Write words, letters, numerals, etc. on the left side of the cards going down. Turn over and write the same thing on the back. The teacher calls out a word, letter, etc. and the child “pinches” the correct answer with her thumb and index finger and holds the card up. The teacher can quickly look around the room to check the correct response.
What’s Up, Duck?
Why? initial sounds; vowel sounds; math facts
What? construction paper, marker, pictures from old workbooks
How? Download the pattern and cut ducks out of construction paper. Glue a picture to the body of the duck. Fold down the wing. Open and write the answer under the wing. Children look at the picture, read the word, and then check by lifting the wing.
Use the Downloads button in the menu to get a Duck pattern.
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PatrickHaller/fineweb-edu-plus
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Have you ever seen a hot air balloon floating in the sky? What keeps them up? Why do they have to be so big? Why don't they usually fly in the middle of the day?
If you've ever wondered about these questions, or if you just think "air is a gas," then have I got challenge for you!
What you'll need to play along:
Begin by filling up your ball to its standard pressure. Have a friend hold the meter stick so that it's sticking straight up from the floor. Drop (DON'T THROW) the ball onto the floor from about waist height next to the meter stick. Measure how high up it bounces. Make sure and measure from the bottom of the ball and repeat 2 or 3 times so that you get about the same amount each time. This measurement will be your "control bounce."
Okay, so here's the challenge:
What will happen to the bounciness of a ball if you cool it down or heat it up?
What you do:Begin by predicting what will happen as you either heat or cool the ball. Will a warmer ball bounce higher than a cooler ball? After you make your prediction, place the ball in a refrigerator or cooler with ice for about 15 minutes. Take it out and try bouncing it again. Remember to drop it from the exact same height on the exact same floor and measure the exact same way! How does this number compare to your "control bounce"?
Let the ball heat up to room temperature again and then use the hair dryer to heat it up for about 2-3 minutes. Test it again. Was your prediction right? What in the world does this have to do with a hot air balloon?
Curriculum Focus: Science/Physics/Air and temperature
An introduction to the scientific principles involved in hot air ballooning. This site is primarily for teachers in the elementary grades.
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PatrickHaller/fineweb-edu-plus
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Reading to Learn: Comprehension Strategies
Rationale: In order to gain insight while reading one must be able to comprehend. However, students often fail to comprehend (and remember) what they have read. Because of this, teachers have been given comprehension strategies that can be taught to children in order to give them a helping hand. One such strategy is called story-grammar. The following activity will show children how to use the story-grammar strategy to help them comprehend what they are reading.
Materials: You will need two copies of ten different conventional stories (The Orphan Kittens by Margaret Wise Brown, Oliver Finds a Home by Justin Korman, Bambi by Felix Salten, Paul Revere by Irwin Shapiro, etc.) that the children will find interesting, Charlotte's Web by E.B. White (with highlighted passages for modeling), a question-answer sheet, and a pencil.
Procedure: 1. Explain to the boy's and girl's that today
they will be learning a strategy that will show them how to go about comprehending
what they read.
2. Have each child come up and choose a book from your selection (There should be two children throughout the room with the same book). Next pass out two question-answer sheets to each child. Tell the children to put the book and one of the question-answer sheets under their desk to be used at a later date.
3. Explain to the children that you want them to listen to you read Charlotte's Web. Tell them that after you read for a few minutes, you will stop, think about the first question on the sheet, and then answer it. Explain that you want them to answer the same question at their desk. You will do this throughout the reading of the book.
4. Now begin reading. After reading a few paragraphs (Read only the highlighted passages for modeling) ask the children to answer the first question: Who are the main characters? Give them two or three minutes to answer, and then read on. After you have read a few more passages, ask them to answer the second question: Where and when did the story take place? Continue this until you have read the entire story and the children have answered the other three questions consisting of What did the main characters do?, How did the story end?, and How did the main character feel? Be sure to let the children know there is no right or wrong answer for the question How did the main character feel? because itís is an open-ended question (Depends on readers interpretation of the story). Now have a class discussion about their answers.
5. The second part of the lesson requires the children to read silently (which is very good for a lot of reading skills such as fluency and comprehension) at their desk for ten minutes. (Model reading silent by telling the students to read by thinking the words in their head without saying them out loud). Ask the children to take out the book that they choose earlier along with the second question-answer sheet. Explain to them how you will set a timer for ten minutes, during which time they are to be reading the book they choose. When the ten minutes are up, ask the children to answer the first question on the sheet in front of them. Give them ample time to reflect on what they have read and then set the timer again. Do this throughout the entire book. (You may want to choose shorter stories or treat this as a daily but weekly, meaning they work on the same books all week, assignment).
7. When the children have finished the book and answered all the questions, have them pair up with the other person in the room who read the same book. Explain how you want them to discuss their answers with each other. If there is a disagreement among them, tell them to talk it over to see why. This will help them see how someone else came to their conclusions. Don't forget to read silently along with the children. (You may want to have one of your students read the same book that you are reading and then discuss it with them. If you do this, write your answers in their language). (This will keep them from feeling over-powered).
8. For a review you can ask the children what five questions they should ask themselves, while reading, to help them comprehend what they have read.
References: Pressley, M., Johnson, C. J., Symons, S., McGoldrick, J. A., & Kurity, J. A. (1989). "Strategies That Improve Childrenís Memory and Comprehension of Text. The Elementary School Journal, (1990, Pp. 3-32).
Click here to return to Elucidations
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PatrickHaller/fineweb-edu-plus
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LESSON 1: WHAT ARE ROCKS AND MINERALS?
1. What are rocks and minerals?
2. What are properties of rocks?
3. What are some vocabulary words associated with rocks and minerals?
Ask students what they think of when they hear the word "rock". Elicit a discussion of what they know about rocks. Use their information to make a KWL chart like the one below.
1. Have students look at the following website to find out what a mineral is and what a rock is. The graphic shows that a rock is made of one or more minerals. Explain that is the mineral that gives a rock its properties.
2. Direct students to look at examples of rocks from the following website: http://ivyhall.district96.k12.il.us/4th/kkhp/RocksandMinerals/rocks.html
Ask children to talk about what they see. Ask questions like:
a. Are the colors all the same?
b. Are they all as hard as each other?
c. Do they look as they have the same texture? (feel)
d. Do they shine? (luster)
e. What do you think is the cause for all these differences?
3. Introduce vocabulary associated with rocks and minerals. Have children log on to http://m-w.com or http://cte.jhu.edu/techacademy/fellows/brannon/webquest/gloss.htm
to find the definitions of the following words:
For a student copy of the database, click here.
4. Distribute a set of three different rocks to each group of 4 students. Have them complete an observation sheet for each rock (See student samples and pictures). They are to describe as many properties as possible. (Color, texture, hardness, luster, cleavage).
1. Have your students bring in a rock they have found. They should list as many properties of the rock that they can. Log on to http://geoahead.com/petrology/identifyrock.cfm and use the rock identifier to try and find out what kind of rock they have found.
2. Log on to http://sdnhm.org/kids/minerals/games/index.html and take a mine quiz!
Go to the Rock Doctor's site and find out about the different properties of rocks! Log on here: http://cobweb.net/~bug2/rock1.htm
FOLLOW UP: This lesson leads to lesson 2- "How are rocks formed?
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PatrickHaller/fineweb-edu-plus
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3rd Grade Oral Language Resources
Children will:• Learn about pets.
• Access prior knowledge and build background about different types of animals and how to care for pets.
• Explore and apply the concept of choosing appropriate pets and caring for them.
Children will:• Be able to define what a pet is.
• Orally use words that name types of animals.
• Extend oral vocabulary by speaking about caring for pets.
• Use key concept words [pets, trick].
Explain• Use the slideshow to review the key concept words.
• Explain that children are going to learn about pets:
• What makes an animal a pet.
• How to care for a pet.
• The difference between pets and wild animals.
Model• After the host introduces the slideshow, point to the photo on screen. Ask children: Where do pets live? (in homes with people).
• Ask students: What are some animals that make good pets? (dogs, cats, parrots, etc.)
• Say: Some items that you need to take care of a pet are a collar, bowl, and cage. What are some fun things you can do with a pet? (go for walks, play fetch, pet them, etc.)
Guided Practice• Guide children through the next three slides showing them pictures of various animals. Always have the students identify the animal about and explain why or why not it would make a good pet.
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 if they or any of their family or friends have pets. After the second game, encourage them to share stories they have about experiences playing with pets.
Close• Ask children: What would happen if you tried to keep a wild animal as a pet?
• Say: Having a pet is a big responsibility because you have to take care of it but having a pet is also fun. Write a short story or draw a picture that shows what it would be like to have an unusual pet.
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PatrickHaller/fineweb-edu-plus
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From Jonathan Gardner's Korean Notebook
Phonology refers to the sounds a language makes. Often times, it bears little resemblance to the writing system. Those of you who know English and who can pronounce it correctly know this to be true.
I will introduce the Korean Phonology from my perspective, which is probably different than what you learned before.
Basics of Phonology
Koreans, like every language, distinguish between consonants and vowels. Consonants are sounds like 'k' and 'd', and vowels are the sounds in between, like 'a' and 'oo'.
The Korean consonants are organized rather differently than English and many other languages. Once you understand the Korean consonant system, you will see that other languages use parts of it, even though they don't realize it.
If you look at your mouth, you will notice that your tongue makes different shapes when it pronounces the consonants. Try right now making the following sounds, and note what your tongue and mouth do:
- 'p', 'f', 'th','t', 'k', 'ng'
You'll note that you started with your lips together ('p'), then you touched your lips to your teeth ('f'), and then you touched your tongue to your teeth ('th'), then your tongue to gums immediately behind the teeth ('t'), followed by the middle of your tongue to the top of your mouth ('k'), and then finally, the back of your tongue to the back of your throat.
This is what I will refer to as "mouth position". Many letters in English share the same mouth position, so mouth position is not enough information about what consonant is being made.
Voiced v. Unvoiced?
In English, we distinguish 't' and 'd', which have the same mouth position, by listening whether one is voiced or not. Feel your throat, your vocal chords, with your fingers when you say "t" versus "d". Note that 'd' is voiced, meaning, the vocal chords are vibrating. The 't' sound, however, is unvoiced.
I tell you this because in Korean, speakers and listeners do not distinguish between voiced and unvoiced sounds. It doesn't matter to them. The sound for 'ㄷ' is sometimes voiced, and sometimes unvoiced. They don't care, it's the same sound. If you're wondering, consonants in the beginning of a word tend to be unvoiced, and those in the middle tend to be unvoiced, although in reality they are somewhere in between, never quite reaching the extremes we have for 't' and 'd'.
Koreans do, however, distinguish between aspirated and non-aspirated consonants. Make the shape of 't', and say it with an airy, raspy voice. You should almost be spitting. That's an aspirated 't', or 'ㅌ'. Now, say the same sound, but try to say it so that a piece of paper hanging in front of your mouth only moves slightly. That's non-aspirated 't', or the 'ㄷ' sound.
In English, the 't' sound is sometimes aspirated, and sometimes not, and we don't care which you use. Some words prefer aspiration, some do not, but who cares anyway?
In Korean, aspiration is a critical discriminating factor. You'll have to learn to listen for it, and learn to say it.
Stops / Double Consonants
In English, we have lots of words with double consonants, and it doesn't matter to us. Take the word "hat" and put it next to "top", and say "hattop". In English, those two words just share the 't' sound to make something like "hatop".
In Korean, when you double a consonant, the air and sound have to come to a complete stop. This is represented with the 'ㄸ', which is called ssang (쌍), which means "twin" or "double".
Words that start with ssang consonants must stop everything before making their sound. This produces a very hard, very interruptive sound, almost like you are a stutterer who is finally able to make his words come out. In the middle of a word, it is
Some of the "softer" consonants also double. These are harder to pronounce, and sometimes Koreans have a harder time distinguishing them. Thankfully, it is rare indeed that these make a difference in the word. The way to pronounce these double-consonants is to hold the consonants with a little more force and a little longer than you otherwise would. Or, in other words, have the single-consonants form a slightly softer and quicker sound than you would in English.
With this introduction, the consonants in Korean are ready to be introduced. I've provided the names for them, so you will know what to call them when someone tries to correct your pronunciation.
|p/b||ㅍ (피옆)||ㅂ (비엽)||ㅃ (쌍비엽)||ㅁ (미음)|
|t/d||ㅌ (티읕)||ㄷ (디걷)||ㄸ (쌍디걷)||ㄴ (니은)|
|k/g||ㅋ (키옄)||ㄱ (기역)||ㄲ (쌍기역)||ㅇ (이응)|
There are some miscellaneous consonants as well, that don't categorize in one of the above groups.
|s||ㅅ (시옷), ㅆ (쌍시엇)|
|ch/j||ㅊ (치읓), ㅈ (지읒), ㅉ (쌍지읒)|
Velars (top of the mouth): ㅋ, ㄱ, ㄲ
The first group of words is the k/g sounds. The all share the same mouth shape as k/g in English.
ㅋ is a strong, aspirated 'k': 'kh' is probably the best way to describe it. Since it is aspirated, you should be moving a lot of air when you say it. The 'k' sound in English usually gets interpreted as a ㅋ so be aware that that's what you're starting at as an English speaker.
ㄱ is a very gentle, almost subtle k/g sound. If you start with the 'g' sound in English, then move it a little closer to 'k', you're probably very close to where you should be. Be sure only a little bit of air moves through the mouth with this sound so as to not confuse it with ㅋ. Usually, 'g' in English gets interpreted as ㄱ.
ㄲ is a forceful stop in the shape of 'g'.
Note that at the end of a word, as long as no sounds follow them, these all behave the same since they form the same mouth shape.
Practice: 카, 가, 까, 아카, 아가, 아까, 악
Alveolar (behind the teeth): ㅌ, ㄷ, ㄸ
The t/d sounds ㅌ, ㄷ, and ㄸ all share the same mouth shape. This is similar to t/d in English but is slightly behind them, higher in the mouth. This is the same position as for ㄹ.
ㅌ is strongly aspirated, like ㅋ. Be sure to move a lot of air. Because of the forward position of the tongue, you are likely to create a little spit that flies out of your mouth if you aren't careful. That's a good thing; it means you are doing it right. The English 't' is often translated as ㅌ.
ㄷ is not aspirated. In addition to being made slightly behind/upward where the English 'd' is made, it also has slightly less voice than 'd'. Make sure that only very little air moves through the mouth as you make this sound. The English 'd' is often translated as ㄷ.
ㄸ is a full stop in the ㄷ shape. Be sure to stop all the air and let this one explode a bit when you say it.
Practice: 타, 다, 따, 아타, 아다, 아따, 앋
Bilabials (two lips): ㅍ, ㅂ, ㅃ
These sounds are made with the two lips touching each other. This is exactly the same as the shape of p/b in English, except the lips sometimes do not close completely, making a sound that could be interpreted as f/v. F/v do not exist separately in Korean, so they just sound like a weird way to make these sounds.
ㅍ is aspirated, meaning, a lot of air has to move through your mouth to make it. This is almost an f sound since sometimes the lips don't fully close when making the sound.
ㅂ is not aspirated, and make be voiced or not. Again, the mouth doesn't necessarily close all the way, meaning it may almost sound as a 'v'.
ㅃ makes complete, tight seal, and explodes with some force.
Practice: 파, 바, 빠, 아파, 아바, 아빠, 압
Nasals (nose): ㅁ, ㄴ, ㅇ
The three nasals are represented by ㅁ, ㄴ, and ㅇ.
ㅁ is made with both lips like ㅂ. Just put them together and hum through your nose, like 'm'. However, this consonant is much lighter and quicker than what we are used to in English.
ㄴ is made with the tongue in the same position as ㄷ. Just stick your tongue there and hum, like 'n' except slightly more backward / upward. Like ㅁ, this is lighter and quicker.
ㅇ is made with the tongue in the same position as ㄱ. This is the English 'ng' sound. Like in English, this is usually made with other sounds, so it is lightly and quickly pronounced.
For ㅁ and ㄴ, sometimes the sounds are doubled, and you can hear the speaker doing this with a longer or more heavy pronunciation of the consonant that matches more closely with what we are used to in English. Practice: 마, 아마, 암마, 암, 나, 아나, 안나, 안, 앙.
ㅊ, ㅈ, ㅉ
These are the ch/j sounds. They are made in the same position as ㄷ, which is slightly behind/above where ch/j are made in English.
ㅊ is the aspirated sound, and is an airy ch sound. Note that you shouldn't let the air stop before pronouncing this, otherwise it may sound like a ㅉ.
ㅈ is a 'j' sound that hints at 'ch'. It doesn't move much are at all.
ㅉ is a strong 'j' sound, stopping the air before exploding.
Note that the mouth shape is the same as for ㄷ, so as a final consonant, there is no difference between this and any of the ㄷ sounds.
Practice: 차, 자, 짜, 아차, 아자, 아짜, 앚.
ㅎ is simply an 'h' sound. It is the thing that you add to ㅂ, ㅈ, ㄷ, and ㄱ to make ㅍ, ㅊ, ㅌ, and ㅋ. If you look at these letters, you'll note that they all have an extra horizontal line, more or less. This indicates, "Move more air through your mouth!"
The 's' sounds are tricky for English speakers to get right.
ㅆ behaves like 's' in English---a long, forceful hissing.
ㅅ behaves like a very weak and subtle 's'. It is quick and light, and almost hints at a weak ㅎ. If you can make this sound without touching your tongue to your mouth, you are doing it right.
Both of these sounds change completely when put before 이. They turn into what in English we know as 'sh'. This is a shibboleth with Korean and many other languages. They simply cannot pronounce 'si'. Ask a Korean to try the tongue-twister "She sells seashells at the seashore" and you'll hear "She sells shesells at the shesore." That is, unless they've trained themselves to pronounce things in English properly.
Because the mouth shape is close to ㄷ, the consonant sounds the same when it is final.
Practice: 싸, 사, 아사, 아싸, 씨, 시, 이씨, 이시, 앗.
Of all the sounds in Korean, this is the one that drives English speakers crazy. It is the one consonant that will tell Korean speakers right away whether you have a thick foreign accent or not.
This sound manifests itself in four distinct ways. Note that in each of these cases, the tongue is behind where it would be for 'd' in English, even a little bit more behind where it would be for ㄷ.
Case #1: Initially, it may sound like and 'l' or and 'r'. In "true" Korean, no words start with ㄹ, so this is a moot point. If you force a Korean to say a word starting with ㄹ, they will most likely make an ㄹ sound as in case #3. But sometimes they will make the sound as in Case #2.
In the many words they have borrowed from Chinese that start with this sound, they simply drop the initial consonant rather than force themselves to say it. That's why the "Lee" family is pronounced "Ee".
Case #2: In the middle of a word, a single ㄹ will make a very light flap like an 'r'. Think of the way people may trill the 'r', especially in Spanish. Now do that exactly once instead of 3-5 times like the Spanish do. You have ㄹ. Another way to think of this is the lightest 'd' you have ever said in your life.
Case #3: When you have 2 ㄹ in the middle of a word, then you get an 'l' sound. This is lighter and quicker than the 'l' we have in English, but it is nonetheless entirely distinct from a single ㄹ.
Case #4: When you have an ㄹ at the end of a word, it forms the shape of an 'l', and then holds that shape after all voicing has stopped.
In NO CASE does the ㄹ every make the "dirty" vowel sound you hear in American English, such as with "hard" or "cord". If you are doing this, you sound like a foreigner.
Practice: 라, 아라, 알라, 알.
When Koreans put two consonants together, they allow no room at all for a vowel to mitigate the difference. In order to pronounce the combination properly, end the first syllable with the shape of the final consonant, then pronounce the second consonant without allowing any space in between. Often this implies a change in pronunciation. Consult the following chart to see how this works in practice.
- Be very careful not to make the ㅇ (ng) sound here.
Korean vowels are very precise. In fact, if you get the vowels of the word right, it almost doesn't matter what consonants you have used, Koreans will understand you.
Korean vowels do not shift based on how the word is used. Any changes in vowels due to grammatical changes are well-defined and precise.
If you want to sound like a Korean, first master your vowels.
One note: A lot of English vowels are actually two vowels put together. Korean vowels are pure, meaning, you do not start with one vowel and end with another. For instance, in English, the long "o" is actually two vowels: "o" plus "oo".
Note that Koreans think of some vowels (아, 오) as "bright" and the rest (어, 우, 으, 이) as "dark". You'll see why this is important as we get into grammar.
The first vowel is a very pure, very clean, 'ah' sound. It is the sound your make when you open your mouth at the dentist. Open your throat, open your mouth, move your tongue down, and let your voice sing in a beautiful, pure way.
아 is considered "bright".
If you start with 아, move your tongue forward, and close your mouth slightly, you will produce the 어 sound that seems to be unique to Korean. This is the vowel that most Americans mess up on, and it is the reason why Korean is considered hard. Master this vowel, and keep it distinct from 오, and you will be able to learn Korean quickly.
어 is considered "dark".
Open your mouth as for 아, but then close your lips into a tight "o" shape. Let your bass voice sing, and let your mouth resonate with all the rich goodness that this vowel possesses. Don't be afraid of making it to deep or too reverberant. The more, the better.
오 is considered "bright".
Make a circle with your lips, and stick your lips out all the way. This is the "oo" sound of 우.
우 is considered "dark".
This is a vowel that English speakers struggle with, although I cannot see why. We use it all the time.
Think of the sound you make when you don't care what the vowel is. This is the sound you make for "a" and "the" when you are trying to say something. This is the 으 sound.
Close your mouth, move your tongue forward, keeping the back of the tongue down. Open your lips about 1/4 of the way, and relax. This is the 으 vowel.
Another way to think of it is to imagine you are paralyzed but trying to say "ee". Start with "ee", and relax, relax, relax, relax.
으 is considered "dark".
This is between "ee" and "i".
Open your mouth a bit. Lift the back of your tongue, almost like you are going to make a "k" sound.
American speakers tend to choose "ee" or "i" and stick with it, while Korean speakers are very consistent with their 이 sound. I suggest thinking of it as one or the other, and then imagining that the Koreans simply pronounce that vowel slightly differently.
In Korean, you can combine vowel sounds to make new sounds. Koreans love their vowels so much they know where these vowels come from.
아 + 이 = 애
This is an 'e' sound, as in 'pet'. It's somewhere between 아 and 이.
Koreans have a hard time distinguishing between this and 에, but the distinction is important.
어 + 이 = 에
This is a long a sound, as in 'gate', except without the extra 'ee' sound we have in English. It is somewhere between 어 and 이.
오 + 아 = 와
This is simply a "wa" as in "water", which is the two vowels pronounced quickly.
오 + 애 = 왜
This is simple the two vowels pronounced quickly, one after the other, "we" as in "wet".
오 + 이 = 외
This sound exactly the same as 왜.
우 + 어 = 워
This is the two vowels pronounced quickly after another, "wo".
우 + 에 = 웨
This is the two vowels pronounced quickly after another, "way" without the final "ee" sound in English.
우 + 이 = 위
This is the two vowels pronounced quickly after another, "wee" or "wi" depending on how you think of it.
으 + 이 = 의
This combination manifests itself in many ways.
- Sometimes, it is the two vowels one after another, a sort of "wee" but without the lips.
- Sometimes, it is simply 이.
- Sometimes, it is simply 애.
이 + vowel
Putting 이 in front of a vowel gives you a 'y' sound.
- 이 + 아 = 야 (ya)
- 이 + 애 = 얘 (ye)
- 이 + 어 = 여 (yo)
- 이 + 에 = 예 (yay)
- 이 + 오 = 요 (yo)
- 이 + 우 = 유 (yu)
In English, we use accents to distinguish some words from another.
Korean is somewhat unique among languages because they do not use accents, or even tones like Japanese and Chinese. They speak like a machine gun.
However, there is some intonation in phrases and sentences. This is usually represented with slight variations in pitch.
In between phrases, Koreans will take a small break. However, they do not vary the tempo of their speech.
Intonation is also heavily influenced on where the speaker originates from. Speakers from the southwest area of South Korea, Pusan and Kyoungsan Province, speaking with exaggerated variations. To speakers in other regions, this sounds combative and emotional. Speakers in Seoul try to speak calmly and almost in a robot-like fashion. Speakers in other regions also have certain characteristics you will see. One area is know for speaking very, very slowly.
The various regions are remarkably consistent in their pronunciation. You shouldn't have a hard time understanding what other regions are saying, especially if you have a moderate ability in Korean to begin with.
Some regions vary the vowels by quite a bit. However, they are remarkably consistent, and understanding them is no different than understanding someone with a speech impediment.
- Practice making the sounds above. Check with a native Korean speaker to see if you are doing it correctly.
- Listen to a Korean speaker making the sounds.
- Try to discriminate the sounds one from another. Focus on the problem areas for English speakers:
- Aspirated vs. normal vs. stops.
- The different vowels and combinations.
- Try to mimic a Korean speaker.
Plan to revisit this section as you progress in Korean. Bad habits creep into your patterns that must be corrected. The better your pronunciation and hearing, the quicker you will hear what others are really saying.
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PatrickHaller/fineweb-edu-plus
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Rocks, man, rocks!
How much fun does teaching about rocks sound? About as much fun as teaching about soil!
Thanks to Reading A-Z, an Aims science project, and our iPod Touches, we managed to learn a lot about rocks and enjoy ourselves at the same time. Oh, thank Heaven!
We began with the question: What makes rocks break?
Reading A - Z has this great little book about rocks. It is a level C book, but it is totally appropriate for the lesson.
|Screen shot of the book.|
Readinga-z.com is awesome!
I love their leveled readers.
This book is great for building background knowledge and learning the proper vocabulary on the subject. Many of my kids have never seen a "mountain" mountain (landfills don't count) in their lives, so reading the word boulder was brand new for them.
Then, we matched the vocabulary words with the proper sentences and added them to the anchor chart.
On to the science project...
The project is called Ice Breakers and it is from an Aims activity book. First, we discuss how rocks can break in nature. The kids speculate how rocks break to make boulders, stones, pebbles, sand, and dust. When one of them finally brings up water, I asked them how would water break the rocks? Do you think it will break if it was frozen?
We fill out the prediction chart:
For the project, you will need water balloons, plaster of paris, and the freezer. I prepared the water balloons ahead of time. I called the kids up one at a time and had them help me mix the plaster of paris and add it to their model rock.
We let the rocks dry in the classroom. Then, we put them in the freezer for two days. After the two days, I took the water balloons out and the kids were amazed to see that the plaster had cracked off and the balloons had broken.
We concluded the activity by using our iPod Touches.
The kids had to verbalize the activity and explain what they had learned using the app Sonic Pics.
The app has them add pictures, text, and their voices to create a little video project (like a power point.)
*I'll have to add one of their projects in another post.
Then, for some writing fun, we wrote about what we would build with a bunch of rocks. They were cute and enjoyed thinking about how we use rocks.
Here's a copy of the writing activity:
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PatrickHaller/fineweb-edu-plus
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Learn All Year Long
ReadWriteThink has a variety of resources for out-of-school use. Visit our Parent & Afterschool Resources section to learn more.
Practice Letters and Sounds Using Online Games
- Set of alphabet cards or index cards with one letter per card
- Large sheet of paper
- Computer with Internet access and printer
- Uh-Oh! Cards
- Online ABC Match game
Depending on the age and ability level of the child you are working with, you may need to help with some of these activities so that he or she recognizes the letters of the alphabet and the sounds they make. Make changes to these activities to meet the needs of the child and to focus on the skills that need practice.
Activities 1 and 2 can be done with one or more children.
Activity 1: Letter Hide-and-Seek
To prepare for this activity, get some alphabet cards. You can buy them or make them using index cards, one letter per card. Depending on how well the child knows the alphabet, cards can include just the uppercase or lowercase versions of the letters or both upper- and lowercase. Hide the cards around the room, if possible, near items that begin with each letter (e.g., the letter l next to a lamp, the letter r sticking out from under the rug).
|1.||Tell the child that you have hidden 26 alphabet cards and that it is his or her job to find them and put them in order. Share that some cards may be hidden near objects that begin with that letter.
|2.||Have the child bring you the cards as they are found. Ask what object each card was near that begins with the letter on the card. (For letter cards hidden not associated with an object in the room, ask the child to think of a word that begins with that letter. Help if needed, making sure to place the stress on the first letter sound in the word.)
|3.||Lay the cards in the order they are found on a large sheet of paper. When all 26 cards are found, have the child put them in order. Tape them to the sheet of paper and hang them on the wall.
|4.||Once the letters are in order, ask the child to say their names and the sounds they make.
Activity 2: Alphabet Uh-Oh!
To prepare for this activity, print the Uh-Oh! Cards, cut them out, and place them in a bag.
|1.||Take turns with the child drawing out a card. Whoever draws a card can say the letter name, the sound it makes, or a word that starts with that letter.
|2.||If the player is correct, he or she keeps the card. If the player draws an Uh-Oh! Card, he or she must put all the letter cards back in the bag. The Uh-Oh! Card can be put aside and is out of play.
|3.||Play until all of the letter cards are out of the bag. The player with the most cards wins.
Activity 3: ABC Match
Have the child play the online ABC Match game. He or she can turn over one letter and one picture card per turn, trying to match the picture with its correct beginning letter. Use the Learn Mode if the child is having difficulty and needs extra help from you in making the matches. The Play Mode lets the child play against a timer and offers a fun challenge. Turn on the sound on your computer to hear the names of the pictures.
If you cannot play the ABC Match game online, print and cut out the cards to play an offline version. Lay all the cards face down (pictures grouped on one side and letters grouped on the other) and take turns turning over two cards, trying to find a letter and picture that match. The winner is the one with the most matches.
Visit the ABC Match page for more information about using this tool.
Knowing that spoken words are made up of individual sounds (also called phonemes). This knowledge is not something children need to learn how to speak and understand a language, but it is important for learning how to read.
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PatrickHaller/fineweb-edu-plus
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14. A class takes a quiz and gets the following scores.
Make up a frequency distribution. Find the mean, median, mode, upper and lower quartiles, interquartile range, and standard deviation. Make up a stem and leaf plot and a box and whisker plot.
The frequency distribution looks like
The mean is the sum of the scores divided by the number of scores.We can use the frequency distribution to find the mean. Since there are 3 33s they add up to 33 x 3. The sum of the scores is the sum of the product of each different score times its frequency. The total number of scores is the sum of the frequencies
We divide the sum of the scores which is 385 by the number of scores which is 11.
so the mean is 35. We are very lucky that the mean comes out even. It quite often doesn't.
To find the median, since there are 11 scores and 11 is an odd number, there will be a middle score which will separate the top 5 score from the bottom 5 scores.
We see that the middle number is one of the 33s, so the median is 33.
The mode is the most common score, which we see from the frequency distribution is also 33.
For the upper quartile, find the median of the scores which are above the median, and for the lower quartile, find the median of the scores which are below the median. Since there are 5 score above the median and 5 scores below the median, and since 5 is an odd number, there will be a score in the middle which will divide the upper 2 score from the lower 2 scores for each of these groups of 5 scores.
The upper quartile is 44, and the lower quartile is 25 so the Inter Quartile Range is
For the standard deviation, we first compute the deviations from the mean.
Then we square all the deviations
To find the mean of the squares of the deviations, we must take into account the frequencies of the sores, and add up the products of the squares of the deviations times the frequencies.
To get the mean of the squares of the deviations, we divide their sum which is 828 by 11 which is the number of scores.
The mean of the squares of the deviations is the variance. The standard deviation is the square root of the variance.
For the stem and leaf plot, look at the scores
The numbers in the ten's places, which are the stems, are 2, 3, and 4
For the box and whisker plot, recall
that the upper and lower quartile were 44 and 25 respectively. Plot these, the median, the max and min on a number line. The box and whisker plot looks like
An outlier is a score that is either 1.5 IQR above the upper quartile or 1.5 IQR below the lower quartile. Since the IQR is 19, 1.5 IQR is 28.5. 28.5 above the upper quartile of 44 would be 72.5, and we do not have any scores that big. 28.5 below the lower quartile of 25 would be -3.5, and we don't have any scores that low.
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PatrickHaller/fineweb-edu-plus
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often do we stop to take a good look at how a bridge is constructed?
This program examines the different forms bridges take and explain
some reasons for these differences, such as the nature of the terrain
they traverse and the weight of the loads they carry. A school's
need for a pedestrian bridge over a busy road provides the central
story for this program.
The program identifies what makes bridges strong and stable, with
reference to the building and joining materials used. Children then
test their own model bridges using old counter weights and come
up with some solutions for collapsed creations. Meanwhile puppets
Dodly and Flyn tackle their own bridge challenge - how to walk their
toy dinosaurs over the model railway line without them ending up
under a steam train!
Why do we need bridges?
Why did the school in the TV program need to build a bridge?
How were bridges built in the past?
What structures are used to make a bridge stronger?
- Show how you can make a paper bridge to support one toy model
- See how many plastic drinking straws you need to build a bridge
that spans a 50 centimetre wide road.
- Build a bridge to support 250 grams. Test it. How can you make
- How can you build a suspension bridge using chairs and rope?
Student Design Sheet - Blackline
Master (PDF - 16k)
Questions for Students
What materials will you use to build a model bridge?
What shape will your bridge be?
What will stop your bridge from sagging in the middle?
What part of your bridge is the strongest?
How will you test your bridge?
Will different parts of your bridge hold the weight?
Which is the weakest part of your design?
How can you make it stronger?
Is there anything you would change? Why?
Find other bridge shapes in magazines and photographs.
Explore the different materials used to build bridges.
Find examples of bridges in your local area /state.
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PatrickHaller/fineweb-edu-plus
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Sally’s Camel has Two Humps!
By Jacque Mills
Rationale: The first step in learning to read is letter recognition. Most children learn all or most of the letters of the alphabet by rote, but many enter kindergarten or first grade still unable to recognize them in print. This lesson will help children recognize and write the letter m by learning a letter symbol and associating it with the humps in Sally’s Camel. They will also learn the phoneme m=/m/ by listening for and saying /m/ in words.
Materials: Paper with a camel outline drawing minus the humps and lined like primary writing paper on the bottom half (one copy for each child), overhead copy of the same, pencils, set of m cards for the class, Good Morning, Muffin Mouse, by Lawrence DiFiori.
1. Introduce the lesson by explaining that we can not only sing and say the letters in the alphabet but we can also see and write them! Today we will learn about the letter m. First I’ll show you what m looks like. (Teacher makes the letter m on the blackboard.) We’re also going to learn what m sounds like. Then we’ll learn to write the letter m.
2. Tell students: Pretend you just finished eating a bowl of your favorite ice cream. Rub your tummy and say “mmmmm, that was good.” Now just say “mmmmmm.” Can you guess what alphabet letter says “mmmmm”? That’s right! “M”! Say “M”. Now say “emmmmmm.”
3. Now we’ll do a cheer for the letter m. First I’ll show you the cheer, and then you’ll do it with me. This is M. M says /m/. Marshmallow, marshmallow /m/ /m/ /m/. Let’s do it three times. (Everybody does the cheer three times.) What does M say? Mmmmmm. Good work!
4. Who can tell me what our mouths are doing when we say /m/? Call on students. What are our lips doing? That’s right, our lips are touching each other. Teacher models mmmm.
5. Now I will say two words and you tell me which word has the sound /m/. You might hear it at the beginning of a word or in the middle of a word or at the end of a word so listen closely. Call on students to answer. Do you hear /m/ in mouse or house? Juice or milk? Bacon or ham? Camel or horse?
6. ( Hand out camel pictures.) Get a pencil out of your desk. Now we will learn to write the letter m. Look at the picture of Sally’s camel. (Show on overhead.) What’s missing in the picture? That’s right! The camel is missing its humps! When we write the letter m, we make two humps, just like Sally’s camel! Watch me write the letter m where the camel’s humps should be. Teacher models. Now you do it! Good work! You’ve written the letter m. Now look at the bottom of the page at the part with the lines. That’s where we’ll practice writing the letter m. Watch me first. Start at the fence line. Draw straight down to the sidewalk. Come straight back up to the fence line and make one hump, two humps, just like Sally’s camel. I’ll come and look at your m and after I’ve looked at yours I want you to make five more the same way. Remember, m has how many humps? Two humps and what does m say? M says mmmm.
7. Hand out m cards. Read Good Morning, Muffin Mouse to the class two times. On the second reading, have students listen for the sound /m/ and have them raise their m cards when they hear /m/.
References: Punch in the Stomach, A Model Lesson
by Dr. Bruce Murray,
Auburn University, www.auburn.edu/~murraba
Alphabet Cheers, observed in the classroom of kindergarten teacher Alice
Smith, Navarro Elementary, Bryan, TX., Fall, 1996
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Orbits: The long and short of comets
Back to the Beginning...
Since comets were created from the same spinning cloud of gas and dust as the planets, they continue that motion, revolving around the Sun like the planets and everything else in the solar system. Like the planets, each comet travels on a regular path, called an orbit. The planets' orbits are very nearly circular, but not quite. Each orbit has the shape of a slightly stretched-out circle, called an ellipse.
Earth's orbit is so close to a circle that if you could look at it from space, you couldn't really tell the difference. But many comets revolve along more stretched-out ellipses with the Sun near one end instead of in the center. It's as if the Sun were twirling each comet on a stretchy rubber band, that gets longer and then shorter again, each time the comet comes back around the Sun.
Coming and Going
Having an elliptical orbit means there is a point for each comet where it is closest to the Sun. At this point we say that it is at perihelion; "peri" means close, "helio" is the root word for Sun. There is also a point where the comet is farthest away from the Sun. At this point, we say that it is at aphelion.
? In perihelion, " peri" means close. What do you think the "ap" in aphelion means?
Here's one more new term: the time it takes a planet or a comet to travel once around the Sun in its orbit is called the orbital period.
? Suppose the "planet" in our definition of period is the earth. Do you know another name for the earth's orbital period? (Hint: think of the calendar.)
Stretching the Point
In the Oort Cloud, a comet's orbit can be changed over many years by gravity, until it is long and thin, with the Sun very close to one end. These comets travel all the way from the Oort Cloud to a point inside the Kuiper Belt and back out again. If the orbit's perihelion is close enough to the Sun, say, less than 5 AU, it then receives enough solar energy to become bright and be seen by the naked eye.
This picture shows a long-period comet orbit. Imagine the other Oort Cloud comets near its aphelion. The picture is not drawn to scale. The actual distance to the nearest star is about twice the size of the whole Oort Cloud.
Since these comets still travel from the Oort Cloud all the way around the Sun and back, they can take from hundreds of years, to over a hundred thousand (100,000) years to revolve once around the Sun. What would you call these comets? Right! They are known as long period comets. Comet Hale-Bopp, which appeared in 1997, is a long period comet. It wont return to its perihelion near the Sun again for almost 2500 years: a long time to us, but a short time for a comet. About five out of every six comets that have been observed are long period comets. The comets that led Oort to develop his theory of the comet cloud were all long-period comets.
Short and Sweet
There are also comets whose entire orbit lies within the region of the Kuiper Belt, the "waistband" of comets that is just beyond the planet Neptune. These comets have periods of about 200 years or less. Because of this, they are known as short period comets. Comet Halley, which last appeared in 1986, is a short period comet.
It takes 76 years for Comet Halley to complete one trip around the Sun. But as you saw, in the Origins section, many objects in the Kuiper Belt have nearly round orbits. Only a few have long flat orbits that come close to the Sun at one end. This picture shows that Halley's orbit doesn't even go beyond that of Pluto. You can just see the comet and its tail inside the orbit of Venus near perihelion. The planets are NOT drawn to scale. They are shown bigger so the viewer can recognize them.
How fast are comets? What is the latest comet's orbit?
to part 2
©Copyright 2000 Regents of the University of California.
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Introduce Vocabulary: Yoko (Wells)
What to Do
Select three Tier Two vocabulary words to teach your students. A list of suggested words appears below. Write the vocabulary words on the board or on chart paper.
1. Introduce the story.
Today we are going to read a story entitled Yoko.
2. Introduce the three vocabulary words you have chosen.
Before we read the story, I want to introduce some new words that we will come across. Please repeat each word after I say it.
3. Read the story.
Let’s read the story. Make sure to listen for today’s vocabulary words and to think about how they are used in the story. If you hear a vocabulary word while I am reading, raise your hand.
4. Define key vocabulary words. See definitions below.
Let’s think about our vocabulary words. The word ______________ means ____________. Does anyone remember how this word was used in the text?
Call on students to answer the question. Then refer to the text to show how the word was used in context. Repeat this process for each vocabulary word.
Now let’s practice what we’ve learned.
Bamboo is a plant with hard stems. What’s the word?
People use bamboo for floor covering or furniture. Did you know a panda eats bamboo shoots?
I’m going to name some items. If you think the item is hard and straight, like a stem, say bamboo. Otherwise, stay quiet. Ready?
- A tree branch
- A curtain rod
- A diaper
- A towel
- A flute
Chopsticks means a pair of thin sticks used by people in Asia to eat. What’s the word?
People in the United States usually eat with a fork instead of with chopsticks. Have you learned how to eat rice with chopsticks?
I’m going to name some foods. If you think the food could easily be eaten with a pair of thin sticks, say chopsticks. Otherwise, stay quiet. Ready?
- Ice cream
- Cooked vegetables
Fret means to worry. What’s the word?
The mom told her child, “If I’m late to pick you up, don’t fret. Just wait and I’ll be there soon.” Do you fret everyday, or are you more relaxed?
I’m going to name some things that might happen. If you think the thing would make someone worry, say fret. Otherwise, stay quiet. Ready?
- It’s a beautiful day
- A bride cannot find her shoes
- You’ve got a picnic planned, but there’s a thunderstorm coming
- Your boat has a leak and you’re a long way from shore
- The birds are singing in the trees
International means concerning more than one country. What’s the word?
Most universities have a lot of international students from all over the world. What’s your favorite international food?
I’m going to name some items. If the item makes you think of more countries besides the United States of America, say international. Otherwise, stay quiet. Ready?
- The stars and stripes
- Uncle Sam
- Flying around the world
- German Oktoberfest
- The Eiffel tower
Seaweed means plants that grow under water. What’s the word?
Some types of lotion have seaweed in them because it’s good for a person’s skin. Have you ever felt seaweed brush against your leg when you’re swimming?
I’m going to name some plants. If you think the plant grows under water, say seaweed. Otherwise, stay quiet. Ready?
- Pine tree
- Elm tree
Sushi is a meal made from fish and rice. What’s the word?
The fish used to make sushi is usually raw. Do you find sushi easy to eat with chopsticks?
I’m going to name some foods. If you think the food would be found in a Japanese sushi meal with rice and fish, say sushi. Otherwise, stay quiet. Ready?
- Small pieces of vegetables.
- Seaweed wrapper
- Candy bars
- Soy sauce
For Advanced Students:
If time permits, have students create more examples for the vocabulary words.
For Struggling Students:
For ELL Students:
In order to help ELL students learn the words, it may be helpful to use realia and/or to teach cognates.
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Motion: Follow the Bee
Can you Imagine a bee flying in a beeline? Try, because this is the most simple motion. In this project you will eventually Invent a bee who will fly on a line of your own making. You may even be Inspired to create other paths your bee might take.
In this project we use:
text, book, watcher, variable, graphing objects, Start Script, Stop Script, forward by, turn by, mouse down, animation, arithmetic
Begin by downloading the project from http://etoysillinois.org/library?sl=2142.
By following the bee, learners can get a basic and kinesthetic sense of constant velocity. They can explore further by graphing the motion and writing their own script to move the bee.
They will start by exploring the motion of an existing bee. Bees, like all objects, have a position in space. If they are moving they have a velocity. Students will learn about these concepts and understand them more deeply by recording and graphing data regarding the bee's motion. After analyzing their graphs, they will invent the motion of their imagined bee. Finally, they will look at each others' projects and inspire each other by suggesting improvements. They can take their project and challenge friends and family to fly their bee straight.
Vocabulary the students will need:
Position (page 2) is where you are in space. In this activity we will be interested in the back and forth position of the bee. We often call that the x direction when its horizontal. If your students click on the bee, the bee will stick to the cursor - click again and the cursor let's go. They can move the bee back and forth. They should notice the x value change in the Bee's x watcher for a kinesthetic and visual input.
Velocity (page 3) is how fast you move through space.
On page 3, learners should click on the bee to start it moving, and click on the green background below the text to pause the bee. Next they should change the velocity in the "bee's v" watcher to explore different velocities. They should try negative ones. By using the two watchers on this page, challenge them to get the bee back when she gets to the edge.
On page 4 they should record the data (time, position) in and two column chart, as the bee moves across the page. They should not change the velocity. They again click the bee to start and click the green below the text to pause and record data - click the bee to continue. Each pair of data points should be a time from the "Bee4's t" watcher and the position from "Bee4's x" watcher. They should record at least 10 points. To start over and record new data, set the time and position to zero.
On page 5, students will plot their data. Once they have completed the plot, you should put them in small groups to discuss the following questions:
1. What should your horizontal and vertical axes represent to get all of your data points on the graph?
2. Describe the pattern of the data plotted on the graph.
3. What is special about the pattern of the data plotted on your graph?
4. Why do you think the data have the pattern you observed?
Here is where your students invent. Have them create a script to have the bee move similar to the way she moved on pages 3 and 4. To get them started have them go to page 8 where they will find the following the directions:
Take tiles from the holder on the right and drop them into the Script Editor at the left to make the bee move like it did on pages 3 and 4. You may need more than one tile in some cases. There are several ways that work. Find as many as you can. Check out Script Tiles in help at the upper left. Enable pen trails to better see the path of the bee.
Next your learners should create another script to make the bee follow their plot line. They can think out of the pink box above. Give them an opportunity to explore each others' scripts, suggest improvements and provide inspiration. Let them imagine, invent and bee inspired from the task above to create new scripts to fly the bee differently.
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Someone asked, “How can you assume that the speed of the raindrop is 8 meters per second?” That number comes from some resesarch we did a few years ago on a squall line (line of cumulonimbus) in the tropics. We were looking at a squall line with Doppler radar. This particular radar “saw” raindrops rather than clouds or air. So our Doppler radar could be used to estimate the raindrop fall speed. In the storm we were interested in, the raindrops in the heavy rain were falling at 8 meters per second. (Horizontally, the raindrops follow the wind pretty well — something you know if you are trying to stay dry in a windy rainstorm. This means that scientists can use Doppler radars to study winds in a storm.) These measurements have been used to check the equations scientists use to predict their speed — basically balancing air resistance with the pull of gravity.
The speed of the drop (or droplet) varies with its size. Very small drops, like those in clouds, fall so slowly that the tiniest breath of upward-moving air can keep them aloft. If you fly through a cumulus cloud, it’s bumpy — the air is moving up and down. So some droplets go up, and some go down. If they are tiny, the sinking droplets simply evaporate. So the cloud stays up there in the sky.
Scientists have also measured raindrop fall speeds with upward-looking radars that can “see” both the drops and air. This way they find out how fast the drops move downward relative to the air. So we know that drizzle drops fall at about 2 meters pers second, and raindrops smaller than ours would fall in between 2 meters per second and 8 meters per second.
Why are the speeds different? Drops fall because they are pulled downward by gravity. The drop speed varies with size because of air resistance. Air resistance slows the drops down. If there were no air, drops starting from the same height would fall together at the same speed. This speed would increase with time due to the pull of gravity. With air, the drops quickly reach a speed at which the pull of gravity is balanced by air resistance.
You can see this effect with a simple experiment. Take a piece of paper, and squeeze it into a ball. Take a tiny pice of paper (less than 1 cm), squeeze it into a ball. Drop them at the same time. See how long it takes the two pieces to fall to the ground. The tiny piece should fall more slowly. If you make the tiny piece even smaller, it will fall even more slowly.
What about snowflakes? They fall very slowly, like downy feathers do when you drop them. Using the paper again, you will find that the paper squeezed into a ball will fall faster than a similar size piece that is not squeezed into a ball.
Scientist holding large hailstone. Photograph courtesy of the National Center for Atmospheric Research.
What about big hailstones? If you guessed that they would fall faster, you are right. Large hailstones can fall at speeds faster than 30 meters per second! How do scientists know? Again, they can track hail with radar. Or, they can make fake hailstones that have the same shape and density as real hailstones, drop them, and measure the time it takes the stones to fall a certain distance. When I started working at the National Center for Atmospheric Research, one of the scientists was dropping fake hailstones down a five-story stairwell and timing their fall. The hailstones were painted so that the surface looked like a chessboard or checkerboard, so the cameras could see how they tumbled as they fell. This was fun to watch! Through the window, that is.
These measurements can then be used to check and refine the equations that describe falling objects.
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New mountains are built when rocks are pushed upwards by the movement of the giant rocky plates that make up the Earth’s crust. The rocks are pushed upwards in two ways: FOLD mountains are formed when layers of rock become buckled, and BLOCK mountains are formed when giant lumps of rock rise or fall. Volcanic eruptions also create mountains. Many mountain ranges have been built up and eroded away since the Earth was formed.
The Andes is the longest mountain range on land. It was formed along the western margin of South America, where two tectonic plates (rocky plates that make up the Earth’s crust) collided. The mountains are still rising by about 10 cm (4 in) every century.
The world’s major mountain ranges, such as the Andes, the Himalayas, and the Alps, are situated along the boundaries where tectonic plates collide. These ranges formed in the last few hundred million years, so are they quite young. The map also shows thin lines of volcanoes that erupt from the ocean floor, forming chains of mountainous islands.
The Himalayas is a range of fold mountains formed by the collision between India and the rest of Asia. When the two tectonic plates collided, the southern edge of Asia buckled. The Indian plate continues to slide under Asia and, to date, has uplifted Tibet to a height of over 5 km (3 miles).
When layers of rock are pushed inwards from both ends, they crumple up into waves called folds. Rocks are too hard to be squashed into a smaller space. Instead they fold upwards and downwards. The immense forces that cause folding can crunch solid rocks into folds just a few metres across.
The rocks that buckle to form fold mountains are made up of layers of sedimentary rocks and igneous rocks. When the layers are folded, the rocks on the outside of a fold are stretched and the rocks on the inside of a fold are squashed. The folding also makes the layers of rock slide over each other.
Block mountains are mountains formed when layers of rock crack into giant blocks. Cracks in layers of rock are called faults. They form when the Earth’s crust is stretched, squashed, or twisted. The blocks are free to slip up, down, or sideways, or to tip over. These movements are very slow, but over millions of years they form mountains thousands of metres high.
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Across is a preposition. It describes the relationship between two persons, places, or things. It is sometimes used with the preposition from.
Example: That house is across the street.
Cross is most commonly a verb or noun. As a verb, it means "to go or place across." As a noun, it means "an object made of two intersecting segments."
Crossed is the past tense or past participle of the verb to cross.
Examples: Will you cross the street with me? (Verb)
Jesus, Peter, and Andrew each died on a cross. (Noun)
He crossed the street with me. (Past tense)
Their trademark is a pair of crossed swords. (Past participle)
Cross can sometimes be an adjective meaning "opposing," "placed across," or "angry."
Examples: They were working at cross purposes.
He was counting the cross ties on the track.
Please don't look so cross.
Across occasionally is used as an adverb.
Example: She ran across to say hello.
Do not use acrossed, crossed, or acrost as a preposition or adverb.
(The words acrossed and acrost are strictly nonstandard. They are sometimes used by writers to show dialect.)
Incorrect: He stared acrossed the aisle at me.
Correct: He stared across the aisle at me.
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Photographs by Thomas McGuire
Written by Martin Richard
We have been talking about glaciers. One way to think about glacier is, they are rivers of ice.
But sometimes glaciers can be much larger than rivers. They can be oceans of ice, like the glaciers that cover Antarctica and Greenland.
What would an ocean of ice do to the land beneath it? What would the land look like when the glaciers melt away?
Let’s start by thinking about rocks in fast-moving streams.
Stones in mountain streams are often round and smooth. How does that happen?
As the water moves them, they bump into other stones. Their corners and edges get knocked off, and they get round as they roll down the stream. As sand rubs against them –and they rub against sand– the smallest edges and corners get knocked off too, and they become polished and smooth. That takes a lot of rolling, so it takes a lot of time.
Now look at these pictures of mountains. The mountains on the bottom are all jagged and sharp. The mountains on the top are more round, more smooth.
So which of these mountains are older?
The ones that are round and smooth are older! Their edges have been worn off.
What could wear a mountain down? And how long does it take?
Water wears the mountain down. Water erodes it away. All those rocks moving down streams and rivers do not move back up the mountain.
Sometimes the water is ice! A glacier! Glaciers are like bulldozers –actually, several lines of very slow bulldozers– and push huge amounts of rock downhill.
Back to our first two questions: What would an ocean of ice do to the land beneath it? It would wear off the edges and corners of the land, making it rounder.
What would the land look like when the glaciers melt away? It would look like the mountains in the top picture!
Those worn-down mountains are in the Hudson Highlands in New York. There is good evidence that they were once covered completely by glaciers, sometimes a mile deep! These mountains were worn down by ice, lots and lots of ice, covering the whole landscape, pushing it down and wearing it away.
The mountains on the bottom are from the Rocky Mountains, in Colorado. They are still growing! They are very young compared to the old, rounded mountains in New York.
How long does it take to wear down a mountain?
Well, the evidence shows that the rounded mountains in New York stopped growing 250 million years ago. (That’s about 20 million years before the first dinosaurs.) So a good answer is, it takes a couple of hundred million years to wear a mountain down, to make a mountain smooth and round instead of jagged and sharp.
The original EPOD can be found here.
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What do you see?
"What do you see?" activities practice the vocabulary in a unit.
- Look at the words or phrases in the word box.
- Each word or phrase has a matching illustration. When you see an illustration, you have a few seconds to click on the word or phrase that matches it.
- If you are correct, the word and illustration will move to the panel on the right. If you are incorrect or if you are not fast enough, the illustration will disappear. It will reappear later in the activity.
- A clock on top of the activity tells you how much time you have left to complete this exercise. Try to match all the words or phrases before time runs out.
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- What is a sentence?
- A sentence is a group of words that expresses a complete thought; it is an independent clause (a group of words that can stand by itself) that contains a subject and a verb.
Example #1 (Sentence)
feel very sluggish today.
Reasoning: This sentence contains a subject (I) and a verb (feel) in the main clause. It contains a complete thought that lets us know what is happening (someone feels very sluggish).
When is a group of words NOT a sentence?
A group of words is not a sentence when it is missing one or more of the following: a subject, a verb, a complete thought. We call this an incomplete sentence or a fragment.
Example #2 (Not a sentence.)
Very sluggish today.
Reasoning: This group of words does not contain a subject or a verb, and there is not a complete thought. To have a subject, we would have to ask: Who or what is very sluggish today? Also, we would have to add a verb such as is or feels in order for this group of words to make sense.
HOT GRAMMAR TIP
There are two ways to determine if a group of words is a complete sentence.
- If you can identify the subject, the verb, and a complete thought.
- Say the group of words out loud as if you are addressing someone and see if it makes sense. If it does not make sense, chances are good that it is not a complete sentence.
Example: If someone said to us: "Is very sluggish today," that would not make sense because we don't know WHO are WHAT might be sluggish today.
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“B, b, Bouncing Balls and Baseball Bats”
Rationale: This lesson will help children recognize and identify the phoneme /b/ represented by the letter B. It will also help children associate the phoneme /b/ with the letter B. This lesson will help children remember what sound /b/ makes by using something to help their memory (“b,b,b,bounce” ). The baseball bat and baseball will help the child remember how to write the letter /b/ and not get it confused with /d/. This lesson will help with phoneme awareness. This will also give them practice with finding /b/ words. Students will get a better understanding of the correspondence by focusing on the mouth movement with the sound.
Materials: Primary paper
Tongue tickler with picture: (Bill and Betty baked brown bread for Barbara's baby.)
The Butter Battle Book by Dr. Seuss
Word cards with words BAM, BOOK, LAD, DAY, BUG, MAP
Introduction: 1. Words we write are really cool because they are like a secret code, but sometimes they can be tricky because we have to learn what the letters stand for. Letters tell us how to move our mouths and what sounds to make. We will be working on learning how to move our mouth to say the letter /b/. We spell /b/ with the letter B. (After I say that I will show them my picture card for the sound /b/.) B looks like two basketballs on top of each other, and /b/ looks like a baseball bat beside a baseball. What do you do to a basketball? What sound does a basketball make when it hits the floor? B,b,b,b,…. bounce!
2. Let’s pretend to bounce our basketball. Bounce, bounce, bounce. Okay, every time you say bounce notice where your lips are. First, they are closed together tightly. Then we push out the air in our mouth with strong force.
3. I am going to find the /b/ in the word bad. I am going to say bad really slow so that I can hear the b,b,bounce. Bbbb-aaa-ddd. I’m going to say it one more time even slower bbb-aaa-ddd. I found it! I found it because I felt my lips close really tightly then push out the air really hard. I heard my basketball bouncing too.
4. Now we are going to try this tongue tickler to hear our sound in other fun words. Bill and Betty baked brown bread for Barbara's baby. Let’s repeat it three times, whenever you hear our /b/ sound pretend like you are bouncing a basketball. Now let’s do it again except for this time when you hear our /b/ sound stretch out the sound to make it sound like this. Bbbilly and Bbbetty bbbbaked bbrown bbbread for Bbbarbbara’s bbabbby. One more time, but this time let’s separate the /b/ from the rest of the word. /B/illy and /B/etty /b/aked /b/rown /b/read for /B/ar/b/ara’s /b/a/b/y.
5. (Have students take out their primary paper and pencil.) We are going to use B to spell /b/. Capital B looks like two basketballs sitting on top of each other. Let’s write a capital B. Start at the roof and draw a straight line down to the sidewalk. Then bring your pencil back to the roof and make a hump from the roof to the fence and make another hump from the fence to the sidewalk. Lowercase b looks like a baseball bat with a baseball lying right beside it. Let’s write a lowercase b. Start at the roof and draw a straight line down to the sidewalk. Then put your pencil on the fence and draw a hump down to the sidewalk. After I check your work draw five more capital Bs and lowercase bs.
6. Activity. Call on students to have them decide which word they hear /b/ in. (bug or fly? Brick or house? Beat or lose?) Now everyone pretend to bounce your basketball if you hear the /b/ sound in these words: beg, shake, bunk, bag, toy, face, back, cow.
7. Practice with a text. Let’s read The Butter Battle Book by Dr. Seuss. The Yooks and the Zooks disagree on which side of the bread butter should be on. This disagreement leads them into a competition. Let’s read to see who out does the other one. While reading if you hear a word that starts with /b/ pretend to bounce your basketball. Then ask the students if they can come up with any other words that start with /b/. Let the students choose a word (different from one in the text) to draw a picture of and have them spell their word below their picture (invented spelling).
8. Let’s practice reading our new letter /b/. Model how to decide whether the word starts with /b/ or not. Example: Which word starts with /b/, bug or mug? Bug starts with /b/ because the B tells me to bounce my ball. It also tells me to put my lips together and push the air out really hard. Here are some for you to try: brick or kick? Bake or make? Plank or blank? Bang or sang?
9. Assessment. Worksheet. Have the students color the pictures that start with the letter b. http://www.tlsbooks.com/letterb_1.pdf
Holcomb, Joanna, Bouncing the Ball with B.
Return to the Awakenings index
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CONFLICT AND WIN-WIN SOLUTIONS: Two Lessons for Grades 3-6
The first lesson introduces students to the concept of conflict; the second has students practice coming up with "win-win solutions." See our conflict resolution programs.
Two lessons for grades 3-6
The first lesson introduces students to the concept of conflict, helps them consider that conflict is a normal part of life and does not have to lead to violence, and asks them to consider examples of conflict in their own lives. In the second lesson, students practice coming up with "win-win solutions" to conflict.
Students will be able to give an accurate definition of conflict.
Students will recall and describe conflicts they have experienced.
Agenda written on chalkboard or chart paper
Gathering: If Conflict Were a Color
'Lay out an array of colored paper on a table or on the floor. (Origami paper is especially good to use; you can get it at museums or art supply stores.) Ask students to choose a color of paper that represents "conflict" to them. Say, "If conflict were a color, it would be ... " and have them get up and pick out a piece of paper. Be sure to have lots of red, as that's the color most people choose. Have students find a partner. Give them a minute or two to share with their partners what color they chose and why.
Go over the day's plan with students.
Defining Conflict: Conflict Web
Write the word "conflict" on the board and draw a circle around it. Ask the students what words or phrases come up when they hear the word, and record their responses as a web: Write their contributions on the board, using lines to connect each word to the word "conflict" or related words. Continue for about three to five minutes (or longer if interest remains high).
A. Using their responses, help them come to a definition of "conflict" as an argument, a disagreement, or a fight.
B. Some questions to ask: What do you notice about the web? Can we make any generalizations about it? Why are most of our associations negative?
C. Write CONFLICT = VIOLENCE on the board to make the point that many people equate the two concepts. Ask, Does conflict equal violence? What is the difference between conflict and violence?
When a distinction has been made, draw a line through the equal sign like this (CONFLICT ? VIOLENCE) to show that conflict and violence do not necessarily go together. Then erase these words from the board. Point out that conflict and violence are not the same thing. Conflicts do not have to lead to violence.
D. Make the point that conflict is a natural and normal part of life, that we all experience conflicts at home, at work, in school, on the street, and that countries also have conflicts with each other.
Remembering Personal Conflicts
Introduction: Since conflicts are a part of life and everybody has them, class members will think about conflicts they have experienced.
A. Tell a story about a conflict you have had recently with another person. Include concrete details of where the conflict happened, who was involved, what happened, how it ended, and how you felt about it in the end.
B. Then ask students to raise their hands if they can remember a time they have had a conflict. Call on a few to describe their conflicts.
C. Divide the class into pairs. Ask students to take turns telling their partners a story about a conflict they have had including who was involved, how it started, how it ended, and how they felt when it ended. Write the words "where," "who," "what," "end," and "feel," on the board as a reminder of what the story is to include. Time them for two or three minutes each.
D. Ask some volunteers to tell their stories to the class. Ask, What happened? Who was involved? How did it turn out? How did you feel?
E. Summarize: Point out that conflicts can end in different ways. Sometimes one person ends up feeling good and the other feeling bad. Sometimes both people end up feeling bad. Sometimes both people end up feeling good. Everybody has conflicts. Conflicts are part of life.
Ask, "What was something you liked about today? Was there anything that seemed hard?"
Ask students to make a circle and join hands. Everyone bends over, hands almost touching the floor. Start saying "Yes" together softly and draw the word out, getting louder and louder as you slowly raise hands into the air. Conclude by throwing hands into the air overhead, completing the word loudly and energetically.
Suggestions for Infusion
Have students write their stories of personal conflicts.
Most stories develop around a conflict, sometimes between characters in a story and sometimes between parts of the self. Whatever story the students are reading, have them locate the conflict and discuss it. What started the conflict? Who was involved? What happened? How did it end? How did each character feel in the end?
Discuss conflicts in the news. See "Teaching About Controversial Issues" for an approach to doing this.
Students will practice thinking up win-win solutions for conflict situations.
Agenda written on chalkboard or chart paper
[Note: This lesson requires a role play set up ahead of class with either another adult, a student, or puppets. See lesson below for details.]
Gathering: Count to Five
The challenge in this game is to have people in the class call out the numbers from one to five without having two people talking at once. Introduce the game by explaining the following rules:
- Anyone can call out a number, starting with one.
- The numbers have to be in order.
- If two people say the same number at the same time, the class has to start over.
Check to see if everybody understands the rules. If not, ask someone who does understand them to explain them to those who don't.
Ask for a volunteer to be the monitor. If s/he hears two people talking at once, s/he raises his or her hand to signal that the game has to start over.
Set a timer for three minutes. If the group doesn't master the task by that time, it will just become frustrated.
Discuss: What made this hard? What would make it easier?
Go over the day's plan and ask if it seems okay.
Introduction: Role-play the following situation with another adult, a student, or with puppets. Freeze the action where the argument is heating up.
A. Claire is in high school, has a big test coming up, and has just settled down to study. Amy, her younger sister, comes home from school, turns on the stereo, and starts dancing. Claire gets up and orders Amy to turn off the stereo. Amy protests, saying she never gets to have fun, and turns the stereo up.
B. Ask the class to describe what's going on. What does Claire need? What does Amy need? If Claire won, what would she get? How would she feel? If Amy won, what would she get? How would she feel?
C. Show students the following diagram of ways the conflict could come out.
Amy gets what she needs
Amy doesn't get what
Claire gets what she needs
Claire doesn't get what
D. Ask for ideas about how this conflict might come out. Have two students role-play one of the endings that is suggested. The two can be the student who suggested the ending (if s/he wants to do it) and a volunteer or two volunteers that you choose.
E. Discuss where the ending is located on the chart. Does Amy get what she wants? Does Claire? Then what kind of an ending is that?
F. Continue with other endings. Role-play at least one ending for each category.
G. When the students have arrived at a win-win ending to role-play, spend some time drawing out as many win-win solutions as they can come up with. Go for quantity. Point out that most conflicts have many win-win solutions depending on what is acceptable to both parties.
Ask a few volunteers, What are some feelings you had about today's lesson? What are some reasons why you feel that way?
Go-round. Who is someone you'd like to work out a win-win solution with?
Conflict Analysis Checklist
Ask the class, "If you were going to help some of the kids in this class find win-win solutions to a conflict, what would you need to know before you could help?"
List all the suggestions on the board. When the class is done giving their suggestions, discuss which ones are similar. Combine similar ones until you have a list of about five.
Arrange in order of importance. Label it Conflict Analysis Checklist. Explain that the list shows the kind of information you need in order to help resolve conflicts in a win-win manner.
Your checklist might look something like this:
1. Who's involved?
2. What did they do?
3. How did they do it?
4. How is "A" feeling? How is "B" feeling?
5. What does "A" say she/he wants? What does "B" say she/he wants? Etc.
6. What does "A" need in order to feel happy with the solution to the conflict? What does "B" need? Etc.
How would this information be helpful? What would you do with the information once you had it? Why might it be helpful to be able to analyze a conflict in this way?
Practice Analyzing Conflicts
Make five or six copies of the Conflict Analysis Checklist for each student, allowing space between each question for writing.
Divide the class into groups of three or four. Ask each group to prepare a skit based on a conflict experienced by one of the members of the group. Give the students five or ten minutes to rehearse their skits. Then have each group present their skit to the class.
After each skit is presented, all the students are to fill in their checklist sheets. They can ask questions of the students who put on the skit if necessary. Go over the answers with the whole class and discuss before moving on to the next skit.
You can also give the students practice analyzing conflicts by using situations from stories the class is reading, situations in the newspaper, actual incidents in the classroom, or situations you think up and present to the class and present with puppets.
We welcome your thoughts and suggestions about these activities! Please email us at: [email protected].
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PatrickHaller/fineweb-edu-plus
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Phonemic awareness is a vital prerequisite
to beginning reading. Children must learn that letters stand for
spellings map out the phonemes in spoken words. Before children are
match letters to phonemes, they need to first develop and strengthen
ability to recognize phonemes in spoken words. Children should not be
to learn all the phoneme identities at once, and it is helpful to spend
individual phonemes. Voiced phonemes such as /m/, /s/, and /f/ are the
to stretch and pronounce by themselves; these phonemes provide a good
point for teaching phonemic awareness.
lesson will help children identify the
phoneme, /f/. Students will learn to recognize /f/ in spoken words by
a meaningful hand gesture and the corresponding letter symbol. Students
practice finding /f/ in spoken words during a read aloud using a
book. Students will also practice identifying pictures of items whose
start with /f/.
Materials: 1) Four Fur
Feet. Brown, Margaret Wise. Hyperion, 1996.
2) Picture Identification Worksheet (with pictures of the following
words: fish, worm, flower, frog, snake, fly, foot,
hand) 3) pencils (for each student)
4)Picture of the grapheme f
and a foot 5) Chart with a picture of
furry feet underneath flowers with the alliteration, "Funny furry feet
found flowers." 6) Primary paper (for each student) 7) Dry erase board
(with primary guidelines) 8) Dry erase
the lesson by reminding students that, "our written language is like a
secret code. The tricky part is learning what letters stand for—the
we make as we say words." [Hold up
the picture with the grapheme f and
a foot.] Today, we're going to
say and listen for the /f/ mouth move. When we see the letter F, we know to say /f/.
anyone ever seen an angry cat? When cats get angry, they say /f/. Let's
to be mad cats; everyone say /f/: /f/. When we say /f/ let's make a
an angry cat. When I count to three, let's sound like angry cats and
while we show our claws. One, two , three… ffffff.
job. Now, let's try a tongue twister. [Hold up chart.] "Funny furry
flowers." Everyone say it three times together. Good, now let's say it
again, but this time, I want you to stretch out the /f/ at the
beginning of the
words. Don't forget to make your claw! Ready? "Ffffunny fffurry fffeet
out primary paper and have students get out their pencils]. The letter f spells the /f/ sound. Let's write the
lowercase letter f. [Model
this for the students on dry erase
board with primary guidelilnes]. First I'm going to start to make a
little c up in the air. Then I straighten it
out and go down to the sidewalk. Last, I'll cross at the fence. Now
turn. When I draw a star on your paper, I want you to make nine more
it. What does the letter f
tell us to say when we see it in a
word? That's right, it tells us to say /f/.
I'm going to show you for to find /f/ in the word elf.
First I'm going to stretch out elf in super slow
motion and listen for angry cat.
E-e-e-e-l-l-l-l-l-f-f-f-f-f-f. There it is! I hear the angry cat
/f/ in elf.
going to ask you to listen for the /f/ sound. I'll say two words, and I
you to tell me which word has the angry cat in it. [Call on individual
to answer.] Do you hear /f/ in skinny
or fat? Tree
or flower? Silly or funny? Grass
or leaf? Now let's listen
to some words. If you hear
/f/ in them, then I want you to make a claw. Read
the following words aloud: laugh, smile, beef, friend,
fish, apple, fruit.
students Four Fur Feet and say: "One
day, a mysterious animal with four fur paws decided to take a walk. He
walked and walked. As he walked around the whole world he saw wonderful
like trains, farms, and boats. Where do you think he is going? What do
think he will do when he gets there? Let's find out."
Fur Feet and talk about the story. Tell students that we're going
the story again. This time have them raise their hands when they hear
words. After the reread, have children draw their version of the animal
four fur feet and use invented spelling to write about what the animal
or where he might go next. Display children's creature messages on a
an assessment, pass out the picture identification worksheet. Help
name each picture on the sheet. Have students circle all the pictures
names start with /f/.
Sarah Byrd. Five Fantastic Frogs. http://www.auburn.edu/academic/education/reading_genie/invent/byrdel.html
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PatrickHaller/fineweb-edu-plus
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Last time we talked about independence of a pair of events, but we can easily go on and talk about independence of a longer sequence of events. For example, suppose we have three coins. Suppose:
• the 1st coin has probability of landing heads up and of landing tails up;
• the 2nd coin has probability of landing heads up and of landing tails up;
• the 3rd coin has probability of landing heads up and of landing tails up.
Suppose we flip all of these coins: the 1st, then the 2nd, then the 3rd. What’s the probability that we get this sequence of results:
If the coin flips are independent, the probability is just this product:
See the pattern? We just multiply the probabilities. And there’s nothing special about coins here, or the number three. We could flip a coin, roll a die, pick a card, and see if it’s raining outside.
For example, what’s the probability that we get heads with our coin, the number 6 on our die, an ace of spades with our cards, and it’s raining? If these events are independent, we just calculate:
the probability that we get heads, times
the probability that we roll a 6, times
the probability that we get an ace of spades, times
the probability that it’s raining outside.
Let’s solve some puzzles using this idea!
Three flips of a fair coin
Example 1. Suppose you have a fair coin: this means it has a 50% chance of landing heads up and a 50% chance of landing tails up. Suppose you flip it three times and these flips are independent. What is the probability that it lands heads up, then tails up, then heads up?
We’re asking about the probability of this event:
Since the flips are independent this is
Since the coin is fair we have
So the answer is 1/8, or 12.5%.
Example 2. In the same situation, what’s the probability that the coin lands heads up exactly twice?
There are 2 × 2 × 2 = 8 events that can happen:
We can work out the probability of each of these events. For example, we’ve already seen that is
since the coin is fair and the flips are independent. In fact, all 8 probabilities work out the same way. We always get 1/8. In other words, each of the 8 events is equally likely!
But we’re interested in the probability that we get exactly two heads. That’s the probability of this subset:
Using the rule we saw in Part 7, this probability is
So the answer is 3/8, or 37.5%.
I could have done this a lot faster. I could say “there are 8 events that can happen, each equally likely, and three that give us two heads, so the probability is 3/8.” But I wanted to show you how we’re just following rules we’ve already seen!
Three flips of a very unfair coin
Example 3. Now suppose we have an unfair coin with a 90% chance of landing heads up and 10% chance of landing tails up! What’s the probability that if we flip it three times, it lands heads up exactly twice? Again let’s assume the coin flips are independent.
Most of the calculation works exactly the same way, but now our coin has
We’re interested in the events where the coin comes up heads twice, so we look at this subset:
The probability of this subset is
So now the probability is just 24.3%.
Six flips of a fair coin
Example 4. Suppose you have a fair coin. Suppose you flip it six times and these flips are independent. What is the probability that it lands heads up exactly twice?
We did a similar problem already, where we flipped the coin three times. Go back and look at that if you forget! The answer to that problem was
Why? Here’s why: there were 3 ways to get two heads when you flipped 3 coins, and each of these events had probability
We can do our new problem the same way. Count the number of ways to get two heads when we flip six coins. Then multiply this by
The hard part is to count how many ways we can get two heads when we flip six coins. To get good at probabilities, we have to get good at counting. It’s boring to list all the events we’re trying to count:
So let’s try to come up with a better idea.
We have to pick 2 out of our 6 flips to be H’s. How many ways are there to do this?
There are 6 ways to pick one of the flips and draw a red H on it, and then 5 ways left over to pick another and draw a blue H on it… letting the rest be T’s. For example:
So, we’ve got 6 × 5 = 30 choices. But we don’t really care which H is red and which H is blue—that’s just a trick to help us solve the problem. For example, we don’t want to count
as different from
So, there aren’t really 30 ways to get two heads. There are only half as many! There are 15 ways.
So, the probability of getting two heads when we flip the coin six times is
where the squiggle means ‘approximately’. So: about 23.4%.
Now for some jargon, which will help when we do harder problems like this. We say there are 6 choose 2 ways to choose 2 out of 6 things, and we write this as
This sort of number is called a binomial coefficient.
We’ve just shown that
Why write it like this funky fraction: ? Because it’ll help us see the pattern for doing harder problems like this!
Nine flips of a fair coin
If we flip a fair coin 9 times, and the flips are independent, what’s the probability that we get heads exactly 6 times?
This works just like the last problem, only the numbers are bigger. So, I’ll do it faster!
When we flip the coin 9 times there are possible events that can happen. Each of these is equally likely if it’s a fair coin and the flips are independent. So each has probability
To get the answer, we need to multiply this by the number of ways we can get heads exactly 6 times. This number is called ’9 choose 6′ or
for short. It’s the number of ways we can choose 6 things out of a collection of 9.
So we just need to know: what’s 9 choose 6? We can work this out as before. There are 9 ways to pick one of the flips and draw a red H on it, then 8 ways left to pick another and draw a blue H on it, and 7 ways left to pick a third and draw a orange H on it. That sounds like 9 × 8 × 7.
But we’ve overcounted! After all, we don’t care about the colors. We don’t care about the difference between this:
In fact we’ve counted each possibility 6 times! Why six? The first H could be red, green or blue—that’s 3 choices. But then the second H could be either of the two remaining 2 colors… and for the third, we just have 1 choice. So there are 3 × 2 × 1 = 6 ways to permute the colors.
So, the actual number of ways to get 6 heads out of 9 coin flips is
In other words:
To get the answer to our actual problem, remember we need to multiply by this. So the answer is
If you’re a pure mathematician, you can say you’re done now. But normal people won’t understand this answer, so let’s calculate it out. I hope you know the first ten powers of two: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. So:
I hope you can also do basic arithmetic like this:
So, the probability of getting 6 heads when you do 9 independent flips of a fair coin is
or 16.4025%. I broke down and used a calculator at the last step. We’re becoming serious nerds here.
Okay, that’s enough for now. We’ve been counting how many ways we can get a certain number of heads from a certain number of coin flips. What we’re realy doing is taking a set of coin flips, say of them, and choosing a subset of of them to be heads. So, we say
Definition. The binomial coefficient
called choose is the number of ways of choosing a subset of things from a set of things.
We have seen in some examples that
Here there’s a product of consecutive numbers on top, and on bottom too. We didn’t prove this is true in general, but it’s not hard to see, using the tricks we’ve used already.
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PatrickHaller/fineweb-edu-plus
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An angle is formed by two rays with a common endpoint. The angle bisector is a ray or line segment that bisects the angle, creating two congruent angles. To construct an angle bisector you need a compass and straightedge. Bisectors are very important in identifying corresponding parts of similar triangles and in solving proofs.
The key points to an angle bisector is that it does -- almost lost it -- it does a couple things.
The first thing is it bisects the angle, creating two congruent angles. So if I have an angle that's in blue here and the red ray is my angle bisector, then it has created two congruent angles. So notice that this red is a ray. That's another key thing.
Now, it also could be a line segment, if you're talking about something in an isosceles triangle perhaps, we could say line segment, and every point along this bisector is the same distance from the two rays that make up the sides.
But how do we measure distance? Well, the shortest distance from a point on this ray to a ray that forms the angle is along a perpendicular. So if you're to construct the perpendicular from the angle bisector to a side, and if you did that down here, then you would say that these two segments are congruent.
So that's the key parts to an angle bisector. Is that it bisects the angle creating two congruent angles, it's a line-- a ray or line segment, and that every point on this ray is the same distance measured along the perpendicular from the rays that make up your angle.
But how do we actually construct that? To do that let's grab our compass and our straight edge and head over to this angle right here. So we know that we're going to create a ray that creates two congruent angles. So the first thing you're going to do is you're going to swing an arc just like if you were duplicating an angle. So from the vertex I'm going to swing an arc so that I create two points of intersection.
Now I want to create a point out here that is the same distance from these two points of intersection. So if you want to, you can change your compass, but you don't have to, for the sake of argument I will. And you're going to swing an arc from each of these end points. So there's one arc from this intersection.
Here's another point of intersection that I'm going to swing an arc from. Now, this point right here is the same distance from both of these end points. So I'm going to connect this point of intersection with my vertex. Thereby creating my angle bisector.
So I'm going to draw this, connect my vertex, and that point of intersection, and what we've created are two congruent angles that when they sum you get the angle that you started with.
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PatrickHaller/fineweb-edu-plus
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In mathematics, a degree is 1/360 part of a circle. Imagine a round pie. Cut it through the middle in two parts. Now cut the halves in two equal parts. Each of the four parts has a right angle where the middle of the pie was. If each of these parts was in 90 equal slices they will all have an angle of one degree. 180 degrees would be half of the pie. 270 degrees would be three-quarters of the pie.
Why ninety and not one hundred? [change]
Ninety is easier to make calculations with mentally. Ninety can be split into equal pieces in many different ways.
- 2×45, 3×30, 5×18, 6×15, 10×9, 9×10, 15×6, 18×5, 30×3, 45×2 - 10 ways
One hundred can only be split in less ways:
- 2×50, 4×25, 5×20, 10×10, 20×5, 25×4, 50×2 - only 7 ways.
In times when people made calculations in their head a lot, they liked the numbers 360, 90, and 12 better than 10 and 100 for this reason. That is also why there are 24 hours in a day (twice twelve), and why a troy pound is 12 ounces.
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PatrickHaller/fineweb-edu-plus
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"Where in the world is......"
AUTHOR: Jean Ann Hollar, Washington
I have students from the third and fourth grade. They have a heck of a time figuring out where any of the places on the map are. Also, they ask if Canada is one of the states. They think that New Mexico is part of the country Mexico. For these reasons, we play a game called "Where in the world is..." every morning.
GRADE LEVEL/SUBJECT: This game can be adjusted to any grade level. I'll give the directions for playing with my third and fourth graders.
PURPOSE: I want my students to know if I'm talking about a country or a state in our country. They should see that there is a World, that World has continents, those continents have countries within them, and those countries are divided up into smaller sections, such as states.
OBJECTIVES: The students will be able to transfer what they see on the globe to a flat map. They will be familiar with large or major land masses as well as major rivers. The students will be able to point out major countries of the world as well as major cities.
RESOURCES/MATERIALS: One large wall map of the world Several globes Tag board and yarn and pins or tape
ACTIVITIES AND PROCEDURES:
Have a large wall map of the world on a bulletin board with space around it. Also, have a globe of the world. Cut out large letters spelling, "Where in the world is....?" and put this above the wall map. Have two spaces available to the right of the wall map. These will hold tag board pieces cut to the same size. They will have different names on them each day. Attach a piece of yarn to the tag board. It will be attached to a different spot on the map each day. The second space for tag board is for later on when city names are added to the question. This also requires a piece of yarn. On the first day, allow the students to become familiar with the similarities between the wall map and the globe. The first day tag board should read "the world".
Days Two through Eight:
Have the name of one of the continents up on the first tag board space when the children enter in the morning. Allow them to use the globe to find the answer to the question, "Where in the world is....Africa?" When the children have had a chance to decide, let one come up and attach the yarn to the correct area of the map that answers the question of that day.
Days Nine through (?):
Take this time to point out major oceans and seas. Each day ask what the students know about the area that is high- lighted. Day (?) When you are ready to begin asking where a country is, begin using the second tag board section for a city in that country.
TYING IT ALL TOGETHER: I use the first part of the school year to practice mapping skills. I have the students map out the classroom, the school, and a fantasy island. As they practice finding real places on the wall map and globe, it helps them see the relationship between the paper and the real world.
Thanks, Jean Ann for such a great lesson plan.
Do you have a lesson plan that would work well for one of the subjects on this site? Would you like to share it with the world?
If so, just paste the information into an e-mail and send it my way. I update the site often, so your great work could be showcased really soon.
Thanks for the assistance and thanks for the great work!
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PatrickHaller/fineweb-edu-plus
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A true-false statement is any sentence that is either true or
false but not both. A negation of a statement has the opposite
meaning of a truth value. A negations is written as ~p.
If we call the statement: cucumbers are green, p then:
p: cucumbers are green - this statement is true.
~p: cucumbers are not green - this statement is false.
If we join two statements we can form a compound statement or a
conjunction. A conjunction could contain the two statements q and
p: cucumbers are green.
q: cucumbers are vegetables.
Conjunctions are noted:
This is read - p and q. Cucumbers are green and vegetables.
A conjunction is true only if both statements that form the
conjunction is true.
If we have two statements that are joined by "or" we have a
p: Bill is travelling to Mexico
q: Bill is travelling to Canada
p or q gives us that Bill is travelling to Mexico or Bill is
travelling to Canada.
Disjunctions are noted:
This is read - p or q.
A disjunction is true if at least one of the statements that
form it is true.
Video lesson: We are given four statements
p: cats have 4 legs (true)
q: hens have 2 legs (true)
r: cats lay egg (false)
t: hens lay egg (true)
Are the following compound statements true or false?
p Λ t
p V r
~p V q
r Λ q
~r V ~q
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PatrickHaller/fineweb-edu-plus
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Basic Addition Introduction to addition. Multiple visual ways to represent addition.
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- Welcome to the presentation on BASIC ADDITION.
- I know what you're thinking:
- "Sal, addition doesn't seem so basic to me."
- Well, I apologize.
- I hope I --
- Hopefully, by the end of this presentation,
- or in a couple of weeks, it will seem basic.
- So lets get started with,
- I guess we could say, some problems.
- Well, let's say I start with an old classic.
- 1 + 1
- And I think you already know how to do this.
- But, I'll kind of show you a way of doing this,
- in case you don't have this memorized,
- or you haven't already mastered this.
- You say, well, if I have
- (Let's call that an avocado.)
- If I have 1 avocado,
- and then you were to give me another avocado,
- how many avocados do I now have?
- Well, let's see. I have 1 ... 2 avocados.
- So 1 + 1 is equal to 2.
- Now, I know what you are thinking:
- "That was too easy."
- So, let me give you something a little bit more difficult.
- I like the avocados. I might stick with that theme.
- What is 3 + 4?
- Hmm. This is, I think, a more difficult problem.
- Well, let's stick with the avocados.
- And in case you don't know what an avocado is,
- it's, it's actually a very delicious fruit.
- It's actually the fattiest of all the fruits.
- You probably didn't even think it was a fruit --
- even if you [have eaten] one.
- So, let's say I have 3 avocados.
- 1, 2, 3. Right? 1, 2, 3.
- And let's say you were to give me 4 more avocados.
- So let me put this 4 in yellow,
- so you know that these are the ones you're giving me.
- So how many total avocados do I have now?
- That's 1, 2, 3, 4, 5, 6, 7 avocados.
- So 3 + 4 is equal to 7.
- And now I am going to introduce you
- to another way of thinking about this.
- It's called the number line.
- And, actually, I think this is how I do it in my head,
- when I forget -- if I don't have it memorized.
- So [on the] number line, I just write all the numbers in order,
- and I go high enough just so I can --
- [so that] all the numbers I am using are, kind of, in it.
- So, you know the first number is 0,
- which is nothing.
- Maybe you don't know; but now you know.
- And then you go to
- 1 (one)
- 2 (two)
- 3 (three)
- 4 (four)
- 5 (five)
- 6 (six)
- 7 (seven)
- 8 (eight)
- 9 (nine)
- 10 (ten)
- It keeps going,
- 11 (eleven)
- So, we're sayng 3 + 4. So let's start at 3.
- So I have 3 here.
- And we're going to add 4 to that 3.
- So all we do is we go up the number line,
- or we go to the right on the number line, 4 more.
- So we go 1 ... 2 ... 3 ... 4.
- Notice, all we did
- is we just increased it by 1, by 2, by 3, by 4.
- And then we ended up at 7.
- And that was our answer.
- We could do a couple of different ones.
- We could say, what is --
- What if I asked you what 8 + 1 is?
- Hmmm. 8 + 1.
- Well, you might already know it.
- 8 + 1 is just the next number [after 8].
- But if you look at the number line, you start at 8,
- and you add 1.
- 8 + 1 is equal to 9.
- Let's do some harder problems.
- And, just so you know,
- if you're a little daunted by this initially,
- you can always draw the circles,
- you can always do the number line,
- and, eventually over time, the more practice you do,
- you'll hopefully memorize these,
- and you'll do these problems in, like, half a second.
- I promise you. You've just got to keep practicing.
- Let's say....
- I want to draw the number line again.
- Actually, I have a line tool;
- so I shouldn't give you all of those ugly looking lines
- that I've been giving you.
- Look at that. Look at that. That's amazing.
- Alright, let me see.
- Oh. Oh. Yeah, look at that.
- Okay. So, that's a nice looking line.
- I'm gonna feel bad to erase it later on.
- So let me draw a number line.
- So let's do a hard problem.
- What is --
- I'm gonna do it in different colors now.
- 5 + 6
- So if you want, you can pause the video and try this.
- You might already know the answer.
- And the reason why I say this is a hard problem
- is because the answer [is] more [than the]
- [number of fingers you have on your two hands].
- So you can't necessarily do it on your fingers.
- So let's get started with this problem.
- Actually, my phone is ringing.
- But I'm going to ignore the phone,
- because you're more important.
- So. Okay. Let's start start at the 5.
- So we start at the 5.
- And we're gonna add 6 to it.
- So we go: 1
- We're at 11!
- So 5 + 6 is equal to 11.
- Now I'm gonna ask you a question.
- What is 6 + 5?
- Well, we're now going to see that, OK?
- Can you switch the two numbers
- and get the same answer?
- Well, let's try that.
- I'm gonna try it in a different color,
- so we don't get all confused.
- So let's start at 6.
- Right? Ignore the yellow for now and add 5 to it.
- 1 ... 2 ... 3 ... 4 ... 5.
- Ah. We get to the same place.
- And I think you might want to try this
- on a bunch of problems.
- And you'll see it always works out --
- that it doesn't matter in what order you --
- "5 + 6" is the same thing as "6 + 5."
- And that makes sense.
- If I have 5 avocados and you give me 6,
- I'm gonna have 11.
- If I have 6 avocados and you gave me 5,
- I'm gonna have 11 -- either way.
- Let's do a couple of --
- Since this number line is so nice,
- I wanna do a few more problems using it.
- Although, as I use it,
- I'm sure I'll just continue to confuse you,
- 'cause I'll write so much on top of it. But --
- Let's see. I'll use white now.
- What is -- What is 8 + 7?
- Well, if you can still read this, 8 is right here.
- Right? We're gonna add 7 to it.
- 1 ... 2 ... 3 ... 4 ... 5 ... 6 ... 7.
- We go to 15.
- 8 + 7 is 15.
- So hopefully, that gives you a sense
- of how to do these types of problems.
- And more than, I guess this --
- and you're gonna learn multiplication in a little bit.
- But these types of problems are,
- when you're getting started off in mathematics,
- these kind of require the most practice.
- And, to some degree, you have to start memorizing them.
- But, over time, you know, when you look back,
- I want you to remember how you feel
- while you are watching this video right now.
- And then I want you to watch this video in, like, three years.
- And remember how you felt when you're watching it now.
- And you're going to be, "O my! This was so easy!"
- 'Cause you're gonna learn so fast.
- So, anyway, I think you have an idea.
- If you don't know the answer
- to any of the addition problems,
- that we give you in the exercises,
- you can press the "Hints," and it'll draw circles,
- and then you can just count up the circles.
- Or, if you want to do it on your own,
- so you get the problem right,
- you could draw the circles,
- or you could draw a number line, --
- like we did in this presentation.
- I think you might be ready to tackle the addition problems.
- Have fun!
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I Like to Shuffle Along in My Shiny Shoes
Beginning Reading Lesson Plan
Brittany Anne Hanie
Rationale: In order to read and spell words it is important that children can identify letters and their phonemes. It has been shown that letter knowledge is one of the best predictors of reading success. This letter will introduce the letters s and h, the sound than corresponds with these letters when combined (sh), and the mouth movements for the combination of the two letters.
Materials: Primary paper, pencil, chart with "Shelby and Shawn like to shuffle in their shiny shoes."; letterboxes for each student with small letters needed for the lesson; One Fish Two Fish Red Fish Blue Fish (by: Dr. Seuss, Random House Books, © 1960); dry/erase board; marker
1. “Today we are going to talk about the letters s and h. We are going to practice these letters together. Who knows what sound s makes? What about h? When we put those two letters together it makes a sound that is a little bit different. This sound is ssshhhh. Can everybody practice making that sound? Very good.”
2. “Remember how we sometimes use tongue twisters to help us remember sounds? Well, I have a new tongue twister for us to practice: Shelby and Shawn like to shuffle in their shiny shoes. Let’s all practice saying this together. Very good. Now this time let’s all try to stretch the /sh/ at the beginning of the words. SSShhelby and SSShhawn like to sshhuffle in their sshhiny sshhoes. That was wonderful. As we are going through our activities today, let’s remember /sh/ by remembering the shiny shoes.
3. “We are now going to practice writing the letters s and h. Everyone takeyou’re your paper and pencil. I am going to make the letter s on the board. Everyone watch me. form a tiny c up in the air, and then swing back. Now, I want you to try. (Each student should attempt to write the letter s). I will now going to make the letter h on the board. Watch me. I will start at the rooftop, come down, and hump over. Now, you try it. (Everybody should attempt to write the letter h). Now I want everyone to practice each letter 3 times. Once you have done this, put the s and the h together and write this combination 5 times. Remember as you are writing what sound the s and the h put together makes.
4. Now that we have completed that activity, I have a fun game I want us all to play. Each person has a set of letterboxes and letters on their desk. We are going to use these letters to help us spell out a word according to its sounds. I will show you what I mean. The word I am going to model is ship. I will first find the vowel for my word which is the i. In this word, the letter i makes the /i/ sound. I will then figure out what this word begins with. I am thinking that sh-ip begins with /sh/. I remember this because I remember sh and shiny shoes. So, I have the sh and the i. Now, I have to think about what this word ends with. Let me think. Sh-i-p. I think this word ends with the letter p. Sh-i-p. This word is ship.”
5. Each child will then practice the words:
3 phonemes: ship, shop, cash, fish, shell
4 phonemes: shift
The letters that will be used for this lesson will be: a, c, e, f, h, i, l, o, p, s, t
6. “I am so proud of each of you for working so hard in your letterbox lessons. I am now going to read the book One Fish, Two Fish, Red Fish, Blue Fish. While I am reading, I want you to raise your hand everytime you hear the sound /sh/. When we are finished reading we will go back through the book and list these words on the board.”
7. “The last activity we will do is drawing a picture. I want each of you to draw a picture of an object that has the letters /sh/ in it. For example I might draw some dirty ashes that are left in my fireplace after a fire. When everyone is finished we will talk about how many /sh/ words we could think of and share our unique pictures with the class.”
8. For assessment, use teacher observation as each child spells words in their letterbox lessons. The main thing to look for is that the child is placing the s and the h in the appropriate places and knows what the letters s and h sound like when put together. Also, check pictures and make sure each child’s picture correlates with a word that contains the /sh/ sound in it.
Success For All
Reading Development Team. Fast Track Phonics for Roots.
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PatrickHaller/fineweb-edu-plus
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At certain times of the year, a message from Mars traveling at the speed of light can take 20 minutes to arrive at Earth. As if that weren't bad enough, space radiation may flip one or more bits, where flipping means turning a 1 into a 0 or vice versa. For this reason, you've been called in to help with the coding. Here is what you are told.
The spacecraft will send a bunch of messages, each consisting of 100 bits plus some extra bits as we discuss below. There is an infrequent burst of space noise that can cause one or more consecutive bits to flip. The consecutive sequence of flipped bits will have a length of at most 20. Moreover, those bursts will happen at most once in the time it takes to transmit 150 bits.
We'll work up to that noisiest case in stages.
Suppose the noise burst could flip at most one bit in the time it takes to transmit 150. How few bits could you add to the message to detect the presence of an error?
Just one extra bit would do it. Count the number of 1s among the 100-bit message. Call that number N. Add an extra bit (the 101st) with a value 1 if N is even and make the extra bit 0 if N is odd. (This is called "odd parity" in the electronic trade.) When the message (along with the extra bit) arrives at earth, there has been an error if the number of 1s among the 101 bits is even. Otherwise there is no error.
1. Next, let's assume that the noise burst will flip EXACTLY 20 consecutive bits or will flip no bits at all. How few extra bits would you then need to detect the presence of an error in the message?
Okay, if you’ve solved that, let's try for the full problem.
2. There can be zero or one noise burst in the time it takes to transmit 150 bits. If there is a noise burst, it will flip some consecutive sequence of at most 20 bits. How few extra bits would you then need to detect the presence of an error in the message? (Hint: I can do it with fewer than 115.)
Here is an open question. How many bits would be necessary to determine where such a noisy consecutive sequence of bit flips begins and ends in the setting of question 2? How would you do it?
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Inside the Igloo
Rationale: For children to have the knowledge and understanding of phonemic awareness, they must first be able to understand short vowel sounds. This lesson will help the children to recognize the correspondence i= /i/. The goal of the lesson is for students to learn to recognize /i/ in spoken words by learning mouth moves and gestures such as having something icky on your fingers. They will also get exposure of the letter and sound being in written words as well.
1.Liz is Six for each student
2.Primary paper for each student
3.Pencil for each student
4.Crayons for each student
5.Chart with tongue twister on it (The important Indian was ill with injuries inside the igloo).
6.Letterboxes for each student
7.Set of oversized letters and letterboxes (teacher copy for board demonstration)
8.Plastic letters for each student (f,i,g,t,s,h,p,m,d,b,r,c,k,l,f,n)
9.Picture of “icky sticky” (child with glue on hands)
10.White paper for each student
11.Picture page with illustrations (swing, watch, brick, cup, crib, grass, pig, mask)
1."We all need to know what different letter sounds make when we are reading. We are going to learn a fun way to remember when i says /i/ in a word today so get ready. Have you ever had glue stuck on your fingers? What sound did you make when you had glue stuck on you? Way to go! You said /i/ck! That is the sound that the short I makes. Let’s all pretend that we have glue on our fingers. When you try to get the glue off of your fingers you say /i/!! Let’s all try! Way to go! One other way to remember the sound is to say the words "icky sticky" (Show picture as you are doing it). Let’s all say it and do it together. "Icky Sticky!!" Awesome job everyone!"
2."Let’s all look at a tongue twister and read it together. (The important Indian was ill with injuries inside the igloo). Good! This time when we say it, let’s stretch out the /i/ sound, and make the 'icky sticky' hand motion. (The i-i-i-mportant i-i-i-ndian was i-i-i-ll w i-i-i-th i-i-i-njuries i-i-i-nside the i-i-i-gloo). Good job!"
3.Have the students tell if they hear the /i/ sound in different words. "Do you hear /i/ in Strip or stay? Wrong or sit? Little or good?"
we all did a great job at making
the /i/ sound (do "icky sticky" with fingers), we are going to practice
the letter i. Everyone needs to
take out a piece of primary paper and a pencil. Watch and model
what I am
doing (model on the board with lines that match their paper). We
the fence and go down to the sidewalk. Then, pick up your pencil
him a dot just about the fence. All of us need to do that five
on your paper while I walk around the room and check your paper.
needs to take out their
letters and letterboxes. Spread the letters out on your desk so
can see each letter clearly. (Use the model on the board so that
can see the boxes and the letters.) Now, we are going to spell words
the /i/ sound in them. Remember to put only one sound in each
Watch me as I spell the word fig. F-f-f-i-i-i-g-g-g. I like
all of my words out loud so I can hear all of the sounds and you should
same. The first sound I hear in fig is /f/. So,
going to put the f in the first
box. What is the second sound I hear? (Do the "icky stick")
hear the /i/ sound. So, I’ll put the
i in the next box. The last sound I hear is /g/, and so I put
in the last box. Let’s read our word. F-i-g. Way to go
have just spelled the word fig! I am going to let you try now and see
can spell these words that have /i/ in them. Use your letters and
letterboxes to spell these words: 2 phonemes: it. 3: ship, fit, him, dig.
4: brick, sink, cliff. 5: spring, print,
crisp. (Tell the
students how many boxes they will need to use for each set of words.) Now we are ready to practice reading and
spelling our words with the /i/ sound. Everyone needs to try
to spell them just the way I showed you. When you are finished,
your hand and I will come check how well you did.
will now pass out the story Liz Is Six to each
are going to read a story called Liz Is Six. This book is
Liz, a little girl, who is having a birthday party. One of the
she gets is a mitt. She and her friend, a pig, play a game of
with her new mitt. It is a very close game and we will have to
book to find out who wins!" Have the students read by themselves.
If a student
has a problem reading the story, tell them to raise their hand for some
guidance. When they are finished reading, ask the students what
they read that had the /i/ sound in them. Write the words on the
Assessment: Pass out a picture page to name the pictures together. Read the names of the pictures on the page with the class. Tell the students to circle the pictures that have the /i/ sound. You could keep up with their grades in the grade book.
Betbeze, Meg. Icky Sticky Fingers!. (Beginning Reading). http://www.auburn.edu/academic/education/reading_genie/innov/betbezebr.html
Murray, Bruce. Wallach and Wallach's Tongue Twisters. http://www.auburn.edu/academic/education/reading_genie/twisters.html
B.A. & Lesniak, T
(1999). The Letterbox Lesson: A hands-on approach for teaching
decoding. The Reading Teacher, 52, 644-650.
(1990). Phonics Reader Short Vowel, Liz Is Six. Carson, CA (USA): Educational Insights.
Return to Passages Index.
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PatrickHaller/fineweb-edu-plus
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Students are learning more about word meaning, and how the meaning of a word can change when a consonant suffix (-s) is added or vowel consonant suffix is added (-es). Students are also learning the rules of spelling words with suffix, and when to use -s or -es. The suffix rule is: use -es at the end of a word when the word ends in ch, sh, x, s, or z. For example: watch - watches, dish - dishes, mix - mixes. We played a fun guessing game today where children needed to choose which suffix to add at the end of a word... we used reporter's notebooks to write our guesses, which was especially important since what the word looks like helps students remember the suffix rule!
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Teaching syllables to kids can be so much fun. Syllables are parts of words. These can be taught using the child’s name. Clap each syllable as you pronounce each syllable. You can start with the names list that you created for teaching the alphabet. For example, one could clap and pronounce Mi-kay-la. Ask the child if they heard 3 parts. Most likely the child will say yes, because she heard you clap three times.
One activity that helps kids with identifying syllables is to categorize them into a chart that is labled 1 clap words, 2 clap words and 3 clap words. Here is an example of a chart with names.
Each syllable will contain one vowel sound. There are six syllable patterns that make up 75% of the words that we read. The other 25% of the words are words that do not follow the patterns and need to be memorized. The syllable patterns are closed, open, silent e, bossy r, two vowels, and consonant + le.
Hearing syllables is a much easier task than seeing syllables, so start with sorting words by how many syllables a word has before you start breaking words up into syllables. Over the course of this month you are going to learn about each of these patterns and how to teach them to young ones.
How many syllables does your name have? How many vowel sounds does your name have? Is it the same number?
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Nurikabe @ Daily Sudoku
Let's work through an example Nurikabe problem. This one is quite straightforward. At any stage below, click the grid for a printable grid.
Nurikabe has 4 rules:
First look at the number 1 close to the center of the puzzle. Remember, each island must contain just one number. The number 1 represents an island with only 1 white square, so we can shade the surrounding squares. The same is true for the number 1 in the top right corner.
No group of white squares may contain more than one number. This means that numbers must be separated by shaded squares. When we have two numbers with one one square between them, that square must be shaded. For example, the 5 and 2 in the top left corner must be separated by a black square.
Concentrate now on the bottom left corner of the grid. Every black square must be connected to form the "wall". The black square in the bottom left corner must not be isolated. It only has one available neighbour, which must therefore be black. Where there is only one possibility, we must extend the wall.
Take a look at the number 2 in the bottom left corner. This island is not yet complete -- it needs a second white square. The number now has only one available neighbour, which must therefore be white. We can put a dot in that square to show that it must be white. The "2" island is now full, and so must be surrounded by black squares.
Take a look at the squares marked with (a). These squares are surrounded, and therefore cannot be part of any island. They must be shaded.
While we're there, we must extend the wall in the top right corner. Look for other spots where the wall must be extended.
Take a look at the 5 in the top left corner. We need to extend the island. Use dots to show which squares must be white.
Which other islands can be extended?
Rule 4 says that 2x2 blocks of filled squares are disallowed. The two squares marked (a) in the left center of the grid must be white, because shading them would violate this rule. Mark them with dots.
In step 2, we filled squares that were separating two numbers. We can extend this logic to fill squares that separated growing islands. Look at the squares marked (a). Do you understand why they must be shaded?
The most common mistake is to focus only on the wall, or only on the islands. You need to swicth from one to the other and back. See if you can extend parts of the wall to stop them becoming isolated, and extend islands and shade around them when they are full.
You're nearly done! Note in the grid shown here, we must fill the squares marked (a) so as not to isolate chunks of the wall.
The remaining islands can be extended in only one direction. The final shaded square links two large sections of wall into one continuous unit.
Well done! Now take a look at some of the puzzles available on the puzzles page. Remember:
|All content © The Daily Sudoku Ltd 2005-2007. All rights reserved.||Comments, questions, problems?|
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PatrickHaller/fineweb-edu-plus
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|Objective(s): By the end of this lesson the student will be able to:
the order of operations to solve math equations.
Pre Class Assignment: Completion of Algebra Lesson 3
In the first
learned that numbers and variables form sentences, or algebraic
"expressions." When you take information from a sentence and turn it
into a mathematical expression, it is called "translating." In another
lesson, you learned that when you write algebraic expressions, use +,
-, and = signs; and for division, use / , the same way you know that
when you see a fraction, it means to divide the top number by the
bottom number. Then, for multiplication, we learned to write the
expression with no symbol or sign between them (such as 3a), with an X
, or using parentheses. The parenthesis is especially useful in longer
problems such as (3y)(4-2x).
But what if there
are no parentheses or brackets? How do you know which to do first? Add,
divide, multiply? Which one?
When there are no
other indications as to which computation to do first, mathematicians
follow The Order of Operations rule. Multiply, Divide, Add,
A good way to
remember the Order of Operations is to think about My Dear Aunt Sally.
The M is for multiply, the D in Dear is for Divide, the A is for Add,
and the S in Sally is for subtract.
HINT: If the problem has only multiplication and division, then work
from left to
HINT: If the problem has only subtraction and addition, then work from
left to right.
Let's Get Started:
13 - 2 X 5
If I just do the
math from left to right, I would say 13 - 2 = 11. Then 11 times 5 = 55.
But the Order of
Operations tells me to multiply first! So, 2 X 5 = 10. Then, I subtract
10 from 13 and get 3.
You can see that
which order you choose makes a BIG difference in the answer! That's why
it's important to follow the Order of Operations.
Now it's time for
you to try a few.
Assignment(s) including Answer key:
1. 10 - 4 + 3
2. 10 + 4 X 2
3. (5 X 4) -15 + 2
4. 12 - 2(3 + 1)
5. 18 + 2(3)
6. (12 - 2)(3 + 4)
7. 4 X 3 + 5
8. 24 - 6 +2
9. 24 - 6 X 2
10. 36/9 - 2
For Answer Key, Click Here
Pre-Requisite To: Basic Algebra - Lesson
For more Articles by this Author, Click Here
For more Lesson Plans in the Subject: Algebra, Click Here
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Skilled readers rely on the spellings of words to
the words found in text. It is important for students who are learning
to rely on phoneme-grapheme correspondences. The goal for this lesson
students to learn to spell and read words using the correspondence o_e = /O/. Students will have the
opportunity to spell words with the o_e
= /O/ correspondence and apply the spelling strategies to reading.
*Elkonin letterboxes for each student
The following letters in a plastic
bag for each
student: h, o, m, e, r, s, c, a, n, d, t, t, i, p, l, c, b, k (two t’s are needed for this lesson)
Large Elkonin letterboxes with
the center of each box for the teacher
The following letters with
Velcro/tape on the
back for the teacher (letters should be large enough for all students
h, o, m, e, r, s, c, a, n, d, t, t, i, p, l, c, b, k (two t’s
are needed for this lesson)
Markers/chalk for white
List of words separated by the
phonemes for the teacher
rose, can, dome, tip
flop, slope, spine,
List of words spelled for each
should be in a different order than when they were spelled)
Flashcards of the following words: flat, smoke, dive, sneak, mope, crush, plop,
Lists of words that are on the
assessment (one for each student)
1. Before beginning the lesson,
it would be a great idea to review some of the long vowel sounds that
were previously learned such as a_e = /A/. To review this
correspondence, the teacher may say "Do you remember
when we learned about the /A/ sound and how there was something special
about it? Does anyone
remember what was so special about this sound, /A/?"
Give students time to respond. If no one responds, take the opportunity
to remind them that “some
words with the /A/ sound have
what we call a silent e. Let’s see if we hear the /A/
sound in the word cane? /c/ /A/ /n/. I hear the /A/
sound, but let’s see if we can
spell this word on the board. The first sound that really sticks out in
my mind in the word cane is the /A/ sound (teacher
writes an a on the board). If we
leave this letter (pointing to
the a) here by itself, it makes the /a/ sound. Is
there anything that we can do to make it say /A/?" Hopefully students
the right response; if not, inform them that we can
add a silent e at the very end. Help them further
understand by telling them that the silent e pinches
the a to
make it say its name. The next sound that I hear the
/k/ sound. (teacher writes a c) The last sound we hear
in the word /c/ /A/ /n/ is the /n sound (teacher writes
an n on the
board). "It seems that we have all the sounds, and we see that this
words says /c/ /A/ /n/, cane."
*Elkonin letterboxes may be made for
each student by cutting
cardstock paper into 4" x 4" squares and taping them together so that
easily fold. For teacher letterboxes, ¼ of a poster board may be
used for each
letterbox, using the same taping method.
- After reviewing, ask the students
"what do you say when you’ve dropped something or you’ve done something
that you didn’t mean to do?" Allow students to answer, hoping that one
says ‘uh oh’. If not, tell them "When I drop something or I do
something that I didn’t mean to do, I sometimes say ‘uh oh’. Well
today, we are going to learn about the /O/ sound and how and where we
find it in words.
- "Just as we just spelled words with
/A/ sound in them, we can spell words with the /O/ sound the same way
by adding a silent e. If I wanted to spell the word bone, I would say the word to my self and stretch it out
so that I could hear each sound - /b/ /O/ /n/. In this word, the first
sound that really sticks out is the /O/ sound." Write the letter o on the board. If I leave this letter (pointing to the o) here by itself, it makes the /o/ sound, but I want it
to make the /O/ sound. To make it say the /O/ sound, I want to place a
silent e at the end of my word. Remember that the
silent e pinches the o and makes it
say its name. Now that I have the /O/ sound, I want to get the rest of
the sounds in the word /b/ /O/ /n/. The next sound that I hear is /b/."
Write a b on the board. The last sound that I hear in
the word /b/ /O/ /n/ is /n/." Explain to the students that sometimes we
place the letter n between the o and
the e because the e is so silent,
it’s almost as if it isn’t there.
- Allow the students to practice finding
the /O/ sound by giving them example words such as joke,
club, and cone. During this time, ask students
for their thought processes in finding the /O/ sound. With each word
that has the /O/ sound, go to the board and allow the students to
instruct you on the spelling.
- "Now that we’ve learned about the /O/
sound and we’ve figured out how to find it in words that we say, we’re
going to see if we can spell words with the /O/ sound in them." At this
time, give students their individual Elkonin boxes and plastic bags.
Ask students to remove their letters from the bag and fold their
Elkonin boxes so that three of them are showing. Also take this time to
set up your letterboxes on the board.
- "Remember when I said that I wanted to
spell the word bone and I said each sound to myself
and then wrote it on the board? Well, that’s what I want you to do as
we begin spelling these words. Each individual sound, NOT letter, goes
into each letterbox." Repeat if necessary. "Since we’re using the
letterboxes, the silent e that we sometimes find at
the end of words goes outside of the letterboxes because we don’t hear
it." For example, if we use the word joke that we
spelled earlier, we would say the word to ourselves so that we hear
each individual sound. When we found the sounds, we would put the /j/
sound in the first letterbox, the /O/ sound in the second letterbox,
and the /k/ sound in the third letterbox." Teacher places sounds in the
appropriate letterboxes as he/she instructs. "If we read this word, it
would say /j/ /o/ /k/. We want it to say /j/ /O/ /k/, so we would need
to place the silent e outside the letterboxes to let
us know that the o is going to say its name.
- "Since everyone has their letterboxes
folded to where only three are showing, I think we’re ready to begin
spelling words! Remember to think about each sound that you hear and
place each sound into a different letterbox. Using three letterboxes,
the first word I want you to spell is home. After I
left school, I went straight home." Repeat the word and same/different
sentence, allowing students to spell the word and place each sound in
the correct box. Take this time to walk around and observe each student
as they begin spelling words. If you notice any problems students are
having, take this time to model for them how to spell the word as you
did with bone, and joke. After
students are done spelling the word, ask them to clear all the letters
from the letterboxes. Continue this procedure by finishing all the
three phoneme words (rose, can, dome, tip), then the four phoneme words
(slope, spine, close, state, flop) and then the five phoneme words
(stroke). Ask students to change the number of letterboxes at the end
of each list.
- Once all the words have been spelled,
give each student a list of words. "Now that we’ve finished spelling
our words, we are going to read this word list from top to bottom. As I
clap, I want you to read each word."
- After reading the list, gather the
students together and give a brief book talk about the book Is
Jo Home? "This is a story about a little dog who really wants to
play with Jo. He searches and searches for Jo so they can play
together. In order to find out what Jo and the dog do, we’re going to
read the story. While you’re reading, I want you to pay attention to
words with the /O/ sound and see how they are spelled."
- For assessment, allow each student to
read Is Jo Home? and take a running record.
Then show each student flashcards with words including o_e = /O/ and previous correspondences learned. Allow the
student to read each word while you check the words on a list, making
note of any miscues. The word list may include words such as flat, smoke, dive, sneak, mope, crush, plop, stone, and crop.
Words with the /o/ sound will be useful in order for students to be
able to distinguish between the short and long o.
Barton, Sarah. Oooohh My!
Cushman, Shelia. Is Jo
Home? Carson, CA. Educational Insights. 1990.
Lesniak, Theresa and Bruce
Murray. 1999. "Teaching Reading."
Teacher. Vol. 52. No. 6. Pgs. 644-650.
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Mars has two small moons, Phobos and Deimos. Phobos is the larger of the two. It is shaped like a potato, about 15 miles long by 10 miles wide. One end is scarred by a giant crater. The impact that created it may have fractured the entire moon, leaving big cracks that travel from one end to the other. Phobos is in such a low orbit that it circles Mars about three times per day. It rises in the west, then sets in the east just a few hours later. As seen from the equator it looks less than half as big as our Moon looks from Earth. Deimos is both smaller and farther out. It takes almost three days to complete one orbit. From the Martian surface, it looks about like Venus looks from Earth.
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One of the hardest things which the boys had to do was to make their own weapons. At first, Greybeard helped them; but, later, they had to do their own work.
So the boys learned to go to the trees that had the best wood for shafts. They learned to cut, and peel, and scrape, and oil, and season, and polish the sticks before they were ready to use. No wonder the boys became tired before all this work was done.
Then they worked very carefully before they could make good spearheads. They hunted for the best stones and learned to shape them very well. When they forgot and struck hard blows, they spoiled the flint points. Then Greybeard would tell them that the strongest and bravest hunters were those who could strike the gentlest blows.
It was work of this kind that was harder for the boys than chasing a wild horse or a reindeer. If they had not known that they must have weapons, they would not have had patience to do it.
While the boys worked at their weapons, they thought of what they would do with them. They thought of the trophies they would bring home and what the people would say. And they learned to sing at their work and to mark the tim
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Lesson plan for 3period of lesson1^^
||||| Lesson Plan for Grade 6 |||||
Lesson 1. Where are you from? Period 3
Key Expressions How do you spell your name?
Where are you from? Materials Power Point sheets
Objectives To ask where people are from and how to spell names and nations.
Activities / Games
1. Greetings – 5 min
2. Introduce today’s learning objectives – 5 min
3. Sing a song to review the previous Key Expressions – 5 min
- Where are you from? –I’m from-
How do you spell China? C-H-I-N-A!
4. Let’s Write – 5 min
- Have students complete the answers to a given question according to pictures.
- Check the answers in pairs.
- Have students read them aloud.
5. Let’s Speak -- 10 min
- Have Students do a role-play using asking and answer “where are you from? How do you spell it?
- Have them present their own idea to class.
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Avoid the Danger Zones!
School Bus Safety!
To be safe when they travel to and from school, follow these simple safety rules:
AT THE BUS STOP:
- Always walk to the bus stop. Never run.
- Walk on the sidewalk. If there is no sidewalk, walk on the left facing traffic.
- Always go to the bus stop about five minutes before the bus is scheduled to arrive.
- While at the bus stop, wait in a safe place away from the road. Do not run and play while waiting.
- Never speak to strangers at the bus stop and never get into the car with a stranger. Always go straight home and tell you parents if a stranger tries to talk to you or pick you up.
- Wait for the bus to arrive, watch for red flashing lights and the stop sign to be extended, and cross only when all traffic has stopped. Look left, right, and left again before crossing.
ON THE BUS:
- Go directly to a seat. Remain seated and facing forward for the entire ride.
- Talk quietly (so the driver will not be distracted).
- If you need to talk to the bus driver: wait for the bus to stop, raise your hand, and call the driver's name.
- Never throw things on the bus or out the windows. Never play with the emergency exits.
- Keep the aisles clear at all times.
- If there is an emergency, listen to the driver and follow instructions.
EXIT THE BUS:
- When getting off the bus make sure you walk (not run) three more steps away from the door. This is the best place to be around a bus. Stay away from the bus wheels and watch out for moving cars!
- Once you get off the bus, go straight home so an adult will know where you are.
- Only get on and off the bus at your designated stop. If you need to get off the bus somewhere else, you will need to have a note from your parents.
- If you leave something on the bus, never return to the bus to get it. The driver may not see you come back and they may begin moving the bus.
Also, if you drop something near the bus, tell the bus driver before you attempt to pick it up, so they will know where you are.
Always remain 10 steps away from the bus to be out of the "Danger Zone" and where the driver can see you. Always cross the street in front of the bus. Never go behind the bus.
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You are eating lunch at a restaurant in the U.S. with a friend, and the restaurant brought you a huge plate of food. You are amazed at how much food American restaurants serve, so you say this.
The portion sizes are so much bigger in the U.S.!
A "portion" of food is the amount that one person is supposed to eat for a meal. If you want to talk about the amount of food that a restaurant, cafeteria, etc. gives you, you use the phrase "portion size". "Portion size" is the amount of food that is given to each person for a meal.
If the weather is really hot, you say that it's "so hot". "So ___" is a way to express an adjective very strongly.
When you want to compare two things, you say "___er" or "more ___". So, for example, you'd say "It's hotter in New York than in London."
Putting these together, if you want to compare two things, and say that the difference between them is very strong, you say "so much ___er":
It's so much hotter in New York than in London.
When it's clear what you're comparing to, you don't need to say "than ___". So, if you're from London and visiting New York, you could say:
It's so much hotter in New York.
When you're talking or writing about the United States, the most common and natural way to refer to the country is to say "the U.S.". This is much more common than calling it "U.S.A." or "the United States".
Notice that you always have "the" in front of "U.S.".
(Print this lesson)
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The Great War ended on 11 November 1918. Technically, this date was an armistice, a temporary break in the fighting while the politicians discussed what to do next. The leaders of all the countries on the Allied side met in Paris in January 1919. It took six months to draw up the treaty terms and then the Germans rejected them.
Why did it take so long to draw up treaty terms? Why were the Germans so appalled by the result? In this gallery you will examine sources from the time. This will help you understand the complex situation in 1919.
The key question in this gallery is: Why was it so hard to make peace at the end of the war?
This worksheet will help you plan your work and present your conclusions.
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Sometimes place value can be the hardest concept (conceptually speaking) for first graders to understand. Yes, they can tell you how many hundreds, tens or ones are in a number...but do they really get it? Well in chapter 6 there are tons of activities to make sure they do get it.
But here's something to think about...a few years ago I was listening to a speaker at a professional development meeting talk about place value and how
Example: I'm at the board showing my students how to add two digits...lets say its 56 + 36. I go through the step of adding the ones first. "Class, 6+6=12. I bring my one down to the ones column then I carry my two over." (I'm sure I'm the only one who's done this). Wait a minute, I'm not carrying over two...I'm carrying over ten. Un-teaching all my hard work.
That was my Ah-Ha Moment in terms of instruction of place value and from that point on my instruction looked a lot different. Just something to think about.
What Are We Teaching:
When in doubt look to your state's course of study standards, or Common Core Standards. If you check out Lory's Page you'll be able to download the Common Core Standards for first and second grades. Thanks Lory!
Debbie lists the most general standards you are sure to find when teaching place value. Some are listed below.
*Counting to 100
*Group counting by tens to fifty or more
*Read, write and understand numbers from 20 to 50 or more (depending on your grade level)
*Use broken counting
*Count by tens off the decade (14,24,34,)
*Putting together and taking apart two-digit numbers
*Developing an understanding of place value as students solve two digit addition and subtraction problems
*Describe Compare and order numbers to 999
*Representing numbers in various ways
Having a supply of Hundreds Charts will allow students to see what happens when you count by 5s,10s, or off decade. Here are my (specially made for my blogging friends) set of designer Hundreds Charts...I call anything with a little color designer ;) Click on the picture to grab your set. Don't you just love the dots?
What Are the Students Doing at Place Value Stations
Race to Fifty or One Hundred
Here is one game my students loved to play. In the game of Race to Fifty or One Hundred, students each need a ones and tens mat, a die and connecting cubes. They take turns rolling the die and counting out that many cubes. When they have a group of ten they can connect those and slide them over to the tens side of the board. The first person to get to 50 or 100 wins.
There was another variation in MWS: Race to Zero. This works in the opposite way. Students start out with the specified number (50 or 100 cubes). They roll the die and take away that many placing them on the ones side. They keep rolling and breaking down their cubes until they reach zero. No matter which way you decide to let your students play, you'll need the game boards. Click on either picture to get your set.
Ants at the Picnic
Here is another collection game. This time students roll 1 die and take that many ants. When they have a collection of ten individual ants they can trade for one rod of ten ants. Students keep rolling, collecting and trading until they collect 50 or 100 ants (depending on which game they play). Click on the picture to collect your game.
Make copies of these charts on colored card stock. Cut them out into a variety of puzzles and then laminate. Give students a blank grid and have them put the puzzle back together again. Click on the picture to get your copy, including the blank grid.
Trading Games Using Money
If you click here and here you can get a copy of all the Money Trading Games I created in an earlier post.
Play $999 Monster Money Challenge
In MWS Debbie called the game $999 Monopoly Money Challenge.
But I created Monster Money. It works the same way as Debbie's game.
Directions:You will need 15 one hundred dollar bills, 25 ten dollar bills, and 50 one dollar bills. Place the money in a
Each student reaches into the bag and removes three bills at a time. Then they each add up the money and whoever has the most gets to keep both players money. They keep track of their money by placing their bills on the corresponding places on the mat( hundreds, tens, ones), making exchanges when possible. Players keep going until one person gets $999.
This game is on page 144 in MWS.
In the meantime click on the picture to get your set of Monster Money.
Playing Make the Biggest Number
In this game students shuffle two separate decks of 0-9 number cards. Both players turn over two cards at a time and try to make the biggest number. The player who makes the bigger number gets to keep both cards or they get a point. At the end of play the student with the most cards or points is the winner. A variation could be Make the Smallest Number. Click on the picture to get your set. I've also included mats using Tens and Ones and Hundreds tens and Ones.
Number of the Day
I use this each year with my first graders. Each student has their own book and it's a part of our daily Math Morning Routines.
Posted on the wall I'll have a sign that says; Today's Number is...I try to choose numbers I feel they need to work on, sometimes it's the number of days we've been in school, it just varies according to what they need.
Students take out their Number of the Day books and copy the number in the center of the page. Then they have to tell me the numbers that are one more, one less, ten more and ten less than the Number of the Day. On the back of that page they have to represent the number in four different ways: tallies, coins, objects, addition or subtraction sentences. I usually make books each nine weeks. I fold the pages towards each other and place the cover page around those pages and staple. Click on the picture to get your copy.
This is not an exhaustive list but it's a place to get started.
Base ten blocks (units, rods and flats)
Numeral cubes (Dice)
Bags of objectives to count (The Dollar Tree has lots of collectibles)
Math and Literature Connections to Place Value
Listed below are a few children's books related to the instruction of place value.
Professional Titles for Teaching Place Value
I hope you have enjoyed my little post as much as I enjoyed putting it together for you. If there is anything I didn't cover that you'd like me to, please let me know. If you like what you see, and download it...leave some love, feedback, suggestions. I hope you find something you can use next year! I have to admit I was stressed out for this post...I had nightmares about the internet going out or my computer catching a bug...I know crazy right.
Don't forget to link up and blog about your thoughts on place value. I can't wait to read your posts!
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Emergent Literacy Design:
Angry Ants and Their Adventure Across Arizona
Rationale: When children are first learning to read, they must first be able to identify both the phoneme and grapheme for all 26 letters of the alphabet. This lesson is designed to help students recognize the phoneme /a/ and its grapheme A or a. To recognize the /a/ sound, students will use their hands to make an eye rubbing motion (like a baby crying) whenever they hear /a/ read in the book A Book. To recognize A and a, students will practice writing each letter on primary paper with the help of a memorable saying.
A Book, Stan and Jan Berenstain (Berenstain Enterprises, Inc. 1997)
White drawing paper
Chart with "Alice and Andrew were mad at the angry ants."
Letter Aa worksheet (URL below)
What Begins with A? worksheet (URL below)
Word cards: A, a, BAT, AT, STUCK, HAD, LUCK
1. "Before we can learn to read, we all have to learn sounds and the symbols that represent those sounds. In our language, we have to learn the alphabet. Watch me talk to you. Do you see my mouth move?" (wait for answer) "My mouth does move! It has to move to make different sounds for different letters. I am going to teach you the sound /a/ today. It has two written symbols." (A and a: show both symbols to the student)
2. "To say /a/, we can cry like a baby, /a/a/a/." (hold hands under eyes and twist them back and forth) "What does my mouth look like? I have my mouth open like a circle, and my tongue is behind my bottom teeth. Try it with me, /a/a/a/a/."
3. "Now, I am going to say a word. I will show you how to tell if it says /a/. Watch my mouth to see if it makes a circle. Bat. B-at. Bb-a-t. Bb-aa-t. My mouth made a circle. I heard /a/ in the middle of bat. The baby was crying, wasn't it?"
4. "I have a sentence written for us to read. It is a little tricky because most of the words start with the same letter. Sentences like these are called "Tongue Twisters" (on chart). Alice and Andrew were mad at the angry ants. You say it. Let's say it like this now, Aaalice aaand Aaandrew were maaad aaat the aaangry aaants. Your turn. We are going to say it one more time but like this, /A/lice /a/nd /A/ndrew were m/a/d /a/t the /a/ngry /a/nts."
5. (For this step, the student will need primary paper and a pencil.) "Here is some special paper for learning to write letters. Remember I showed you the two symbols for /a/. One of the symbols (show the capital A to the student) is called capital A and the other (show the lowercase a to the student) is lowercase. Let's write both letters. To make a capital A, start at the bottom and draw a slanted line to the right all the way to the rooftop. Start from that point and draw a slanted line to the right all the way to the bottom. Last draw a line in the middle of the two lines you just made. To write a lowercase a, make a circle between the middle line and the bottom line. Then draw a straight line behind/on the right side of the circle from the middle line to the bottom line (it has to touch the circle). Now make nine more of each."
6. "I am going to say two words at a time. I want you to listen to see which word you hear /a/ in. Remember to watch for my mouth to see if it makes a circle, and listen for the baby crying. Cap or set? Bite or mat? Bowl or pan? Ram or hit? Now I am going to say some random words. See if you can hear /a/. If you hear /a/, do your hand motion. Band, of, tap, bat, tip, sap, kid, cup, class.
7. "I have a book to read. It is called A Book. This book has a lot of words that say /a/ like the baby crying. While I am reading, I want you to do your hand motion just once when you hear /a/. I will read slowly so you can hear the baby crying, and remember to watch my mouth for the circle." Read A Book. "Now let's think of something else the angry ants might have advanced across. Write the name of what you chose and draw a picture. Make a spelling if you are not sure how to spell the name of what you chose for the ants to advance across." Display students' work.
8. Show BAT, and model how to tell if it is bat or bit: The a tells me to cry, /a/a/a/. This word is b-aaa-t, bat. Now, you try some: AT: at or it? STUCK: stack or stuck? HAD: had or hid? LUCK: lack or luck?
9. Distribute both worksheets. Students should color pictures and trace picture names. Also there is practice for writing A and a. On the second worksheet, students identify the pictures and draw a line to the a. Have students read phonetic cue words from Step #8.
Byrne, B., & Fielding-Barnsley, R. (1990). Acquiring the alphabetic principle: A case for teaching recognition of phoneme identity. Journal of Educational Psychology, 82, 805-812.
Bruce Murray. Emergent Literacy Lesson. "Brush Your Teeth with F". http://www.auburn.edu/academic/education/reading_genie/sightings/murrayel.html
Return to the Solutions index.
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Rationale: In beginning readers, it is necessary that they understand that words are made up of phonemes and the phonemes are represented by letters. Children first need to be able to identify phonemes in spoken words. This lesson will teach the students to write upper and lower case f , identify objects that start with the letter f, and hear the /f/ sound in spoken words by relating it to the symbol f.
paper (one sheet for every student)
Pencils (one for every student)
Pictures that begin with the letter f and some that do not. Ex: flower, fish, frog, bear, frown, tree, dog.
Large cut outs of the letter F – upper and lower case.
Dry erase board and marker
Plain drawing paper
One copy of Flip and Flop by Dawn Apperly
1. Explain why: Tell students that every letter has a mouth move that makes that letter’s sound. “Today we are going to learn about the letter f and the sound it makes - /f/. I will show you how to say the sound and how to write upper and lowercase f. Then I will show you some pictures and you will tell me if it begins with the /f/ sound. After lots of practice, you will be able to find the /f/ sound very easily!”
2. Ask students: “Have you ever seen a cat get very mad? When cats get mad, they say /f/. Let’s pretend to be angry cats and say /f/ (make hands into claws).
3. “Let’s try a tongue twister. I’m going to say it first, and then I want you to repeat after me. Five fantastic frogs flipped forward off their lily pads. (Wait for students to repeat). Now I want to say it together, but stretch out the /f/ sound and make your claws like an angry cat every time you say /f/. FFFFive fffantastic fffrogs ffflipped ffforward offfff their lily pads.”
4. Put up cut outs of capital and lower case f. Have students take out primary paper and pencils. “We can write the /f/ sound using the letter f. I’ll show you how to write it. Let’s start with lower case f. Start to make a little c up in the air, then straighten it out, go down, and cross at the fence. Everybody hold up your letter f. Excellent! Now I want you to make nine more just like it.” Once students finish, model capital f. “Now let’s make capital f. Go down, over for his hat, over for his belt, but no shoes. Everybody hold up your capital f. Good job! Now make nine more just like it. Now every time you see the letter f, you will know it makes the /f/ sound.”
5. “I’m going to show you some pictures and I want you tell me if these words start with the /f/ sound.” Put up pictures flower, fish, frog, bear, frown, tree, and dog. Call on students and ask how they knew the picture started with the /f/ sound. Make sure to correct any wrong answers.
6. “Now I’m going to say some words and I want you to tell me if they start with the /f/ sound. I’ll show you how. The word is first. F-f-f ir-st. F-f-f ir-r-r st. F-f-f – there it is! First! Now you try. Do you hear /f/ in fly or cry? Flop or drop? French or pinch? Far or car?” Let students answer as a group, and call on an individual student and ask how they knew.
7. Pass out plain drawing paper and crayons to students. Have them draw a picture of something that starts with the letter f and label it. Ask a few students to show their drawing to the rest of the class. Optional: Display their work on a bulletin board with a large letter F at the top.
8.Read the book Flip and Flop. Have the students raise their hands every time they hear the /f/ sound.
9.Pass out worksheet with pictures of objects that start with f and some that do not. Have them color in the pictures that start with f.
Estill, Laura Finding F http://www.auburn.edu/rdggenie/guides/estillel.html
Graves, Lindsay Four Funny Fish http://www.auburn.edu/rdggenie/constr/gravesel.html
Bruce Mouth Moves and Gestures for Phonemes
Apperley, Dawn Flip and Flop, New York, Scholastic,
Click Here to return
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Fun questions getting students to talk
|:: esl resource center ::
Activity type: : this activity involves students asking each other personal questions in order to develop fluency.
Level: Intermediate students and above
- There are a variety of ways that you can get the students to ask the questions which are listed below.
- You can dictate the questions i.e. read out some of the questions and get the students to write them down. Once you have done this, ask the students to read the questions out to you. Check that they have written the questions down correctly.
- You can stick the questions around the classroom. Tell the students to mingle around the room. When they get to a question, they should stop and ask the nearest student to them the question.
- If you want to add novelty value, play music. When you stop the music ask the students to find the question nearest to them on the wall and to discuss it.
- Alternatively you can hand out one question per student and ask them to mingle and ask as many people they can in class the question. At the end of the mingle activity, tell the whole class to give feedback on the questions that they asked.
NOTE: all of the above ideas are useful for students who feel inhibited when speaking. When mingling, they do not feel so much on the spot and are more likely to speak.
- Once the students have mingled, do necessary error corrections. For homework, you can ask the students to write their own answers to the questions that they would like to write about. This will further practice the language that they have used.
- What was the happiest event in your life?
- What three things could you not live with out?
- Who is your best friend?
How long have you been friends for?
- What would you say was the happiest time in your life?
- What achievement are you most proud of?
- What is your favorite time of day?
- What’s your favorite type of weather?
- What is your favorite word and why?
- What is your favorite sound and why?
- Who do you most respect?
- Who would you like to change lives with for a day, if you could?
- Who do you think you take after in your family?
- What is your favorite place and why?
- What do you want to achieve in the next 5 years?
- What do you like about yourself?
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Understanding and Graphing the Inverse Function
- 0:06 Inverse Functions
- 2:24 Five Steps to Inversing a Function
- 2:46 Examples
- 5:31 Graphing Inverse Functions
- 6:52 Lesson Summary
Did You Know…
This lesson is part of a free course that leads to real college credit accepted by 2,900 colleges.
If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.
If I tell you that I have a function that maps the number of feet in some distance to the number of inches in that distance, you might tell me that the function is y=f(x) where the input x is the number of feet and the output y is the number of inches. You might even tell me that y = f(x) = 12x, because there are 12 inches in every foot. But what if I told you that I wanted a function that does the exact opposite? What if I want a function to take the number of inches as input and return the number of feet as output? Could you tell me what this function is?
Inverse functions are exactly that. If we have a function y=f(x), then the inverse function is written as y= f^(-1)(x), and it does the exact opposite of the function. What happens if you put a function and its inverse into a composite function such as f^(-1)(f(x))?
Let's take a look at an example. Say we start with 4 feet. Well, our function is f(x)=12x because there are 12 inches in every foot. If we plug in 4 feet to start, then f(4) = 12 * 4 = 48 inches. Now if we take the inverse function, and the inverse function is going to be f^(-1)(x) = x(1/12). So, if we take 48 inches, then our inverse function, f^(-1)(48) = 48 / 12 = 4 feet. Okay, so you might be able to find f(x) and f^(-1)(x) just based on your understanding of inches and feet, but how do you do it in general?
Five Steps to Inversing a Function
- Write your function out in terms of x and y: y=f(x).
- Swap the x and y variables: x=f(y).
- Solve for y as a function of x.
- Set y = f^(-1)(x).
- Check the composite function: f^(-1)(f(x)).
Following these steps, let's say we have a function f(x) = 3(x - 1) + 2.
We're going to write this out in terms of x and y: y = 3(x - 1) + 2. Then we're going swap the x and y variables, so we're going to write this as x = 3(y - 1) + 2. This can be a confusing step if you're not careful, but at its heart, all you're doing is putting x everywhere you see y and putting y everywhere you see x. Then you're going to solve for y as a function of x. So I'm going to subtract 2 from both sides, x - 2 = 3(y - 1), divide both sides by 3, (x - 2) / 3 = y - 1 and add 1 to both sides and I end up with y = 1 + (x - 2)/3.
I'm going to call what's on the right-hand side my inverse function, f^(-1)(x) = 1 + (x-2)/3. Finally, I'm going to check my answer, so I'm going to find f^(-1) of (f(x)). To do this, I'm going to write f(x) = 3(x-1) + 2. I'm going to plug that in as input for my inverse function, so f^(-1)(x) = 1 + ((3(x-1) + 2) - 2)/3. I have my input here, so I'm just going to solve and simplify for f^(-1)(x) = 1 + (3(x-1))/3: f^(-1)(x) = 1 + x - 1. And sure enough, f^(-1)(f(x)) = x, which is exactly what we'd expect.
So what about a function like y = round(x)? Remember that round(x) just rounds our input to the nearest integer: round(4.2) = 4. However, round(4.8) = 5 and round(5.1) = 5. In this case, do you think that you can find an inverse function that can take 5 and give your either 5.1 or 4.8? No, round(x) is a function that has no inverse.
Graphing Inverse Functions
What about the function f(x) = x^3 + 3x? I can write it out in terms of x and y: y = x^3 + 3x. I can then swap the variables, x = y^3 + 3y. I can then solve it for y - but that's not immediately obvious to me. Is there another way? Let's go back and look at an easier function, like f(x) = 3x - 6. I end up with a graph that looks like this, a simple line. Now I'm going to graph the inverse, which is f^(-1)(x) = (x + 6)/3. So the inverse is this blue line; it looks a lot like the original function, except it's mirrored.
The inverse function will undo the function. That means that the inverse function of the function will give you back what you started with. But not all functions will have inverses. For example, y= round(x) doesn't have an inverse. You can find the inverse function with our five-step process. If you graph a function and its inverse, they're 45-degree reflections of one another. That's an easy way to find the inverse or get an idea of what the inverse function looks like for really complex functions.
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An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
Explore the different tunes you can make with these five gourds.
What are the similarities and differences between the two tunes you
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
This article, written by Nicky Goulder and Samantha Lodge, reveals
how maths and marimbas can go hand-in-hand! Why not try out some of
the musical maths activities in your own classroom?
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
Suppose you are a bellringer. Can you find the changes so that,
starting and ending with a round, all the 24 possible permutations
are rung once each and only once?
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This came up in another lesson, so I'm repeating it here. Yes, we all need it, even though it seems elementary and simple.
Nominative Case: The category of nouns used as the "grammatical subject" of a sentence. Think of the word "nom," which means "name." So nominative means the "name of something"... whether its a pronoun, actual name, or noun. Subjective just means related to being Nominative.
Don't get hung up on terms... but focus on the correct usage.
The pronouns in these sentences are used nominatively.
I went to town.
She went to town.
He went to town.
They went to town.
And so on....
Objective case: nouns that are the "objects" of verbs. Objects "receive" the action.
These pronouns are used objectively.
Carol gave it to me.
Carol gave it to her.
Carol gave it to them.
Carol gave it to us.
And that prompts the question about the "you" and "me" rule. Or when to use the nominative or objective case of other pronouns.
Mary and I went to town.
Carol went with Mary and me to town.
Carol went with her and Mary to town.
The test to know which case to use? Remove the "other person" from the sentence. Which sounds proper?
I went to town... OR... ME went to town.
Carol went with I to town... OR... Carol went with ME to town.
Carol went with HER to town... OR... Carol went with SHE to town.
Get the idea? Any questions?
"What remains of a story after it is finished? Another story..." Eli Wiesel
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noun clause is a clause (containing a subject and a verb) that
can replace a noun.
The examples below show how they are
I don't know her. (not a noun
I don't know who
I don't know where
I don't know when
she moved to the United States.
Noun clauses often use words such
as when, what, why, who and other question words, but the speaker
may or may not be making a question.
You can also begin a sentence with a noun clause:
Why he did that is a mystery.
(It is a mystery)
What she's doing is very interesting.
(That is very interesting.)
A good knowledge of noun clauses
will help your English, but it's important to practice their
Here are some examples of sentences that use
1. Do you
know how old they are?
2. This father is wondering what
his son will do in the future.
3. I can't remember
what time the flight arrives.
Because noun clauses are often used with question words, many students make
I don't know who is that woman. (incorrect!)
I don't know who that woman is. (correct)
He wants to find out where was she born. (incorrect!)
He wants to find out where she was born. (correct)
Remember to put the subject before the verb in a noun clause.
In the next lesson, we'll learn how to use "that" at the beginning of a
Next: Lesson Seven
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Introduce Vocabulary: Peter’s Chair (Keats)
What to Do
Select three Tier Two vocabulary words to teach your students. A list of suggested words appears below. Write the vocabulary words on the board or on chart paper.
1. Introduce the story.
Today we are going to read a story entitled Peter's Chair.
2. Introduce the three vocabulary words you have chosen.
Before we read the story, I want to introduce some new words that we will come across. Please repeat each word after I say it.
3. Read the story.
Let’s read the story. Make sure to listen for today’s vocabulary words and to think about how they are used in the story. If you hear a vocabulary word while I am reading, raise your hand.
4. Define key vocabulary words. See definitions below.
Let’s think about our vocabulary words. The word ______________ means ____________. Does anyone remember how this word was used in the text?
Call on students to answer the question. Then refer to the text to show how the word was used in context. Repeat this process for each vocabulary word.
Now let’s practice what we’ve learned.
Fussing means moving around and worrying a lot. What's the word?
The mom was fussing around her sick child. If you're not feeling well, you might be fussing.
I'm going to name some people. If you think the person might be moving around and worrying, say 'fussing'. Otherwise, stay quiet. Ready?
- A baby who is hungry
- A happy, sleeping baby
- An auntie worried about her niece who scraped her knee
- A teacher who is missing one of her students
- A child playing with friends
Mutter means to talk quietly so others can barely hear it. What's the word?
A teacher can’t hear it when the student mutters the answer. If you want people to understand you, you should speak loudly, not mutter.
I'm going to name some people. If you think the people are speaking so quietly that others can barely hear, say mutter. Otherwise, stay quiet. Ready?
- A cheerleader at a game
- A fireman asking if everyone is out of a burning building
- A woman in a library reading to herself
- A man in a grocery store trying to remember what he needs to buy
- Children playing on a slide
Rascal means a person who does sneaky or naughty things. What's the word?
Sometimes raccoons are called rascals because they like to steal things. Your Dad might call you a rascal if you jump out of a hiding place and scare him.
I'm going to name some behaviors. If you think the behavior is sneaky, say rascal. Otherwise, stay quiet. Ready?
- Hiding classmates' markers
- Turning out the light when someone is reading
- Putting grease on a doorknob
- Helping set the table for supper
- Riding a bike to school
For Advanced Students:
If time permits, have students create more examples for the vocabulary words.
For Struggling Students:
For ELL Students:
In order to help ELL students learn the words, it may be helpful to use realia and/or to teach cognates.
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It's Thursday again, and time for another little lesson from the English teacher.
A reader asked to address the use of the words lose and loose. Good question!
First, the definitions.
Lose is a verb meaning to misplace or to come to be without something.
- Did you lose your cell phone?
- I think you're going to lose a tooth.
- It's sad to hear about a child's losing his mother.
Loose is almost always used as an adjective meaning free, not restrained, not fitting tightly.
- I have lots of loose change in my purse
- You have a loose tooth!
- Those pants are really loose on you.
I think that most writing mistakes with these words come about because of the way the words are pronounced. Lose is one of those English words that breaks all kinds of pronunciation rules. Lose looks as if it should rhyme with nose or hose, doesn't it? It doesn't seem possible that the sound of "oo" could be present in a word that has one "o" and a silent "e." So writers often throw in another "o." That's understandable. But words that have "oo" plus an "se" are pronounced with a hard "s" sound, not a "z" sound, such as moose, goose, noose, and caboose.
Perhaps the best way to remember to use the word lose is to connect it with two words that are almost never misspelled: loser and lost. I'll bet you've never read about the TV show The Biggest Looser, do you? Nope. Everyone seems to know that the word is loser. And no one ever writes of being hopelessly loost; lost is a word over which no one struggles. So if you find it difficult to remember that the verb you want is lose rather than loose, just remember that you don't want to be a loser. The right word is just the root of the word loser: lose. Or remember this: You'd be lost without the right word. Lose is the root of lost.
So here's a little quiz for you. Fill in the blanks with lose or loose:
- I need to _______ 10 pounds.
- These jeans are so tight, and they're supposed to be really _______ on me!
- Let go of me! Turn me _______.
- I'm afraid I'll _______ my way in the dark.
If you answered 1. lose; 2. loose; 3. loose; and 4. lose; you've got it!
Please let me know if you have any questions about English grammar or if there's a particular point you'd like for me to address in one of these little lessons. I want these to be a blessing to you!
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Yet some students still have trouble with reading comprehension. Comprehension is the ability to fully understand what you have read. It can also include more advanced skills such as being able to draw conclusions based on the reading material.
Try these ideas to help your child with comprehension:
Encourage your child to form pictures in his head of what he is reading. If he has trouble with this, have him actually draw the pictures at first.
Have your child name at least one thing in the material that reminds him of something he already knows.
Have him tell you what he thinks are the most important parts of the story or text. What is the main idea? If he’s reading a short story or a novel, who are the main characters? What conflicts do the characters face?
Practice critical thinking, a key skill for middle school students. Ask your child to give you his thoughts about the material. Does it make sense? Should the author have presented it in a different way? Did characters in the novel make good choices?
Copyright © Parent Institute
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Here’s a story that will help children understand why it’s important to be kind to their classmates. Cut a large heart out of red construction paper and hold it in your lap as you begin to tell the story below:
This is a story about a special friend named (imaginary name). He always came to school with a smile on his face and a big heart full of love for his classmates. (Hold up the big heart.) (Name) listened to his teacher, did his best work, and helped his friends. However, some of his friends weren’t always so kind. Joe made fun of his shoes and broke a little of his heart. (Tear off a piece of the heart and let it drop to the floor.) Ann said, “I’m saving this seat and you can’t sit here” at story time and broke a little more of his heart. Sammy wouldn’t share his crayons (tear off a little of the heart) and Sara called him a mean name. What are some other things that might break his heart? (Let the children name other things that cause hurt feelings as you let the pieces fall to the floor.) By the end of the day his heart was all in pieces and it was so sad.
Who can tell me how to put his heart back together? What are some kind things you can do for your friends? As children name different acts of kindness pick the pieces of the heart off the floor. Glue the pieces together on a poster as a reminder to have a kind heart. Encourage children to write friends’ names on the poster when they are kind and helpful to them!
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rivers by Margaret and Elizabeth
We're Margaret and Elizabeth, and we're hitting the links...at the Science Museum of Minnesota! Our local science museum actually has a mini-golf course that was designed so kids can learn about rivers while putting. As we played on this specialized course, our minds wandered from holes-in-one to how real rivers work. Our DragonflyTV question: What do rivers do to the land?
What did we do?
We spent time at the museum exhibit on rivers, and chose some things we wanted to learn more about. We packed up our canoe and headed for a local river to check it out!
What did we find out?
Our canoe ride showed us how rivers meander; or twist and turn, and how the water deposits rocks and pebbles on the inside of each curve. We also learned how sediment layers develop in water; and how humans change river flow with dams.
- Collect some sand and pebbles, and do a sediment investigation. Make sure you have pebbles and sand grains of various shapes and sizes. Mix them all up. Get a clear jar or bucket with water in it. Pour in the mixture of sand and pebbles. Watch them settle to the bottom. Which grain size settles farthest down? Why? Stir up the sand and pebbles with a stick and let them settle again. Do the same size grains always settle farthest down?
- Study how water meanders on a driveway. This works best if your driveway has a little slope. Stand at the top of the driveway, and then slowly pour water from a small bucket onto the driveway, letting it run down the slope. Watch the water's path. The water won't carve a path in the driveway, of course, but it will "choose" a path to follow. Watch the leading edge of the water, as it runs into stuff like cracks, dips or pebbles, and see how it moves left or right to get past the obstacles. Draw a picture of the path the water leaves behind.
- Use this rivers investigation as a science fair project idea for your elementary or middle school science fair! Then tell us about it!
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Play Word BINGO with your student!
- Create BINGO game cards by writing words in a grid on a piece of paper.
- Make small flashcards with words on them. These cards will be used as the game pieces.
- Have your student pick one of the flashcards, read it, and match it with the corresponding word on the BINGO game card.
- Play the game with your student until one of you has a BINGO.
- For variety, try matching words on the BINGO card with their definitions.
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Your Mark, Get Set, Read!!!
Independence Lesson Design
Independence Lesson Design
Reading fluency is the ability to recognize words accurately, rapidly, and automatically. In order for children to really enjoy reading, and to better understand what they are reading, they must read fluently. Fluent readers must begin to read with automaticity so they can focus on the meaning of the text. Instead of having to spend time decoding individual words, a fluent reader can recognize and decode words instantly, thus allowing them comprehension and enjoyment of the text. In this lesson, students will learn how to improve their fluency by learning and using strategies such as cross checking. In this lesson, students will also increase their fluency skills with repeated readings as well as one-minute reads.
Book: Pat's Jam by: Sheila Cushman. Carson, CA. : Educational Insights, c1990. (one copy per student and one for teacher)
Stop watch (1 per student pair)
A track made out for students to see their progress (Draw or trace a racetrack on poster board and cut out. Have a start and finish line. The track should contain numbers such as 0, 5, 10, 15, 20, etc., in which the students will place their car on the track according to how many words they read. Place sticky tack on the back of the cut out race cars with student's name and have students place on the track after reading to show the number of words read and their progression.)
A cut out of
a race car (One per student- Find or draw
racecar and cut out. Write the student's name on the car.) Partner
record sheet (1 per student):
record sheet (1 per student):
Name: ______________________ Date: ___________ Book:
After each reading my partner, :
2nd reading 3rd reading
1. Read more words correctly yes/no yes/no
2. Read smoother yes/no yes/no
3. Read faster yes/no yes/no
One minute read (1 per student):
Name: _________________________ Date: ___________ Book:
After 1st read _______
After 2nd read _______
After 3rd read _______
Begin by explaining to students the importance of reading fluently. "WE ALL WANT TO BECOME BETTER READERS. TODAY WE ARE GOING TO LEARN SOME WAYS TO BE MORE FLUENT SO THAT WE CAN READ FASTER THAN WE CAN RIGHT NOW. IF WE READ FASTER AND DON'T HAVE TO CONCENTRATE ON INDIVIDUAL WORDS, , WE CAN UNDERSTAND WHAT WE ARE READING AND THIS MAKES READING MORE FUN.”
Using crosschecking can be very useful when students get stuck on difficult words. Explain to students how they may use crosschecking. "I am going to read a sentence from a book and show you how crosschecking can be helpful. The bate is black and can fly. Wait! That didn't make sense, let me go back and check. Oh, it says the bat is black and can fly. I know this because bats can fly and they are black. Now I want you all to try. I'm going to read this sentence and I want you to use crosschecking to figure out what it should say. Raise your hand when you know. 'The girl is made because her brother broke her doll.' How can you tell what it should say?”
Model how to become a fluent reader. “I AM GOING TO SHOW YOU THAT YOU CAN BECOME A FLUENT READER THE MORE YOU READ AND REREAD. write the sentence on the board: I went to the park to swing. “I-----WWWEEENNNT----TO-----THE----P---PAARRRK-----SSSOO. WAIT THAT DOESN'T SAY SO. LET ME TRY THAT AGAIN. I-----WWEENT-- WENT--TO---THE---PAARRRK-----TO----SSSSWWWIIINNNG. OH, SWING. OKAY, LET ME TRY THAT AGAIN. I-----WENT---TO---THE---PARK-----TO----SSSSWWWIIINNNG. NOW I'VE GOT IT, I WENT TO THE PARK TO SWING.” Ask the students if they understood what you read the first few times. ask them why they think it was easier to understand you the last time versus the other times. Explain to students that the more fluent they become, the more they will understand what they are reading.
Let the students practice reading fluently. “YOU ALL ARE GOING TO READ A BOOK CALLED PAT'S JAM BY: SHEILA CUSHMAN. PAT AND PAM ARE FRIENDS. THE TWO DRIVE TO THE STORE AND GET A HAM AND SOME JAM. WHEN THEY LEAVE THE STORE AND GET BACK IN THE VAN, THEY REALIZE THEY DON'T HAVE ANY GAS. WHAT DO YOU THINK THEY ARE GOING TO DO? WILL THEY HAVE TO WALK ALL THE WAY HOME? WELL, YOU HAVE TO READ THE STORY TO FIND OUT. I WANT YOU ALL TO READ THE BOOK TO YOURSELF AND THEN REREAD IT.” Once all the students have had time to read the book, ask them some comprehension questions to check for students understanding of what they read. “WHO WERE THE MAIN CHARACTERS? DID THEY DRIVE A CAR? WHAT DID THEY GET AT THE STORE? WHAT WAS THE PROBLEM WHEN THEY LEFT THE STORE? HOW DO YOU THINK THEY GOT HOME?”
Break students up into pairs. Each pair will be given a stopwatch and 2 partner Record sheet. The students will take turns reading as many words as fluently and accurately as possible in one minute. One student will read as the other one records, then they will switch. Tell them, "I WANT EACH OF YOU IN YOUR PAIRS TO READ THE STORY OUT LOUD. ONE OF YOU WILL START OFF AS THE TIMER AND RECORDER WHILE THE OTHER ONE TRIES TO READ AS FLUENTLY AND ACCURATELY AS POSSIBLE. THEN, YOU WILL SWITCH ROLES AND DO THE SAME THING. YOU WILL END UP READING THIS STORY THREE TIMES WITH YOUR PARTNER. MAKE SURE IF YOU ARE RECORDING AND TIMING THAT YOU ARE JUST PAYING ATTENTION TO HOW THEY ARE READING AND THE TIME. REMEMBER, WE DO NOT MAKE FUN OF EACH OTHER. I EXPECT YOU TO TAKE YOUR JOB SERIOUSLY DURING THIS ACTIVITY."
For assessment, have each individual student come up to the teacher's desk to take a one-minute read. The students will reread the book they just read while the teacher is assessing the child's reading fluency. The teacher should have a stopwatch that beeps so that the students know when to start and stop without the teacher having to yell stop. The one minute read sheet will be used to mark their progress. There will also be a place at the bottom for comments to write in anything noticed during their one minute readings that they may need to work on. This could be things such as their breaks in between words and their voice pitch. The students will be moving their racecar as far as how many words they were able to read in the one minute on the track. I will explain to the students that their goal is to get all the way around the racetrack.
Lauren Dooley, 3,2,1 READ!
Tabetha Rape, Let's Go Reading
Jam by: Sheila
CA. : Educational Insights, c1990.
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| Linking/Action Verbs Practice
Linking Verb: A linking verb is a verb that links a word in the predicate to the subject. That word will either be a noun (predicate noun), which will rename the subject or an adjective (predicate adjective), which will describe the subject.
Action Verb: A verb that shows action. It may or may not have a noun or pronoun following it that receives the action of the verb (direct object).
There are some words (sense words) that will be linking or action verbs depending on how they are used in a sentence. For example:
Mary seems to like the house.
The house seems large.
Write down the verbs in the following sentences. Then tell whether they are action or linking verbs.
1. The ghost appeared in the doorway.
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An exponent is a number that tells how many times the base number is
used as a factor. For example, 34 indicates that the base number 3
is used as a factor 4 times. To determine the value of 34, multiply
3*3*3*3 which would give the result 81.
Exponents are written as a superscript number (e.g. 34) or preceded
by the caret (^) symbol (e.g. 3^4).
Some facts about exponents:
- Zero raised to any power is zero (e.g. 05 = 0)
- One raised to any power is one (e.g. 15 = 1)
- Any number raised to the zero power is one (e.g. 70 = 1)
- Any number raised to the first power is that number (e.g. 71 = 7)
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Lesson #1: What’s Respect?
Activity type: Brainstorm & Discussion
- BEFORE students arrive, WRITE “RESPECT” on the board.
- ASK: What does RESPECT mean? Brainstorm definitions/synonyms.
- ASK: Why is treating others with respect important in groups?
- ASK: What does it looks like when you treat someone with respect? Give an example that you’ve experienced in the past day or so. Examples (if kids are stuck): Say “please” and “thank you.” Return things that people lend to you. Listen when someone else is talking.
- ASK: What does it look like when someone disrespects you? Give an example from your own (recent) experience. Examples (if kids are stuck): People make fun of the way I look. Don’t listen to what I have to say. Push me around or threaten me.
- ASK: What is self-respect? What’s an example of someone acting like they have self-respect? What behavior might indicate low self- respect? How does self-respect connect with treating others respectfully?
- EMPHASIZE: Communities work best when we treat each other with respect. Respect needs to be a 2-way street otherwise something’s off balance and people don’t feel safe physically or emotionally.
READ and DISCUSS:
ASK: Was Manuel showing respect for Carlos? What would you do if you were Manuel? Is doing that going to get you more respect in the future? Will it increase your self-respect? How might it help/hurt the friendship? Has this ever happened to you? How do you usually handle it?
READ and DISCUSS:
ASK: Did Michelle show respect for Carrie? What would you do if you were Michelle? What would you do if you were Tanya? How does keeping other people’s secrets show respect for them? What are some times when keeping a secret may hurt more than it helps?
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Clifford Learns About the First Thanksgiving and So Do We!
By Marci Ruiz
- Grades: PreK–K, 1–2
Over a three week time period, the students learn about the pilgrims in terms of: why they left England, their voyage to America, the challenges they faced when they arrived, and their relationship with the American Indians. As a culmination of this unit, we have a feast with another class. We come as the pilgrims bearing gifts, sharing our harvest, and thankful for our survival. The children in the other class come to the feast as the Indians who helped us.
- Tell why the pilgrims came to America.
- Name two of the ships that brought the pilgrims to the new land.
- Tell some of the ways the Indians helped the pilgrims survive their first year in America such as showing them:
- How to plant corn.
- Which plants were safe to eat?
- Which plants were useful?
- How to fish.
- How to hunt.
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PatrickHaller/fineweb-edu-plus
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Date: 19 Jan 1995 13:13:05 -0500 From: Margaret Gallegos Subject: Question What is the Pythagorean Theorem?
Date: 19 Jan 1995 14:09:42 -0500 From: Dr. Math Margaret Patterson Subject: Re: Question Hi there. Thanks for writing to us. The Pythagorean Theorem has to do with the lengths of the sides of a right triangle. A right triangle is any triangle which has one right angle (an angle of 90 degrees) - like this: |__ If the sides next to the right angle are of lengths a and b, and the third side is of length c, then (a*a) + (b*b) = (c*c). When people say this, they say, "a squared plus b squared equals c squared because when you multiply a number by itself like a*a, you call it a squared. This can be written as a^2. |\ | \ 2 2 2 a | \ c a + b = c | \ |____\ b Some numbers that work in this equation are, 3,4, and 5, and 5, 12, and 13 So if you are told that you have a right triangle whose sides are 3 and 4, like this: |\ | \ Then you can use this theorem to find out what the 3 | \ c third side is. | \ 3*3 + 4*4 = 9 + 16 = 25 = 5*5, so c=5 |____\ 4 Let us know if you have any other questions. -Margaret, Doctor on call.
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994-2013 The Math Forum
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PatrickHaller/fineweb-edu-plus
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Lesson 1—The Scale
In writing music there are many things to study, as counterpoint, theory, harmony, and rhythm. In the past, when most of our hymns were written, these subjects were more common.
In the next few lessons we will study what the singing schools of our country taught about writing hymns.
In this first lesson we will cover what scales and intervals are. A scale is a series of eight tones made up of certain intervals. An interval is the difference in pitch between tones.
We will look at the C scale to discover a major scale and two kinds of intervals.
The C major scale covers from C to C on the piano.
It has eight tones and is called a major scale, because it has a series of whole and half steps in a certain order.
First, we must discover what are whole and half steps. We can do this by looking at the piano keys. Below are the keys from C to C.
From C to D is one whole step, because there is a black key between C and D. From E to F is a half-step because there is no note between E and F. If there is any black or white key between two notes, the interval is a whole step. If there are no keys between two notes, the interval is a half-step.
Now, we call from C to C on the piano a major scale, because there is a pattern of whole, whole, half, whole, whole, whole, half steps. This pattern is in all the major scales. On the piano keys below find the pattern of w, w, h, w, w, w, h intervals.
Try finding the same pattern of intervals in the G major scale. It is a series of eight tones starting at G and ending at G. Note the G major scale has an F# note in it to make it a major scale.
Find the same pattern of steps in the D major scale. Note that there is an F# and C# to make it a major scale.
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PatrickHaller/fineweb-edu-plus
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Uhhhhh I'm not sure???
In order for our students to become amazing readers we must teach them the sounds of the each letter. Once they know these sounds they will be able to recognize them when reading; thus, making them successful readers. In this lesson I will be teaching the u=/u/. The students will understand recognize and understand the letter. Also, they will have many tasks to perform to better help them practice the written and spoken words containing u=/u/.
* Cards with words: run, tug, cub, slap, neck, sack, pick, skunk, and bump.
* Primary paper and pencils for each student.
* Poster containing a tongue twister: Uncle Bubba bumped his umbrella up.
* Letter box lesson: r, u, n, t, g, c, s, l, p, n, e, k, a, b, and m.
* Pictures for assessment:
* Fuzz and Buzz: one copy for each pair of students.
1. I will review the previous letters and sounds we have learned. Then I will introduce the correspondence u=/u/. I will explain and tell the students the sound that the /u/ makes. This letter says /u/. To make this sound you will open your mouth making sure to keep your tongue still and say /u/. Pretend as if you do not know the answer to a question. You are thinking and you say /u/. To help us make our sound, we are going to pretend as if we do not know the answer to a question. Let us pretend to think hard and scratch our heads. Let me see everyone say /u/ and scratch your head. Good Job!'Next I will help the students find the letter in words.
2. Next we will practice finding the letter u in written words. I will hold up words and together we will find which word makes the /u/ sound. For example: 'Do you hear /u/ in b-u-m-p or s-t-a-m-p? I hear /u/ in bump. Now I want you to try but remember when you hear the sound /u/ to scratch your head.
3. Then pass out the primary paper and pencils (each student should receive 1 piece of paper and 1 pencil). 'First we are going to practice writing u. We will start at the fence, go down to the sidewalk, and curve back up to the fence and then a straight line down from the fence to the sidewalk. Remember we do not pick up our pencils. Now let's try a few.' Have student practice a line of u. 'Now, I want everyone to write me a message about a bug they do not like.'
4. Next we will practice a tongue twister. I will say the tongue twister one time through, then I will have the students say each word after me. Then we will review the tongue twister many times before we put the whole thing together. Then I put the poster up with the tongue twister on it. 'Now we are going to practice our tongue twister. Make sure to keep your eyes on the board so you know what we are saying.' First I will say the tongue twister then we will say it together. Uncle Bubba bumped his umbrella up. 'Ok now repeat after me.' Have the students repeat the tongue twister. 'Now this time when we read we are going to stretch out the /u/ when we hear it in a word. UUUUncle Buuuubba buuumped his uuumbrella uuup.
5. Now we will begin the letter box lesson. I will draw boxes on the board. I will also provide students with paper boxes and letters to make the words we will spell as a class (make sure to give only lower case letters). First I will explain the lesson and then model the lesson for the students. 'Now we are going to spell some words that have the /u/ sound in them. I have twp boxes up here so this means we are spelling words with two sounds. The first word we will spell is upon. What sound do we hear first? That is right. We hear /u/. That means we will place u in the first box. What sound do we hear next in up? That is right we hear /p/ so we will put our p in the second box. Next we hear /o/ and /n/. Now let's add them all together u-p-o-n. Good job! Now we are going to do one more as a class. The new word is stump. What sound do we hear first? That's right we hear /s/. We will finish spelling stump as a class. 'Now I am going to say some words and I want to you practice putting the different sounds in the boxes.' I will continue saying words, sounding them out and placing letters in the boxes. After each word, the students will wait and we will go over each word. After will practice with 3 phoneme words, 4 phoneme words and 5 phoneme words. Words listed below, review words included: 3-- [run, tug, cub] 4--[slap, neck, sack, pick] 5--[ skunk, and bump].
6. Next we will use these cards and practice reading some words. This word is pump. Start with /p/, and then add the /u/. Now put both sounds together /pu/. Now let's add the last sounds. What do you hear next? Right we hear /m/. What's the last sound you hear? That's right /p/. Now let's put the whole word together.... Fish the cards with the class.
7. Now students will be placed into pairs with one book per pair. 'Today we are going to read about Buzz and Fuzz. Fuzz is a bear who sets out to find some honey. But when he is out something terrible happens. In order to find out what happens we must read the book Fuzz and Buzz. '
8. For the assessment give the students worksheets for them to list the names of the pictures. Circle the words that have the /u/ sound.
Cushman, Sheila. Fuzz and the Buzz. Educational Insights.
Return to Caravans Index:
Return to Caravans Index: http://www.auburn.edu/academic/education/reading_genie/caravans.html
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PatrickHaller/fineweb-edu-plus
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Talk about: One
Click on the image to enlarge it. Click again to close. Download PDF (171 KB)
These are level 3 geometry and number problems from the Figure It Out series.
identify features of two dimensional shapes (Problem 1)
multiply and divide numbers by multiples of 10 (Problem 2)
explore fractions (Problem 3)
fit puzzle pieces together to form a square (Problem 4)
The Talk About pages on pages 21–24 are designed for small group discussions to be followed by a whole-class round-up.
Give students about 5 minutes to discuss the similarities and differences of a triangle and a circle. Each group must have someone taking notes. You could let each group send out a “spy”, who can report back ideas from other groups. Students may choose to focus on a range of characteristics:
As a result of the whole-class round-up, a number of questions may arise that, in turn, become the subject of a whole-class investigation. Students may debate the number of sides and vertices that a circle has. It can be thought of as a polygon that has an infinite number of sides and vertices.
Students could make a table of regular polygons. From this, they will see that as the number of sides increases, the polygon becomes more like a circle:
This shows that a circle is the limiting case. The limiting case is the case which defines the limit (boundary, end point) of a process. In this instance, as the number of sides and vertices increases, the shape approaches the limiting case, a circle.
In this problem, students need to show that they understand the decimal system. If students consider the place values of whole numbers and decimals, they will see that division by 10, 100, or 1 000 causes the decimal point to move to the left.
For example, consider 250:
Dividing by 10 can be interpreted as “How many tens are there in ...?”
Dividing by 100 can be interpreted as “How many hundreds are there in …?”
Students can use a calculator to find out what happens to 250 as it is divided by 10, 100, and 1 000.
In the case of 25.0, 2.50, and 0.250, the zero has no effect because it is not acting as a place holder.
Students will see that there are 21/2 (2.5) hundreds in 250. Use pattern to show that 250 ÷ 1 000 is 0.250. Because 250 is a quarter of 1 000, there are 1/4 (0.25) thousands in 250.
As a number is divided by 10, the value of each digit becomes one-tenth of its previous value. This effect is best described as the digits shifting one place to the right relative to the decimal point. With division by 100, the shift is two places, and with division by 1 000, it is three places. So, consider the whole number 497:
497 ÷ 10 = 49.7
497 ÷ 100 = 4 .97
497 ÷ 1 000 = 0 .497
Students may wish to use a physical model of the problem, such as strips or squares of paper. An important feature is that the strips or squares used to represent the custard squares are of the same size. Using this idea:
Students will see that two-thirds is greater than one half, and therefore the three people sharing five custard squares get more.
For the pieces to form a square, the total number of small squares forming the square must add to a square number (1, 4, 9, 16, 25, 36, …).
There are only 14 small squares, so two small squares must be added for the pieces to form a 4 x 4 square. Encourage students to add one square to two different pieces to make this work. A number of solutions are possible, for example:
Answers to Problems
1. Answers will vary. Comments could include:
a. The triangle has sides, but the circle does not appear to have any.
b. Both are closed figures with reflectional and rotational symmetry, and you can find the centre of both shapes.
2. a. The digits shift 1 place to the right in relation to the decimal point.
b. The digits shift 2 places to the right when dividing by 100.
c. The digits shift 3 places to the right when dividing by 1 000.
3. Three people sharing 5 custard squares get more (1 2/3 compared to a 1 1/2).
4. No. You cannot form a square because there are only 14 small cubes. There are not enough small squares to form a 4 x 4 square, and there are too many for a 3 x 3 square.
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PatrickHaller/fineweb-edu-plus
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Introduction to Limits Introduction to the intuition behind limits
Introduction to Limits
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- Welcome to the presentation on limits.
- Let's get started with some-- well, first an explanation
- before I do any problems.
- So let's say I had-- let me make sure I have the right
- color and my pen works.
- OK, let's say I had the limit, and I'll explain what a
- limit is in a second.
- But the way you write it is you say the limit-- oh, my color is
- on the wrong-- OK, let me use the pen and yellow.
- OK, the limit as x approaches 2 of x squared.
- 13 00:00:42,55 --> 00:00:46,34 Now, all this is saying is what value does the expression x
- squared approach as x approaches 2?
- Well, this is pretty easy.
- If we look at-- let me at least draw a graph.
- I'll stay in this yellow color.
- So let me draw.
- x squared looks something like-- let me use
- a different color.
- x square looks something like this, right?
- 23 00:01:10,73 --> 00:01:20,04 And when x is equal to 2, y, or the expression-- because
- we don't say what this is equal to.
- It's just the expression-- x squared is equal to 4, right?
- 27 00:01:27,65 --> 00:01:33,1 So a limit is saying, as x approaches 2, as x approaches 2
- from both sides, from numbers left than 2 and from numbers
- right than 2, what does the expression approach?
- And you might, I think, already see where this is going and be
- wondering why we're even going to the trouble of learning this
- new concept because it seems pretty obvious, but as x-- as
- we get to x closer and closer to 2 from this direction, and
- as we get to x closer and closer to 2 to this
- direction, what does this expression equal?
- Well, it essentially equals 4, right?
- The expression is equal to 4.
- The way I think about it is as you move on the curve closer
- and closer to the expression's value, what does the
- expression equal?
- In this case, it equals 4.
- You're probably saying, Sal, this seems like a useless
- concept because I could have just stuck 2 in there, and I
- know that if this is-- say this is f of x, that if f of x is
- equal to x squared, that f of 2 is equal to 4, and that would
- have been a no-brainer.
- Well, let me maybe give you one wrinkle on that, and hopefully
- now you'll start to see what the use of a limit is.
- Let me to define-- let me say f of x is equal to x squared
- when, if x does not equal 2, and let's say it equals
- 3 when x equals 2.
- So it's a slight variation on this expression right here.
- So this is our new f of x.
- So let me ask you a question.
- What is-- my pen still works-- what is the limit-- I used
- cursive this time-- what is the limit as x-- that's an x--
- as x approaches 2 of f of x?
- 60 00:03:29,59 --> 00:03:30,21 That's an x.
- It says x approaches 2.
- It's just like that.
- OK, so let me graph this now.
- So that's an equally neat-looking graph as
- the one I just drew.
- Let me draw.
- So now it's almost the same as this curve, except something
- interesting happens at x equals 2.
- So it's just like this.
- It's like an x squared curve like that.
- But at x equals 2 and f of x equals 4, we
- draw a little hole.
- We draw a hole because it's not defined at x equals 2.
- This is x equals 2.
- This is 2.
- This is 4.
- This is the f of x axis, of course.
- And when x is equal to 2-- let's say this is 3.
- When x is equal to 2, f of x is equal to 3.
- This is actually right below this.
- I should-- it doesn't look completely right below it,
- but I think you got to get the picture.
- See, this graph is x squared.
- It's exactly x squared until we get to x equals 2.
- At x equals 2, We have a grap-- No, not a grap.
- We have a gap in the graph, which maybe
- could be called a grap.
- We have a gap in the graph, and then we keep-- and then after x
- equals 2, we keep moving on.
- And that gap, and that gap is defined right here, what
- happens when x equals 2?
- Well, then f of x is equal to 3.
- So this graph kind of goes-- it's just like x squared, but
- instead of f of 2 being 4, f of 2 drops down to 3, but
- then we keep on going.
- So going back to the limit problem, what is the
- limit as x approaches 2?
- Now, well, let's think about the same thing.
- We're going to go-- this is how I visualize it.
- So as x approaches 2 from this side, from the left-hand side
- or from numbers less than 2, f of x is approaching values
- approaching 4, right? f of x is approaching 4 as x
- approaches 2, right?
- I think you see that.
- If you just follow along the curve, as you approach f of 2,
- you get closer and closer to 4.
- Similarly, as you go from the right-hand side-- make sure
- my thing's still working.
- As you go from the right-hand side, you go along the
- curve, and f of x is also slowly approaching 4.
- So, as you can see, as we go closer and closer and
- closer to x equals 2, f of whatever number that is
- approaches 4, right?
- So, in this case, the limit as x approaches
- 2 is also equal to 4.
- Well, this is interesting because, in this case, the
- limit as x approaches 2 of f of x does not equal f of 2.
- Now, normally, this would be on this line.
- In this case, the limit as you approach the expression is
- equal to evaluating the expression of that value.
- In this case, the limit isn't.
- I think now you're starting to see why the limit is a slightly
- different concept than just evaluating the function at
- that point because you have functions where, for whatever
- reason at a certain point, either the function might not
- be defined or the function kind of jumps up or down, but as you
- approach that point, you still approach a value different than
- the function at that point.
- Now, that's my introduction.
- I think this will give you intuition for what a limit is.
- In another presentation, I'll give you the more formal
- mathematical, you know, the delta-epsilon
- definition of a limit.
- And actually, in the very next module, I'm now going to
- do a bunch of problems involving the limit.
- I think as you do more and more problems, you'll get more and
- more of an intuition as to what a limit is.
- And then as we go into drill derivatives and integrals,
- you'll actually understand why people probably even invented
- limits to begin with.
- We'll see you in the next presentation.
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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Foot Book Lesson Plan
- Grades: PreK–K, 1–2
About this book
- The Foot Book by Dr. Seuss
Set Up and Prepare
Divide students into pairs. With oak-tag, use the book as a model to cut out "clown feet" and "red feet." Make the clown feet about 11 inches long and the red feet about three inches long. Make enough feet for each pair of students in class. This will give students both large and small feet to experiment with.
After reading the story, pass out one of each of the feet to the student pairs. Give students time to color the feet. Explain that they will be using them to measure objects in the room, as well as the room itself. Model how to place the feet alongside an object to measure it. Use paper and pencil for recording. After students have had some time to take measurements, meet as a group to share and discuss findings.
Supporting All Learners
Keep personalities and learning styles in mind when pairing students.
Have students use their own feet to make a template and measure objects in the room.
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PatrickHaller/fineweb-edu-plus
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Spelling Practice Ideas
Here are some fun ways to study your spelling words:
Type 'Em- Type all of your spelling words on the computer. You can e-mail them to your teacher.
Fancy Lettters- Use old magazines, catalogs, or newspapers to cut out letters and glue them doen to spell your words.
Spelling Baseball- Draw four bases on a piece of paper or set up four chairs to be the bases. Pitcher selects a word.
If batter can spell it correctly, he moves forward one base.
If batter cannot spell word, he remains where he is.
Child receives point every time he passes home base.
Spelling Bingo- Each player folds a piece of paper four times so you have sixteen boxes.
Each person makes his own game board and chooses sixteen words from the current list
and past lists (or use the same word more than once). Write one word in each box.
The caller says a spelling word. If a player has the word on his card, he traces
over it with a pen or colored pencil. If the playerdoes not have the word, he turns
his paper over and writes it on the back. For a real challenge, play blackout bingo.
Snowman- Snowman is a non-violent wersion of Hangman. Draw a snowman with hat and
three buttons. Play like hangman, but erase a part of the snowman for each guess.
The object is to guess the word before the snowman melts.
Water Wash- Use a paintbrush and water to write your words on the sidewalk.
Trace Arround- Print one of your spelling words neatly. Take a colored pen and
draw an outline around the word, closely following the shapes of the letters. Close your
eyes and remember the shape. Now try to write the the word.
ABC Order- Write your words in alphabetical order.
Then write them in reverse alphabetical order.
Riddle Me- Write a riddle for each word.
Connect the Dots- Make a square of four rows of dots with four dots in each row.
Before taking a turn, player must spell a spelling word.
If the word is correct, he connects two dots.
When a player forms a squares he can write his initials in the box.
Player with the most squares at the end wins.
Story, Story-Write a story using ALL of your spelling words.
Sentence Please- Write a sentence for each spelling word.
Colorful Word- Use two different color pens to write your spelling words.
Use one color to write the consonants and the other for the vowels.
Do this one more time. Close your eyes and picture the word in your mind.
Now try and write the word with just one color.
Memory Game- Make pairs of word cards. Flip them over and try to match the pairs.
Finger Tracing- Use your finger to spell out each of your words one letter at a
time on your mom, dad, or grandpartents back. Then it's YOUR turn to feel and spell.
This also works well when you trace on the inside of your forarm.
Practice Test- Take a practice test
(this is especially good on Wednesday night before the REAL test)
Scrabble- Use Scrabble tiles to spell your words.
Sing Them Loud, Sing Them Song- Have your parents sing the letters of a spelling word
to you in a loud voice. You echo the spelling and then sing it again softly.
Now BOTH of you sing the word in the voice you choose.
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PatrickHaller/fineweb-edu-plus
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When kids in grade 6 walk into the woodshop for the first time they have already heard about the project from their siblings and are SO excited to get started.
So here are my learning objectives:
-The students will learn to creatively solve a problem within a set of guidelines.
-The students will learn to measure, apply the measurements and create a cutlist
-The students will learn to safely use a drill press and a scroll saw.
-The students will learn to effectively learn to glue.
-1/4" square graph paper.
-3/8" MDF 8.5" by 11"
-1/4" wood strips 3/4" by about 3' per student
-7/16" steel ball bearing. (per student) You can get these from electric motor rebuild places or just look under bearings in the 'pages.
-12" Forstner bit
-Sanding board. (or just plain 120G paper sheets)
Submitted by HD Stafford Middle School for the Instructables Sponsorship Program
Step 1: Starting the Design
I goto the board and start drawing a big rectangle than ask for where a start and finish should be. Than i ask the kids to describe paths from start to finish... the catch is the line can't touch or cross. Often i'll get kids to come up and draw paths as well. Eventually i guide them to a design thats interesting but not too twisty. They all say "thats TOO EASY!!" so i ask them to make it tricky by adding holes... They quickly figure out that holes placed in the right spots.... at the end of long runs or on the outside of a curve or in a way that makes the ball have to curve back and forth... make it tricky. Than i ask HOW we're going to make sure the ball follows the path... The kids figure out that walls will control the ball.
I set them all up with pages and say that i want 4 different paths with walls and holes all quick sketched in 20 minutes. They freak out and ask for more time. I say "NO WAY!" and yell GO!!! They love that its kind of a race...
This gets their brains going.
At the end of the 20 minutes (or whatever they need... i fudge it...) i say to stop and give them rules... i write them on the board...
Choose 1 and use the graph paper to draw it.
-All up/down and left /right. No angles. (tough to build)
-The ball takes up a space of 4 squares. So do the holes. This means that they must allow space for the ball to roll around the holes.
-The walls take up 1 square wide. The kids have to allow room for the walls.
-You have to allow at least 3 squares wide in between walls.
I than get the kids to start a rough but accurate drawing of the path.
They than add the walls roughly. check out the pictures...
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PatrickHaller/fineweb-edu-plus
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By: Jessica Pieplow
For children to read and spell words, it is imperative that they understand that letters stand for phonemes. Also, spellings map out the phonemes that are found in spoken words. By practicing correspondences, which is composed of a grapheme and a phoneme, a child will come to have a better understanding letters, phonemes, and the mappings of phonemes in spoken words. In this lesson, the students will learn the correspondence, oa = /O/. They will be able to recognize the /O/ sound in spoken and written words in connection with the letter representation of oa.
Elkonin letterboxes and letterbox letters (oa, t, l, d, c, s, p) for each child,
dry erase board and markers,
Bo and Rose books for each student,
primary paper and pencil for each student,
pre-made worksheet with sentences that contain the oa= /O/ correspondence,
another worksheet with pictures and corresponding words
1. Begin by learning the oa= /O/ correspondence to review the long O sound. Have students think of words that make the long O sound. Write the words that are given on a small dry erase board. Some of these words may be the written with oa, but some may not.
2. Discuss the /O/ sound and explain that there is more than one way to represent this sound. Look on the board and select the words that represent the /O/ sound with the letters, oa. (If there is not one up there, show the students some words with the selected correspondence. Circle the oa correspondence in all of the words on the board.
3. Now is the time to introduce the tongue twister for the correspondence. Write this sentence on the board so that the students can see the words. Then, read the sentence to the students. "This is our tongue twister for the long /O/ sound. Load the boat to travel the moat. Now we are going to go through and underline our long /O/ sound. Load(underline) the boat(underline) to travel the moat(underline). Now, let's all say this tongue twister together. Clap your hands one time when you hear the long /O/ sound." Make sure that the students clap each time it is appropriate in the sentence. Do this twice.
4. "Great job! This time let's drag out our long /O/ sound in our tongue twister. "Loooooaaaaaaad the booooooaaaaat to travel the mooooooaaaaaat."
5. Now, it is time for the letterbox lesson. Review the rules with the class first. For example, "If there is one sound but two letters, how many boxes need to be used? One" After reviewing the rules, go over a few examples with the students, explaining what you are doing and why. To do this, draw letterboxes on your dry erase board so that the students can see and model examples. For example, "Okay class, I have drawn 3 letterboxes. I am trying to spell the word boat. Okay, so let me break it up. b- O - t. b- O- t. Okay. In my first box, I need the b sound, so I'm going to be a b in the first box. For the second box, I need the O sound. I can spell that with an oa. SO, if going to be oa in the second box for my O sound. T is my last sound. For the last box, I'm going to put a t. So let me but it all together. Boat. Great! That's boat. Now, you guys try a few. First, let's get out our letters oa, t, l, d, c, s, p. Our first word is soap (3 letterboxes). The next word is boat (3 letterboxes). The next word is coat (3 letterboxes). The last word is load (3 letterboxes). Great job class! Now let's go back, and I'll spell the words and you guys will read the words."
6. "Now, we are going to read, Bo and Rose.
When you come across a word with the correspondence that we've learned today, I want you to write it down on your own sheet of paper. When everyone is through reading, we can go through and see if we found all of the words."
7. To assess my students, I will create a worksheet that focuses on the new correspondence. The students will be directed to read through the sentences, circling the words that represent our oa= /O/ correspondence. Also, there will be another sheet with pictures and decodable words. The students will match the correct word with the correct picture.
York, Lindsay. (2003) Meet Lee, the Sleepy Bee. A beginning reading design created by Lindsay York. Auburn University, Reading Genie Website: retrieved July 7, 2003.
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Field Hockey Drills For Kids
These field hockey drills for kids will get them in shape and ready to play. The sport of field hockey requires a lot of running, stopping and starting. Shooting to score is a key element. Use these drill to motivate the kids with a bit of fun and play incorporated into learning and working out.
- Up and Back. Begin field hockey drills for kids with simple running. Just running back and forth is boring, so instead, play a game of up and back. Line the kids along one end of the field and instruct them to run to the half-field line and back. Then add to the half-field line, back to the beginning and then all the way to the other end. Then add half-field, back, all the way and back to the half-field mark. Finally, go from start to half-field, back, then all the way, back to the half-field, back to the opposite end then a long run all the way back to the start. Make it a race to motivate the players to be competitive and work harder.
- Dribble dribble. The next piece in field hockey drills for kids involves practicing dribbling. Now that they can run the length of the field, add a stick and ball to the mix. Line the team up at one end of the field, each with their stick and ball and have them dribble, or move the ball with the stick, repeating the Up and Back drill.
- Down the line. Building on the previous field hockey drills for kids, line the kids up at one end of the field each with a stick in hand. Only give a ball, or puck, to the player on the left end of the line. On go, the first player passes to the second player. The second then to the third and down the line. When the last player receives the ball, they then begin passing it back down the line. This skill is difficult as they are running. Have them begin at a jogging pace and build to a run.
- Across the field. Now that the team can pass, build on the previous field hockey drills for kids by lining the players diagonally across the field from one end to the other. Have them pass the ball, or puck, up and back.
- Shoot and score. Now that they have running and passing down, line them up at the half-field line and give them all a ball. On go, each player, beginning at the left end of the line, shoots the ball at the goal. Repeat until they can all hit the goal. This will improve on their aim.
- Run and score. The final piece in field hockey drills for kids is letting them run down the field and shoot for a goal one at a time. This incorporates all the offensive skills at once.
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PatrickHaller/fineweb-edu-plus
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S1 English Homework. Exercise 12.
Copy the following note into your jotter
This is the word used for showing what one person or thing has to do with another person or thing - usually where they are in relation to one another. E.g. over, under, between, on.
Choose a preposition from the list and complete the following sentences in your jotter. Only use each preposition once.
on before over into past under
up in down behind near
through opposite between among
on before over into past under up in down behind near through opposite between among
1. My best friend lives in the house _____ mine.
2. Put the lid ____ the potato pot please.
3. Your jacket is in the cupboard _____ the stairs.
4. Her house is the first one_____ the sweet shop.
5. The boy climbed ____ the fence to escape.
6. I'll drop you off ____ your house.
7. We will need to get ___ at 8 o'clock tomorrow.
8. Put your toys back ____ the toy box!
9. Brush your teeth ____ you go to bed.
10. The girl ran ____ the hill.
11. The room you are looking for is ___ those doors.
12. That's the boy who sat ___ me on the bus.
13. I'd like to live ___ Germany when I'm older.
14. He was stuck ____ the car and the wall.
15. I found the ball _____ the flowers.
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PatrickHaller/fineweb-edu-plus
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