Lesson 4- Year 1 Patterns Fractals, and Categories

Materials: geometric shapes (foam stickers)

Patterns, Fractals, and Categories

·         Continue the pattern.

·         Dots: red, blue, green, red, blue, green, red, blue…?

·         Dots: small, medium, big, small, medium, big, small, medium…?

·         Square, triangle, circle, circle, square, triangle, circle, circle, square, triangle, circle…?

For all of these, draw them on a whiteboard, or make them out of stickers or other small things. Don’t just say the things in the pattern! First of all, for little kids, it’s hard to keep a lot of things in their head at a time, and also, it gets them more involved. If the kids figure out the patterns right away (which they did in this case), offer some harder patterns, for a challenge. An example is, “Big square, small square, big triangle, small triangle, big circle, small circle…”, and to make it even more challenging, the pattern can include sizes, shapes, and colors.

·         Sort these into groups.

·         Red big square, green big circle, red small triangle, blue small triangle, blue small circle

Kids seemed to be very excited that a problem can have more than one solution, and they worked together for a while, and discussed what categories were possible. Encourage teamwork.

·         Venn Diagrams

·         Who has a brother, a sister, or both?

·         Who likes to play (a sport that kids like), (another sport), or both?

Kids though it was cool that a math problem could use real life. More problems should be used that are actually incorporating math into real life, to show the kids that math is used in life, not just in math class. Kids also liked that for these problems, they themselves got to decide what would be in the Venn diagram (for the sports, they decided the sports from the Venn diagram, and for the brothers and sisters, it was actually related to them)

·         Invent your own pattern; make it and have a partner figure it out.

There were two categories of what kids did: either they made an unsolvable pattern that was random, or they made a really easy and basic pattern. The kids loved this activity, because they actually got to create a pattern, AND, have someone solve it!

• Discussion: where do we see patterns around us?

On this question, kids seemed to expect that I would give them examples myself, and they needed a bit of encouragement to get them thinking. They gave some good answers; zebras- they have stripes that are patterns, and a spiral, that keeps spinning more and more in, and more and more out.

·         Explain what fractals are, and if possible, give visual illustration and pictures of them.

Kids were interested, but didn’t really care if something was just a pattern, or a fractal.

 

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• Finding patterns in poetry:

o   “ One fish,

o   Two fish,

o   Old fish,

o   New…?”

o   Any other poems you can think of that have patterns?  Any songs?

These little kids aren’t old enough to know any more poems, except the one already given to them as an example. If the teacher (or parent) knows any more pattern poems, they could share them with the children, but children can’t think of any themselves.

·         Continue my pattern  (sample Raven matrices)

Kids liked this activity, and enjoyed that they had to visually figure something out as well as mentally. These weren’t very hard for the kids, but it took them a bit of time. Don’t help the kids as soon as they can’t solve something! Let them learn to think and solve things on their own. Only if they are really struggling, a few hints can be given. If the kids get enough time, they should be able to figure it out on their own.

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• Take turns making a pattern out of geometric shapes (stickers)

Kids liked working together to create a pattern. It is a good skill for the kids to be able to create patterns, because it increases their understanding and knowledge about patterns, and makes it easier for them to recognize one, and figure out what the pattern is.

·         20 questions game (on the carpet; take turns asking 20 questions to guess my object)

This is a good cool-down activity that uses creativity and logic. Only play this game to use as a cool-down activity! If it is played earlier than the after all the problems have been solved, the kids wouldn’t want to go back to working!

Explore at home: http://www.shodor.org/interactivate/activities/NumberCruncher/

Lesson 1- Kids and Graphs

(Some material adapted from "L'enfant et les graphes" by Frédérique Papy; Georges Papy; Danielle Incolle)

Materials: toy microphone, whiteboard or paper, poker chips, flashcards (optional), tangrams

1.      1. Name game- everybody says their name and a silly or interesting thing about themselves

Use a toy microphone, or any other object (pencil, marker, etc.) to pass around the room. The rule is, if you have the object, you can speak. If you don’t have the object, you have to be silent. Kids are more enthusiastic to talk if they have a pretend microphone, because they have the feeling that everyone is paying attention to them, and that they are “announcing” something. The most common answer that kids gave when they were asked for an interesting or silly fact about themselves was an activity that they like. If the kids are shy, don’t worry! Almost all little kids behave like this when it is their first class.

2.      2. Brothers and Sisters Discussion- There are many kids on a playground- every dot represents a person. How many girls are on the playground? (draw an oval with many dots inside it)

Kids get confused on this one, because they don’t have enough information to figure out the number of girls on the playground, but they think that the teacher wants an answer. They don’t know what to expect from the teacher yet, because it is the first lesson, and most of the kids just start guessing about how many kids there are. If the kids are not paying attention, ask them to count the total number of kids on the playground.

3.      3. How could we show pointing on the diagram (children point to sisters) Now, can you figure out how many girls there are on the playground? (Add arrows to the diagram).

The kids figured out quickly, that to show pointing on the diagram, they had to use arrows. At first, draw some simple arrows (one child points to the other), then slowly increase the level of complexity (two children at each other), and then have a very challenging part, where many kids point to one child on the diagram, and that child points to someone else. The first time around, almost all of the kids said that it was possible to find the number of girls on the playground, because there were arrows pointing to them. Then, after I asked the kids about the girls that didn’t have siblings, everyone changed their answers. For the first few lessons, some of the kids might not answer a question not because they don’t know the answer, but because they are shy. Encourage the kids to share their thoughts and not to worry if they are correct or not.

4.      4. Can you find the brothers? Explain. What about the boys that aren't brothers to anyone?

At the begging, the kids thought that if one child was pointing to another, it meant that they were a brother, but very soon, they realized their mistake. Let the kids think! Don’t rush them or tell them the answer right away! Later the kids figured out that if one child was pointing to another, and that child wasn't pointing back, it meant that the child pointing was a brother. They also realized that if two kids were pointing back and forth at each other it meant they were both girls. Let kids come up to the board, and explain their ideas of which dots are boys or girls, and how they figured it out. They understood that the lonely dots could either be boys that aren't brothers to girls, or girls that aren't sisters to anyone.

5.      5. Add different color arrows- children point to brothers now, and children point to sisters - discuss with the class

If it becomes too confusing and complicated for the kids, erase some of the arrows. Let the kids draw some arrows by themselves. Drawing arrows is a hands-on activity, and kids get less tired and bored if they do hands-on things.

6.      6. Dragon Nim- A dragon took 6 brothers and 6 sisters. One of the brothers wants to escape. The dragon suggested a game: 6 blue and 6 red poker chips in two columns. The 13^th chip is a magic apple. Take up to 3 chips from each column in one turn. If you take the poisoned apple, the dragon will eat you. Get a partner to play the game with.

Kids love it, and concentrate much more if there is a story tied on to the problem or puzzle, even if the story makes no sense at all. Kids like it even more if the story is silly. The kids really liked the game, but got tired pretty soon. Don’t expect them to stay on task for too long, because they are very young! Any variation of Nim is fine, and separating the poker chips into columns is optional, and isn’t required to play the game. The poker chips can just be lined up in a row instead of being separated into columns.

7.      7. What doesn't belong-

1.      Bird, bee, snail, airplane

2.      Big red square w/ hole, small red square, big red triangle, big green square

Careful! Don’t let kids start getting mad at each other because they don’t agree on which object doesn't belong. At this age, kids can easily start fighting after an argument. Give the kids a minute to think on their own about which object doesn't belong, and then discuss with the group. Frequently, kids will start asking questions similar to “But which answer is correct, then?” Explain to the kids that in many cases, there is more than one solution to a problem. 

8.      8. Venn Diagram- butterfly, crow, airplane, train, ship- use flashcards

Flashcards can be used to make this a hands-on activity, but just drawing the objects on the board will also work fine. To make Venn Diagrams with the flashcards, yarn or string can be used to form a Venn diagram, and the flashcards can be put inside it. An idea for the categories is things used for travel, and things that fly. Let the kids think of their own categories, though. More interesting ideas can come from the kids.

9.      9. Tangrams- cool down/ optional homework

Use tangram pieces (plastic or paper) to give the kids to play with for a cool down at the end of the class, or as an optional homework, if any of the kids want to do it.

Lesson 3- Year 1 (without notes) - Robots and Algorithms

1.      Give them a few examples of questions:

Is tomorrow Friday?

Do you have a brother?

Is 1+1=3?

Do witches fly on elephants?

2.      Now you ask me a couple of questions that I can answer yes or no to.

3.      Can you answer yes or no to all questions?

4.      Can you give me an example of a question that you can’t answer yes or no to?

For example,

Why is the sky blue?

What is the color of a dragon’s head?

5.      I will think of an object, and you can ask only yes or no questions, can you figure it out?

6.      Play Robot. Let the kids give directions to achieve a goal.

Ask the kids to hide a toy in the room, and one by one, give me instructions of how to get to it.

7.      Say the opposite of the given word

1.      Fix

2.      Find

3.      Sit

4.      Open

8.      Can you find the opposite of the words:

1.      Orange-fruit

2.      Paper

3.      Box

4.      Square

9.      Algorithms: In what order do you do this? Describe.

1.      Close the facet, open the facet, dry hands, and wash hands.

2.      Go to school, wake up, go to sleep, eat breakfast, put on your socks

3.      Imagine and describe what an orange/egg would look like, taste like, and smell like

10.  Does order matter?- have a short discussion

11.   First, I should ask everybody to explain to me how to put a toy into a flipped over box, even though I’m a robot, and don’t know much stuff. Ask the parents (or if they don’t want to, then the kids), to achieve something with everyone else’s instructions.