Lesson 10- Mobeuis Strip- Year 1

1.      Make a normal loop (ring), just to show the kids the difference later between a normal loop and a Mobius strip.

2.      Make a Mobius strip. Ask the kids what it is. Is it just a plain loop of paper?

3.      How many sides do you think it has?

4.      Have a toy animal move around the edge of the Mobius strip. What happened? Where did it end up? Mark the starting point with a pencil.

5.      Explain what a Mobius strip is, and how it is made.

6.      Cut down the middle of the Mobius strip. What will happen? Did it divide into two pieces? A larger strip formed! Do you think that we can make an even bigger strip?

7.      Cut down the center of the larger strip. What happens this time? The same thing? Keep repeating this, until it forms a huge loop.

8.      Cut down the edge of a Mobius strip. What will happen now? It divides into two rings interlocked with each other!

9.      Magic trick with dice- what number is on the other side? Let the kids guess.

1Matchstick puzzles (below)

·         Flip a house upside down. How many matchsticks do you have to move?

·         Turn the fish around.

·         Make three triangles into four.

1  Shape Shuffle

Lesson 8- Perspective, Illusions, and Distance

*A student asked a question about why the moon seems to follow you while driving, and that inspired this lesson

Materials: toy, Incredible Visual Illusions- You Won’t Believe Your Eyes! ,or just the optical illusion pictures used in this lesson, craft sticks

Summary: This was an unusual lesson, because a lot of kids were sick, and the ones that came weren't paying much attention. Next time, I would split this lesson into two separate lessons, one with optical illusions, and the other one about perspective.

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1.      Why does the moon always stay in place as if it is not moving, while the trees are always moving when we drive?

Answer offered by the kids:

“The moon is big!” – Possible response from teacher: “What if it was something that was small and we could barely see it, but it was very far away? Would it still seem to stay in place all the time?”

Kids thought after the comment, and then decided that as long as we can see the object, if it is far enough away, it would seem to stay in place, and not go away from us.

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A great activity on this topic suggested by Maria Droujkova:

1. Draw 2 parallel lines on a paper; add perpendicular lines (so it looks like a railroad)
2. Put the paper behind the window laying down on the windowsill.
3. Take a transparency; lay it against the window; use markers to trace the railroad you see through the window.
4. The resulting railroad tracks will not be parallel anymore.
5. Now, take two lego men and start moving them along the railroad, at the same speed.
6. It will look like at the same time interval, the lego men cover different distances, since the distance between two railroad ties in the front seems to be bigger than the distance between the railroad tracks in the back.
7. For the moon, which can be considered to be at  in infinite distance, the speed of movement is almost negligible.

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2.      Ask the kids to sit right next to a toy on the floor, and see how far they can move without turning their head. Then put a toy on the opposite side of the table, and ask them to move until the toy comes out of their view. Can you see the toy longer if it’s on the opposite side of the table, or if it’s right next to you?

This activity was interesting for the kids, but it was a mistake that I put a hands-on activity at the beginning of class. DO NOT put hands-on activities at the beginning of class. First of all, the kids get very involved in it, and then they want to keep doing it, and also, they start to think that since they've already done the hands-on activity, they don’t have to pay attention anymore, because they already did the fun stuff!

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3.      How do we measure distances? Can distances only be measured with a ruler? Measure distances in steps, sitting people (let them sit on the floor), and toys.

At first, when I asked the kids if distances can only be measured with a ruler, they said, no, they can also be measured with a meter stick! Again, it would be better if this would be closer to the end of class, because the kids actually do something. Also, hands-on activities should be spread through the entire class, not bunched up one after another, as in this lesson.

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4.      How does an airplane look like in the sky? Is it big or small? Why do you think it looks that way? Take a toy, and show close up in front of the kids’ faces, and then slowly move it away. What happens? Why?

Kids had a pretty good answer: “Airplanes look small in the sky because they are so far away, and there are many things around us that are closer to us, and look much larger compared to the far away airplane.” At this age, kids have an intuition that things closer to us seem larger, and things farther away seem smaller, but they don't yet know why.

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5.      Show the kids the illusions in the Incredible Visual Illusions- You Won’t Believe Your Eyes- discuss what is going on and why.

                                                       

      

                           

As soon as I showed them those two illusions, they wanted to start seeing more, and wouldn’t let me move on to the next activity. It was hard for the kids to understand why the pictures were optical illusions, and how they worked, but they still liked them.

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6.      Optical Illusions can use color, light and patterns to create images that mislead our brains. Optical illusions occur because our brain is trying to interpret what we see and make sense of the world around us. Optical illusions simply trick our brains into seeing things which may or may not be real.

This is actually a good explanation of optical illusions, and kids understood it well.

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7.      Do the Extra Floating Finger Illusion, and the Hole in Your Hand Illusion.

The kids thought it was extremely cool that they themselves could make an optical illusion. When kids just see an optical illusion on a picture, it feels fake, but when they themselves can make an optical illusion, they prove to themselves that optical illusions are real.

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8.      Is this possible:

Try making it with craft sticks to double-check the kids’ answers.

The kids were all certain that it was possible, but after we tried making it with craft sticks, they realized that pencils can’t interconnect like in the picture.

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Is it possible that the blue trees are the same size?

There were two different answers from the kids. Some kids said that the blue trees were the same size, and found it easy to explain this way. Other kids were certain that the trees were different sizes, because when they put their finger on top of the far away blue tree, it was higher than the top of the closer blue tree. This shows that some kids at this age still don't understand that the linear measurement depends on the difference between two points - final and initial, not just the final one. This was noted by A.K.Zvonkin in his book " Math from three to seven" as well.

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Is this possible? 

If kids don’t understand how this is possible, this is a possible hint: “Are the people actually standing on the man’s hand?” After this hint, the kids figured out right away that the people are just standing behind the man, and the man is just sticking his hand in front of them, making it look like they are standing on his hand.

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The two yellow lines are the same size!

The kids didn’t seem amazed at this one, and seemed to know that the lines were the same size from the really beginning. The kids checked themselves by placing their fingers on the sides of both of the yellow lines, and they were parallel. 

Lesson 7- Symmetry and Snowflakes

Materials: several papers, scissors, safe mini mirror, pencils

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1.      Make cuts in the paper:

If I make no folds, and 1 cut, how many cuts will there be?

If I make 1 fold, and 1 cut, how many cuts will there be?

If I make 2 folds, and 1 cut, how many cuts will there be?

If I make no folds, and 2 cuts, how many cuts will there be?

If I make 1 fold, and 2 cuts, how many cuts will there be?

If I cut on the side, will the cuts be in the middle when I unfold it, or will they be on the edge?

Kids liked this activity, even though it was a bit too hard for them. Even though these little kids can’t imagine things in their head very well yet, it’s still a good activity for them to do, so that they can improve their mental rotation, at an early age.

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2.      How can I fold a square piece of paper into a triangle? Is it possible?

The kids figured this out really fast. “Fold it in half diagonally!”

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What about a triangle piece of paper into a smaller triangle?

This one was a bit harder, but still, it took them almost no time. “Fold it in half through the center again!”

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3.      Take turns going around the table, and ask every person to draw a shape on a folded snowflake. After everyone draws a shape, cut all the shapes out, and see what snowflake comes out.

This doesn’t exactly improve kids’ mental rotation skills, but kids learn that just from folding a piece of paper, and then cutting out pieces, can make a beautiful design. The snowflakes end up very pretty, and it gets the kids to pay attention more. It is a hands-on activity, and kids enjoyed it. Put the scraps from the snowflake into the recycling bin right away, because kids start playing with the scraps, and it is very hard to stop them! Also, do not give little kids sharp scissors! 

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4.      Cut a piece of paper into a circle. Will a circular snowflake work?

The kids were sure that a circular snowflake was impossible, (arguing that a snowflake has sharp corners, making it impossible to create from a smooth circle),  until we actually made one. It is interesting to see how kids respond to this question, and to see how they react.

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5.      Divide the page in half by vertical line; draw a shape on one side; ask the students to draw a mirror reflection on the other side. Check your work with a mini-mirror.

The kids were very happy that they were allowed to draw. Let the kids draw their own object also, and let them try drawing a mirror reflection over the line.

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6.      Easy snowflake symmetrical designs – color symmetrically. (Snowflake designs below)

For this activity, to get more teamwork, pass the design around the table, and let every child color one specific part of the design, and after everyone is done coloring, to see if everyone made a symmetrical design together. Teamwork is good for little kids.

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7.      Symmetrical movement (I raise my right arm, you raise your left, etc.)– work in pairs.

Wonderful! Have one child act as a mirror, and one child to be a real person doing the motions. When kids get to stand up and move around, they concentrate much better. 

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8.      Get Othello (board game), and make symmetrical designs.

The kids liked this activity, and they took turns making symmetrical designs with me, and other kids in the group. This is very funny, but it is what I observed during the class: When I told the kids that the problem they were solving was a game, even if it wasn’t, the kids started getting much more involved in it, because they thought that it was a game.J

Lesson 9- Year 1 - Games again!

·        Chocolate Fix- start from the beginner level, and slowly start advancing (if kids are stuck, help them out with hints)

·        Rush Hour- take turns moving the cars

·        Hoppers- beginner level

·        IZZI- give the kids some time to play around and make some designs with it, taking turns adding one block to the pattern every time

·        Shape Shuffle

·        Nim

·        Inverse Nim

·        War with cards- each partner takes out two cards, and whoevers add up to more, takes everything

·        If there is any time left, play robot, or 20 questions, depending on the kids’ mood.

Lesson 6- Reflection and Association

Materials: lunchbag, three different colored cubes, a sheet of paper for every child, index cards, poker chips, balance scale, weight cubes

References and inspirations: “Math from three to seven” by A.Zvonkin

1.     1.  In a lunchbag, make a tower of three cubes in this order: red, blue, and green, one on top of another. Don’t let the kids peek into the lunchbag. If I take the top cube from the tower, what color will it be? What color will the bottom cube be?
Kids reacted quickly, and had no problem visualizing the order of the cubes. The problem can be changed to a more complex variation- (more cubes; which cube is in the middle, what order were the cubes placed into the lunchbox, etc.)

2.      a. Draw these objects upside-down: house (square+ triangle on top), Christmas tree, car (rectangle with two wheels), sun, and together draw a stick figure- on the board.
Kids loved this exercise, and even after the group finished solving the problem, some kids continued drawing things upside-down. It was pretty easy for the kids to draw the figures upside-down, and if the kids are observed doing it easily, a more challenging figure could be presented.

b. Work in pairs. Have a piece of paper (with a drawing on it) in between you (face each other), and draw what the other person sees. Compare. Where you right?
This version of the problem was a bit harder for the kids than the previous exercise. A few kids were seen drawing the picture that they see, and then flipping the page over to get the picture (upside-down) that their partner was looking at- cheating of course, but very creative.

3.      Prepare three piles of index cards, with 4 cards in each pile. Every index card will have a 1 with a 2 on the back, 2 with a 3 on the back, and 3 with a 4 on the back. Ask children to work with a partner. A card will be held in front of every child’s face, between them and their partner. The kids have to figure out what number their partner has. (Can you figure out the number that your partner has on the other side of the index card?)
The kids figured what number their partner had easily, when the child had a 1 or a 4 on their card. But as soon as kids started getting 2s and 3s on their cards, they got confused and couldn’t figure out how knowing what your partner had was possible. After a few hints (what is the other person thinking, what are the possibilities of numbers that your partner can have, etc.), the kids slowly started to develop an understanding of how they could figure out what number their partner had. All the kids figured out the solution to the problem at about the same time.

4.      Get 7 blue plates, and 4 red plates, representing a plate for each prince and princess. ( you may use plastic plates or poker chips). Tell a story:” Once upon a time, there was a ball, and many princes and princesses were invited. The princes and princesses came, and took themselves plates. Every prince had a blue plate, and every princess had a red plate. But then, they found out that the food wasn’t ready yet, and they went to play in the garden. Then the cook came. He wanted every prince to have cookies, and every princess to have a mini-cake. But the princes and princesses already left, and only their plates were left. How can the cook figure out how many cookies and mini-cakes he has to make, for everybody to get what they needed? How many princes and princesses were there?”
Kids had no trouble with this one whatsoever, but had an argument about how many plates there were for the princesses J

5.      Make the kids sit in a circle, and play a “word chain”, by telling something to one another that has to do with the previous thing that they were told by association. At the end of the chain, see what the word was that ended up to be, and then say what the first word was.
The instructions for this problem should be a bit clearer, because at first, the kids thought that they had to say something that sounded similar to what they heard, not had a relation to the word, or was in the same category.

6.      Guess the weight – use scales. Take a few toys, stickers, poker chips, and other little things, and have the kids guess how many grams (little cubes) each of them weighs. Then see the actual weight.
Most of the kids either had no complete idea of the weight, or were almost perfectly correct every time. Pencils/crayons, erasers, paper clips, markers, building blocks, small toys, poker chips, and stickers, are some ideas and examples of what objects the kids can weigh. Let the kids put the little blocks (each weighting a gram) onto the scale by themselves, taking turns, because that makes the exercise more of a hands-on activity, and young kids enjoy that.