####
*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.*

*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*

*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.*

Masha, I too use Zvonkin's book with my son. We also use it as inspiration at our weekly Russian playdates. I'll continue checking your blog for more ideas.

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