## The Activities

**Topic: Estimating.**Book: Betcha! by Murphy. Two friends walk around town estimating the number of people, cars, and jelly beans they see.**Topic: Estimating, Counting.**Predict how many Unifix cubes can fit in a small bowl. How many Unifix cubes tall are you? How many Unifix cubes tall am I?**Topic: Logic.**A little boy rides the elevator alone to and from his 15th floor apartment. Whenever he goes down, he goes all the way down to floor one. Whenever he goes up, he takes the elevator up to the 7th floor, then the stairs up to the 15th. Why?**Topic: Geometry.**How many rectangles are in various pictures? How many triangles?**Topic: Spatial Reasoning.**Cover a checkerboard with rectangular tiles that are two squares long. Are some boards impossible to cover? Why?

## How did it go?

This week we had four kids, after a couple weeks with just two kids per circle. The kids were all interested in the activity and stayed on task really well.

#### Unifix Estimating

First we each guessed how many cubes would fit in a cup. Then each kid tried to get as many as possible inside.

The guesses ranged from four to eight. At first everyone fit 9 in their cup (with the lid sealed). But I managed to fit 11 in. After a lot of trying my son managed to squish in 12 cubes, much to his excitement.

Next we guessed how many cubes tall each kid was. We estimated by hold a stick of 10 cubes up to the kid’s body. A taller kid then decided to estimate his height by adding a few to the other kid’s height. The guesses were around 59 – 64 cubes. It was quite challenging to stick together that many unifix cubes, but the kids all stuck with it, and ended up with ~68 cubes per kid. We then guessed that I must be 100 cubes tall. I laid on the floor while kids made a very long unifix pole, and when we counted, it was 90 cubes long

#### The Boy in the Elevator

I got this story from Math from Age Three to Seven by Zvonkin. A little boy rides the elevator alone. When he goes down from the 15th floor, he goes all the way to the bottom. But when he goes up, he only goes to the 7th floor then walks up the stairs the rest of the way. Why?

The first suggestions were that maybe he wants exercise. Or maybe he doesn’t like the other buttons. At that suggestion, I drew them the buttons to see what they looked like:

I taped them up to the wall. No one had much to say about this, but then I asked one kid what would happen if her little brother pressed the buttons? She said he may be too short. Then another kid suggested maybe the boy was too short to reach the 15, and could only reach up to the 7. And on the way down, he can reach the 1 button easily.

#### Counting Shapes

In this activity, I showed the kids pictures of shapes I had drawn and we tried to find all triangles or rectangles in the picture.

At first the kids only see four rectangles in a picture like this. But after some looking, they noticed the big rectangle around the outside edge. Then later they noticed the long thin rectanble highlighted in green, and lastly the squareish rectangle in black. All the kids enjoyed this activity.

#### Tiling Checkerboards

I gave the kids a bunch of tiles that each would cover two squares on a checkerboard. Then I gave them increasingly interesting checkerboards to try to cover.

First they got a 4×4 checkboard which everyone easily covered.

Next was a 5×5 board:

Notice that one square is uncovered. The kids spent several minutes trying to rearrange the tiles to cover the last square. Eventually I suggested that maybe it’s impossible? If so, can you explain why? One kid suggested the tile is the wrong shape. Or maybe you should be allowed to let the square hang off the edge of the checkerboard?

Eventually, my son counted the squares on the board (5 on top, 5 down the side => 25 squares) and he said: “it’s impossible! 25 is odd, and the tiles can only cover an even number”. We checked it out with the other kids and eventually they were convinced.

Next was this board:

My son said it should be possible because there’s an even number. But no one could do it. A couple kids suggested they would need to put the squares diagonally. I asked about the color of the remaining squares? We noticed it was always two white squares left. I asked if one tile can ever cover two white squares? The kids tried it and said no, but were not fully convinced.

This was the last board. Everyone immediately said it was impossible. One kid pointed out it would be possible if you could overlap the pieces, but no one had a clear explanation of how they were sure it was impossible otherwise.