# Even + Even = ? (Age 6)

## The Activities

1. Topic: Infinity. Book: The Cat in Numberland, Chapter 2, by Ekelund. In this chapter, all the numbers are living in the infinite hotel,when along comes Zero, who also wants a room. How can they fit him in?
2. Topic: Proofs, Even and Odd Numbers. Define even and odd numbers. Then play with blue blocks adding even + even, and see if the result is even or odd.  Will the result always be even? What happens if you add odd plus odd?
3. Topic: Sorting. Sort the number tiles 1 – 100 on the number board.
4. Topic: Gravity. We took turns dropping objects off the balcony. Which object will hit the ground first?

A balled-up tissue vs. a flat tissue

## How did it go?

We had only three younger kids this week, so it was a pretty easy circle. The big kids were reading a book Galileo, who experimented with gravity by dropping items off the Leaning Tower of Pisa, so David wanted to drop stuff off our balcony. I figured that’d be pretty distracting to the little kids, so we decided to do it as a joint activity.

#### Cat in Numberland

This is one of my favorite books…it really emphasizes the wonder of infinity, and that some questions are not easy to answer.  In this chapter, the number Zero needs a room in the hotel. Ultimately, all the numbers decide to move up one room: One will stay in Room 2, Two in Room 3, etc. This leaves Room 1 empty, so Zero can move in. Finally the numbers each re-label their rooms to match themselves.

The kids were very interested in the book. One girl said she was worried that some very big number would no longer have a room, because they all moved up one room. I said that that big number could stay in the room for the number one bigger.

After the book, I said that the number Negative One knocked on the door and wanted a room. What can we do? At first the kids thought Negative One would have to sleep outside, or build a separate hotel, but then someone proposed moving the numbers up one room again. This seemed to work.

Even and Odds

First I asked the kids what is an even number? Kids started naming numbers: 4, 6, 12. My son started counting by 2s.  I then got out unit blocks and gave each kid a handful. I asked if that was an even or odd number of cubes? Some kids answered by counting the blocks and then knowing that 22 is even.  I showed the kids that instead, you could make two rows of blocks, and if the rows were the same length then number is even.

Even after this explanation, so kids wanted to instead count the cubes, but I kept demonstrating that what I really cared about was not what the number is, but whether it is odd or even. I showed that I could tell this without knowing how many cubes there were.

Next we tried a few addition problems with cubes: four + six, is it even or odd? 12 + 14? Is every even + even always even? Why?

The kids had some intuition about why even + even would be even, but it was hard to put it in words. One girl said something like “same number + same number means the answer will have the same too”.

Next we explored odd + odd, and found that it seemed to always be even. Why? One kid suggested that you could combine the two left over cubes to make even rows.

#### Sorting

We had a few minutes left before it was time to drop things off the balcony, so I got out the 1 – 100 board, and the number tiles. I seeded the board with four or five numbers, and then the three kids worked together to put in the rest of the numbers. They are much better at this than when they started circle. In the beginning it took them forever to sort the tiles on the side of the board that shows the numbers. This time it took about 7 minutes to sort the tiles on the side with no number labels. All three were able to place ’78’ in the right place by finding the ’71’ and counting up.

Dropping Stuff off the Balcony

See David’s blog entry for a full description, but this was fun and wild as you might expect. The older kids expected everything to drop at the same speed because they had read the book about Galileo. The little kids had no expectations, but really enjoyed having stuff thrown off the balcony, and seeing which would hit first.

Everyone enjoyed how slowly the tissue fell.