# Two Dice that Add up to Thirteen

## The Activities

1. Topic: Counting. Book: From the Garden: A Counting Book About Growing Food, by Dahl.

2. Topic: Indirect Counting. I told the kids a story about Princes and Princesses at a party. The Princes were blue poker chips, and the Princesses were orange poker chips. The King and Queen want to know whether there are more princes or princesses. However, the kids won’t stop moving around so it is hard to dance. The queen calls for a dance, and each prince and princess pair up.  There is one prince left over.  Which are there more of?

Next the cook hands out plates for each kid, blue plates for the princes, and orange plates for the princesses. But then the cook realizes that dessert is not ready yet, and sends the princes and princesses out to play.  But how can the cook know how many ice creams (for the princes), and pies (for the princesses) to make?

A Prince and Princess Ready to Eat

3. Topic: Probability, Charts, Counting. Give the kids 2 dice, and have them roll the dice, add the total, and fill out a probability chart to see which number is rolled 5 times first.

4. Topic: Conservation of Quantity. Show the kids a stack of 12 Keva blocks.  Ask them how many are there.  Now rearrange the blocks in a different shape, and ask them how many there are now. Keep doing this until the kids protest that the number of blocks is always the same.

A tricky structure to count.

5. Topic: Sequences. Have the kids arrange story sequence cards in order, and then read the stories.

## How did it go?

#### Counting in the Garden

This is a simple book that just shows different quantities of vegetables, from 1 to 12. The kids enjoyed taking turns counting the vegetables.

#### Princes and Princesses at a Party

The kids wanted to count the # of princes and princesses.  As soon as they’d start, I’d move the princes and princesses (poker chips) around, and say they were playing.  The math kids were very willing to keep counting even though there was no way to tell which chips they had already counted.  One kid counted 12 princesses, one counted 17 before I stopped him.

After the prince and princesses lined up to dance, all the kids quickly realized that there were more princes since one was left over.  After the princess and princesses left to go outside, one kid immediately said the cook could count the plates.  The kids enjoyed counting each color of plate.

#### Probability Race

I showed the kids the dice, and how to fill out the chart. Sum up the two dice, and then fill in the proper box.  We did part of a race as a large group, and then I broke them into a groups 3 and 2.  The kids all enjoyed throwing the dice (sometimes too hard), and counting the dots. They quickly caught on to how to use the chart, though several kids colored in the bottom square where the number was written, instead of starting on the square above.

The funniest interaction was when Kid A rolled two 6s and counted the dots to get 13.  He filled in the ’13’ box on the chart.  Later, Kid B (A’s partner), rolled two 6s, and immediately said “That’s 13!”.  I suggested he should check, and he figured out it was twelve.

We finished one race this time before the kids got too antsy. 7 won.  We’ll do this again in the future, and collect a group of charts to see if the kids notice any patterns.

#### Conservation of Quantity

I brought out a stack of 12 Keva blocks. First I asked a the kids to count the stack. Kid A got 11, but Kid B and Kid C both got 12, so we decided it must be 12.  Then I took the stack of blocks are rearranged them into a sun shape.  I asked “NOW how many are there?”  Kid D immediately said that there would still be 12, because I didn’t take any away.  However, the other kids were very happy to count them, and got 12.

Next I arranged the blocks into a stacked tower.  Kid D again said there were still 12, but the other kids wanted to check.  The blocks were much harder to count in this configuration.  Kid A got 8, and Kid B got 13.  Kid B started to explain loudly that Kid A must be wrong because he hadn’t counted all the blocks.  We check the number by all counting together while taking apart the structure, and we got 12.

Next I put all the blocks in a line.  The kids counted and saw there were 12. Then I showed them that I was taking 1 away.  Kid B and Kid D shouted that there were 11 left now, but some of the other kids counted to be sure.  I took away another 1, and they all guessed 10 now.  Then I took away 2, and that stumped them. Eventually Kid B guessed there would be 6 left, but we counted and got 8.  I kept taking away more blocks…once we got down to 4, the kids didn’t need to count anymore.  When we got to 0, the kids all laughed.  I asked Kid A to count the 0 blocks and he paused and then laughed.

#### Story Sequences

We have a box of story cards with 4 cards in each story. The stories are about things like carving a pumpkin or scooping ice cream.  The kids each got 2 turns to make a story, and then I read the story to each of them.  4 of the kids got their stories right every time (though it took some thinking for some of them).  The 5th kid had a bit more trouble, and both times mixed up two of the cards.  Kid D immediately saw the problem both times, and helped correct the stories.

At this point the kids were getting restless and were ready to play, so we ended circle 10 minutes early.