It’s great when kids go to math club and get to throw things. In this session, kids threw rubber dice that bounced and rolled, and put LOTS of math in play.

When the dice landed, kids counted how many times each digit 1 through 6 showed up. There are 6 possible numbers, so each digit should show up on about 1/6 of the dice.

We’re training future board-game winners here. Why? Because that trained them to think about probability, which gets WAY more interesting when you roll 2 dice. Some totals happen more often than others: snake eyes (1 + 1) are rare, while lots of pairs add up to 7. Next time they play Monopoly, they’ll know why the orange set rocks!

Get on a Roll and ask your kid to figure out all the ways to add 2 dice. Then see what fraction of the options generate each total. For an Extra Challenge, explore rolling 3 dice! Which total is the easiest to roll – and ask why the mirror image pattern happens again! Click the accordion below for the answers!

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Get on a Roll

How many ways to roll this total:

2: just 1 way – snake eyes: **1 + 1**

3: 2 ways: **1 + 2**, **2 + 1**

4: 3 ways: 1 + 3, 2 + 2, 3 + 1

5: 4 ways: are we seeing a pattern? 1 + 4, 2 + 3, 3 + 2, 4 + 1

6: 5 ways: 1 + 5, 2 + 4, 3 + 3, 4 + 2, 5 + 1

7: 6 ways: 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1

8: 5 ways: 2 + 6, 3 + 5, 4 + 4, 5 + 3, 6 + 2

9: 4 ways: 3 + 6, 4 + 5, 5 + 4, 6 + 3

10: 3 ways: 4 + 6, 5 + 5, 6 + 4

11: 2 ways: 5 + 6, 6 + 5

12: just 1 way – train tracks: 6 + 6

Then prompt your kid’s curiosity:

- Why does the number of rolls make a mirror image as you go from low to high?
- Why do some numbers have an odd number of choices? It’s because doubles happen only 1 way with the left and right dice.

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Extra Challenge

If your kid is ready, explore rolling 3 dice!

3: just 1 way: 1 + 1 + 1

4: just 3 ways **1 + 1 + 2** x its 3 permutations

5: 6 ways: **1 + 2 + 2** x 3 permutations; **1 + 1 + 3** x 3 permutations

6: 7 ways: 1 + 1 + 4 x 3 permutations, 1 + 2 + 3 x 6 permutations since they’re all different (123, 132, 213, 231, 312, 321), and 2 + 2 + 2

7: 15 ways: 1 + 1 + 5 x 3 permutations, 1 + 2 + 4 x 6 permutations, 1 + 3 + 3 x 3 permutations, and 2 + 2 + 3 x 3 permutations

8: 21 ways: 1 + 1+ 6 x 3 perm, 1 + 2 + 5 x 6 perm, 1 + 3 + 4 x 6 perm, 2 + 2 + 4 x 3 perm, and 2 + 3 + 3 x 3 permutations

9: 25 ways: 1 + 2 + 6 x 6 perm, 1 + 3 + 5 x 6 perm, 1 + 4 + 4 x 3 perm, 2 + 2 + 5 x 3 perm, 2 + 3 + 4 x 6 perm, and 3 + 3 + 3

10: 27 ways: 1 + 3 + 6 x 6 perm, 1 + 4 + 5 x 6 perm, 2 + 2 + 6 x 3 perm, 2 + 3 + 5 x 6 perm, 2 + 4 + 4 x 3 perm, 3 + 3 + 4 x 3 perm

11: 27 ways: 1 + 4 + 6 x 6 perm, 1 + 5 + 5 x 3 perm, 2 + 3 + 6 x 6 perm, 2 + 4 + 5 x 6 perm, 3 + 3 + 5 x 3 perm, 3 + 4 + 4 x 3 perm

12: 25 ways: 1 + 5 + 6 x 6 perm, 2 + 4 + 6 x 6 perm, 2 + 5 + 5 x 3 perm, 3 + 3 + 6 x 3 perm, 3 + 4 + 5 x 6 perm, and 4 + 4 + 4

13: 21 ways: 1 + 6 + 6 x 3 perm, 2 + 5 + 6 x 6 perm, 3 + 4 + 6 x 6 perm, 3 + 5 + 5 x 3 perm, 4 + 4 + 5 x 3 perm

14: 15 ways: 2 + 6 + 6 x 3 perm, 3 + 5 + 6 x 6 perm, 4 + 4 + 6 x 3 perm, 4 + 5 + 5 x 3 perm

15: 7 ways: 3 + 6 + 6 x 3 perm, 4 + 5 + 6 x 6 perm, and 5 + 5 + 5

16: 6 ways: 4 + 6 + 6 x 3 perm, 5 + 5 + 6 x 3 perm

17: 3 ways: 5 + 6 + 6 x its 3 perms

18: just 1 way! 6 + 6 + 6