http://www.freefoto.com/images/11/12/11_12_64Dice_web.jpg 
A lesson on probability I think most primary teachers will have done in their time involves getting children to roll two dice, add up the scores and find which totals occur most often. Children can make predictions before hand, test them and then find out whether they match. This can then lead on to discussions about why they may or may not match any preconceived ideas which in turn can then lead on to talking about theoretical probability of each total and children can work them out.
Here are all the possible outcomes of rolling two dice:
1

2

3

4

5

6


1

2

3

4

5

6

7

2

3

4

5

6

7

8

3

4

5

6

7

8

9

4

5

6

7

8

9

10

5

6

7

8

9

10

11

6

7

8

9

10

11

12

So, the probability of rolling each total is:
2 = 1/36
3 = 2/36
4 = 3/36
5 = 4/36
6 = 5/36
7 = 6/36
8 = 5/36
9 = 4/36
10 = 3/36
11 = 2/36
12 = 1/36
Most would leave it here. I certainly have in the past. That was until I went to a MathsJam and was set the challenge of coming up with other dice that had the same probabilities as a normal pair. It struck me that this would be a fantastic extension activity to the one above and would keep kids going for hours trying different things out, as it did us in the pub, trying to come up with different ways to make our dice.
There is in fact one other way to make the dice, known as Sicherman dice, which give the same probability. They are numbered 1, 2, 2, 3, 3, 4 and 1, 3, 4, 5, 6, 8. You could also develop this to see if children can make dice where the probability of getting all totals is the same, or say, the chance of totalling 6 is 4/36. There's also the possibility of exploring other types of dice eg 10sided or only odd numbers etc. It's definitely an idea I'll be saving for a future opportunity.
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