My guess: there are 6 ways (listed by the student at left), and there are 2 dice, so each way can happen in 2 orders, and 6*2 is 12.

To test: ask the kid how many ways there are for three dice to total 4. See if they come up with something like 1+1+2, 1+2+1, 2+1+1 and thus some final answer like 9 or 18 instead of 3.

I think this is about right. They accounted for all the options of how to make 7 with two dice in the list on the left side. However, they didn’t realize that they had already accounted for two dice by listing 1 and 6 along with 6 and 1, so they multiplied their 6 possibilities times the two dice and got 12.

Julie

This item is also a great way to have students begin to think about probability through binary (yes or no conditions). If we are looking for a sum of seven does it matter what the first die rolls? No…all values 1-6 can part of the sum to create a seven. So the probability for the first roll is 1 and then the second roll is the one (in this case) that matters in that there is only one roll (addend) that will properly create a sum of 7 with first roll. Therefore the probability is 1 x 1/6. Too often our instruction doesn’t include this more efficient means of analyzing probability which requires students to use good logical thinking.