All Possible Combinations

When introducing how to determine all possible combinations of a given set of data or objects, we start slowly. We start listing out different combinations when looking at two spinners - one with the numbers 0-9 on it, and one with the colors red, green, blue, and yellow on it. The kids usually start volunteering different combinations, like 1 and green, 2 and blue, 5 and red, etc.

Where the thinking comes in is when I ask them if we've found all possible combinations. It doesn't take long for them to figure out they need some organization for their combination. Enter the tree diagram! We begin listing out our combinations using a tree diagram, then check to make sure we get all possible combinations. We usually only have to do this process two or three times before the kids see the relationship between the tree diagrams and multiplication. When you give kids tedious work, they naturally find the shortcuts on their own! :) 

I do point out it's important they understand the process of the tree diagram to see why the multiplication strategy works! It's SO important they understand the "why" of math!!!