Here is a way to teach patterns and combinations in math with ice cream flavors!

My goal this school year is to do some type of hands-on mathematical thinking activity with the boys once a week.  Learning to do mathematical operations is important, but it is also important to develop logic, number sense, and mathematical thinking.

Our ice cream math problem came from the book About Teaching Mathematics by Marilyn Burns.  (This book is geared toward classroom teachers – I read it in college.)  The problem is simple:  How many different double dip ice cream cones can you make from one flavor, two flavors, and so on?  Can you predict how many cones can you make with 31 flavors?

To assist their thinking, I cut out paper ice cream scoops.  Gresham (6) and Aidan (10) worked together to make a chart with the different possibilities.  We chose to count chocolate on top of vanilla as different than vanilla on top of chocolate, and as it turns out, that was a good choice!  I’ll explain more later…

Gresham (6) was really good at figuring out the possible cones and noticing when we had left some options out.  When they got to four flavors, Aidan drew them out on paper.

After four flavors, the pattern was easy to see.  The number of different double dip cones that you can make is equal to the number of flavors multiplied by itself.

If we had not counted chocolate on top of vanilla as different from vanilla on top of chocolate, we would have gotten this pattern:

1/1

2/3

3/6

4/10

The pattern here is very interesting: Line 1 to line 2 on the number of double dip cones list is +2, then +3, +4, etc.  These results are much more difficult to make into an equation!  The math for that is way past elementary school, but I think it’s really interesting to explore both ways of solving this problem.  It’s really good for kids to realize that their are often different ways to attack and solve a problem.

After we were done with the paper ice cream scoops, I had Owen glue them down into “pattern cones,” so we had a little math learning for everyone from ages 4 to 10!

We really should have had ice cream after we finished this math lesson!  I don’t know why I am just now thinking of that!