Teaching Mathematical Patterns and Combinations with Ice Cream Flavors

Teach patterns, combinations, and permutations with ice cream flavors!

Let’s do some ice cream math! This hands-on math activity is interesting for kids and really leads to some great thinking and discussions.

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 different cones can you make with 31 flavors?

I would recommend this math activity for 3rd – 5th graders.

This post was originally published in August 2013 and updated in May 2025.

The math concepts involved here are combinations and permutations.

Combinations and permutations both involve combining items from a set. A combination is where you select items from a set and the order of the items does not matter. An example of this would be choosing three fruits from a fruit bowl.

A permutation is when you select items from a set, and the order DOES matter. An example of this would be the numbers for a combination lock or the letters and numbers on a license plate. GW47H is not the same license plate as 7W4GH even though the included letters and numbers are the same.

Ice cream cones are the perfect way to explore combinations and permutations!

Supplies Needed for Ice Cream Math:

• Construction paper
• File folder
• Brown marker
• Scissors
• Cardboard
• Pencil

First, you’ll need to cut out some ice cream scoops and cones. Honestly, the cones are optional, but you’ll definitely need the ice cream scoops.

I made patterns for both the cones and the ice cream scoops out of cardboard. Then we traced them on construction paper and cut them out.

I highly recommend having kids help cut out the scoops and cones! The tracing and cutting practice is so good for fine motor skills. My 5th grader found it hard to trace the pattern, and I realized that we don’t do nearly as much of this kind of work than we should!

For the cones, I used file folders. They are just the right color, and we made them look even better with marker lines. But brown construction paper would work well too.

We made chocolate, vanilla, strawberry, and mint chocolate chip ice cream scoops.

Then I explained what we were going to do. How many double dip cones can we make with 2 flavors, 3 flavors, and so on? Janie thought this was quite interesting!

We started by laying out the possible combinations of cones with chocolate and strawberry.

Janie quickly realized that we needed to decide whether chocolate on top of strawberry would count as the same thing as strawberry on top of chocolate. Good question!

We decided to count them as two different cones, which makes this activity a permutation.

(This is a good idea because it makes the math easier, but you’ll want to discuss both options. I’ll explain more below.)

With two flavors, you can make 4 different cones.

We moved on to 3 flavors and found that we could make 9 different cones.

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.

Here are our results:

So for 31 flavors, you can make 961 cones!

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

1/1

2/3

3/6

4/10

5/15

6/21

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.

If you are working with learners at different ability levels, you can use these same materials to create a fun pattern activity.

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!

Want more Hands-On Math Activities for Kids?

Here’s a huge collection of Hands-On Match Activities for 1st – 5th grades.