2-Scoop Ice Cream Cones-Math

posted Sep 28, 2016, 6:27 PM by Patrick Johnson
This week, students were introduced to this number sense task that can be solved in different ways.

First, students were asked: 
How many unique 2-scoop ice cream cones could be made with only 1 flavour of ice cream? 
The answer is 1 (for example, chocolate for the bottom scoop and chocolate for the top scoop).

Next students were asked: 
How many unique 2-scoop ice cream cones could be made if there were 3 flavours of ice cream available at the store? 
The answer is 3. 
-chocolate, chocolate
-vanilla, vanilla
-vanilla and chocolate (which is the same as chocolate and vanilla since order of the scoops does not matter).

Next students were given the below task:

When students were done, we displayed their work on our math Bansho wall to discuss student's math strategies.

Some groups used a guess and check strategy. They tried different ways to make 2-scoop ice cream cones without repeating cones.

Other groups used an idea of an organized list. Starting with one flavour, they added other flavours to make 2-scoop ice cream cones until there were no more cones to make with that flavour.

This group used an organized list. They also made sure not to repeat 2-scoop ice cream cones. They started with peach ice cream in the first column. In the next column they used blueberry ice cream (note they did not repeat the peach-blueberry combination). They also noticed that the number of cones decreased by 1.

This group assigned a number to each of the ice cream flavours and proceeded to make the 2-scoop ice cream cones by combining the numbers in a list.

Finally we worked through a solution together. We simplified the problem by assigning numbers to the flavour (like the group above). Students noticed patterns very quickly. We found out:
5 flavours of ice cream produces 15 unique 2-scoop ice cream cones: 5+4+3+2+1
10 flavours of ice cream produces 55 unique cones: 10+9+8+7+6+5+4+3+2+1
We also applied this solution to Baskin Robbins and found out that with 31 flavours of ice cream, we predict there would be 465 unique 2-scoop ice cream cones.

In this task we realized that there are different ways to solve a problem, but that some strategies will get you there quicker than others.