Math Tasks With Multiple Solutions: Practice What You Preach


In Part 1 of this series, I advocated for more math tasks that have multiple solutions because they get students to take ownership over generating a solution that works; I decided to practice what I preached. I created a Dan Meyer’s inspired math task, shared it with him, and got as many results as possible using Formative.

Here’s the video that sets up my task:

My Full Math Task (you can access it without logging in):

In the video, I cut the brownie pan into 8 pieces and want to share it equally among four friends; but one can’t make it to the party. Thus, the student needs to figure out how to cut the leftover two pieces and prove that each person gets the same amount of the entire pan.

The 3 Types of Solutions People Found Two Split The Remaining Two Pieces

Did I Practice What I Preached?

Looking at the examples above, I clearly created a task with multiple solutions, but most of those solutions aren’t pragmatic. While students can cut the remaining two pieces any way they  want as long as the number of pieces are equal and are a multiple of 3, most students wouldn’t actually consider that in real life. And so they wouldn’t naturally find all those solutions. But Dan’s Meyer’s task is full of pragmatic solutions.

Let’s compare…

Pragmatic Solutions in My Task-

In my task, most students only split the remaining pieces into thirds (solution #3) since they are splitting the cake among three people. And it’s a stretch, but some might care about the number of cuts they make and make a single one (solution #2).

Pragmatic Solutions in Dan’s Task-

On the other hand, “Nana’s Chocolate Milk” has so many sensible solutions because it encourages students to really consider what matters most to them. Based on the video, some students think the most sensible solution is to double the recipe for two people while others care about keeping the final product 1 cup of milk to 4 scoops of chocolate. Still others want to save ingredients and add just enough to preserve the original ratio of milk to chocolate.


Why Making Tasks With Sensible Solutions Matters

Making tasks with as many sensible solutions as possible is important for a few reasons:

  • if there are a lot of sensible solutions, chances are students will find them all which will lead to more interesting class discussions
  • when a student finds a sensible solution, they see the point of doing the task in the first place and are more eager to defend them
  • students who usually don’t get a chance to shine WILL since they are allowed to think creatively and draw from life experiences

In the end, I didn’t quite practice what I preached because my task didn’t have many sensible solutions. Students deserve tasks with sensible solutions because they prove that what students do in Math class reflects problems they face in their own lives.