Day 11: the boomerang task for pre-algebra

Systems of equations won’t be for a while, but I wanted to give the students a preview of what to expect down the road. I was out on Friday for a data retreat and part of the plans I left were for the students to work independently for 15 minutes on the Boomerang Task from the Mathematics Assessment Project.


Many solved or nearly solved this problem in early 7th grade fashion using guess and check because they have not been exposed to systems using the substitution, graphing, or elimination. I know this is a high school task, but I thought the class would benefit from knowing that later on they will be learning about some of these methods.

Since most used guess and check the work was all over the place. I can’t tell you how many times I wrote as their feedback, “How can you organize your work?” A few recognized the one combination that worked, but they lacked proof that that was the only solution.  Because I didn’t provide explicit feedback that said, “Create a table” it never occurred to them to do that.

Before sending them off in their groups I stated the directions on the whiteboard:

Your task is to produce a solution that is better than your individual solutions. Criteria for success: Your work is organized and labeled so that someone not knowing the problem can understand your thinking.

Clarity and additional time made all the difference.


Most group work looked similar to this. No one had previous experience with substitution so it would have never occurred to them to do it.

boomerang table

I asked this group to create a table so the class could see another representation of how to solve it.

To close the lesson I showed them a more complete table and exposed them to the substitution method.


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