Students Justify their Thinking with “Would You Rather” Math

Today I posed a question to my grade 5/6 students that I came across on John Stevens Twitter feed (@jstevens009).

The question I posed was “Would you rather have a stack of quarters from the floor to the top of your head, or $200?”

I asked students to think about which they would choose, and to explain why they made the choice that they did.

This was the first time we have done a “Would you rather” question in math, and I was anticipating the mathematical discourse and thinking that this activity would prompt.

There was some interesting conversation that happened before students started on their written responses that were not captured in their written justifications.  I wish there were some way I could capture that.

Here is a justification one of my students :

M, Grade 6

  • This student didn’t take any chances estimating the thickness of a quarter; he asked me for one so he could measure it!  I gave him two and he measured them on a ruler and determined that one quarter is about 1mm thick.
  • He then used a series of ratios to determine that 1000 quarters would be one meter.
  • He did a rudimentary measurement of his height using a meter stick and determined that he was 1m and 42cm tall.
  • He knew that 42cm would be 420mm, or 420 quarters.
  • He determined his height in quarters:  1420 quarters tall.
  • Using long division he determined how much money in dollars 1420 quarters comes to by dividing it by 4.  He got $355.
  • He chose to take a stack of quarters to the top of his head


Unfortunately, there were many responses from my students were not justifications at all:

R, Grade 5

The question I am grappling with right now is what I am going to do to address the answers that do not include any mathematical thinking or any justification.  There were more students than I wish to admit did not have any justification to their answers.  Today was our first day back after Christmas break so maybe they are just a little rusty.  It was also a new activity; perhaps I didn’t explain my expectations very well.

Either way, I there are some things I need to address with students.  I am considering modelling a justification to this question or one similar, but I don’t want to prescribe how students are to think about the problem… the point of the activity was for them to decide on an approach not for me to choose one for them.

I am also considering creating some sort of rubric for justifications that will give feedback for improvement that somehow does not force a particular strategy.   I use a checklist for questions students need to explain their thinking (Answer, Why, Examples, Generalize, Clarify, Limitations), but it doesn’t fit well for this Would You Rather activity.


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