Productive struggle, collaboration, and rigorous thinking


Jordan Rappaport, Brownridge Public School,YRDSB

“Allowing students the opportunity to practice inquiry before instruction makes math come alive. It challenges them to engage in struggle, collaboration and rigorous thinking, and it increases participation in lessons.” Michael Giardi


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We are going to make our own, aren't we

Since September, students have come to appreciate the value of extensions and premise that PROBLEMS are never REALLY done, “there is always more” as they like to say.


And staying true to the spirit of a 3-Act Task, I provided just enough information to spark curiosity so that the students would be encouraged to ask questions.


It didn’t take very long for a few students to exclaim, “we’re going to make our own, aren’t we?” To which I responded, “Yes, yes we are”.  Their smiles grew and their enthusiasm was contagious!




Solving for the area of unfamiliar shapes

In this task, the goal was for students to make connections to different area relationships and use their knowledge of familiar shapes to solve for the area of unfamiliar shapes.


  1. As a first step students identified the problem and the information they needed to solve it. 
  2. Next, students were put in visibly random groups #VRG.
  3. Then they began working through the problem on vertical non-permanent surfaces #VNPS.


As they reasoned and worked their way through the problem, I kept the students in what @pgliljedahl calls ‘flow’; maintaining a balance between the challenge of the task and the abilities of the students working on it.



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Students were so immersed they asked to skip recess

For a full week students completely immersed themselves in the above, asking to stay in at recess, lunch, and even asking to work on it when they should have been in other classes.


As we got deeper into the task, new learnings and connections naturally emerged, which were all connected to our end goal.


For example, instead of creating our "pixel art" on Wipebooks using 1x1 squares, the group pondered the question: what if we used post-it notes as we saw in R2D2 Sticky-Notes from @MrOrr_geek.


If we used post-it notes, what dimensions do they come in (we found  1.5x2 and 3x3)?



  • Would we use only one type of post-it note or a combination?
  • What would the cost be?
  • What would be the most reasonable?
  • What evidence do we have to support the reasonableness of our solutions?


There you have it

This experience confirmed my belief around the IMPORTANCE of a productive struggle and problem solving in a collaborative framework to really get math students using their skillset to think critically to arrive at creative solutions to problems.