Productive Struggle

In grade 10 today we were working on solving quadratic word problems. We also were working on thriving through productive struggle.

Here’s an example of one of the questions. We know the sidewalk area equals the garden area, and we’re solving for the value of x, the uniform width of the sidewalk.

Groups worked together at the walls. We reflected a bit about how we all know each other’s names and we can all work together reasonably well. It’s been a semester of growth in teamwork!

Many groups used area model approaches to divide the sidewalk into sections. There was some struggle about making equations for area vs perimeter. We worked through that struggle for quite a while! Groups helped groups, we tried several approaches.

This group landed on an approach where they found outside dimensions of (42+2x) and (20+2x). They knew they needed to subtract the garden area, and then that equals the same as the garden area. Once we get to a trinomial=0 we can sig the quadratic formula and solve.

This group kept with the area model, and had the 4 corner x squares, and added 2 rectangles that were 20x, and 2 rectangles that were 42x. The total would be 840. This led to the same trinomial in the end.

We did a few more problems after this one. It’s important to practice a lot of different types of problems so that we get confidence in thinking through the process.