We started our unit on Geometric Measure & Dimension with a Mathematics Assessment Project formative assessment lesson on Evaluating Statements about Length and Area.
I chose the card that each group would explore ahead of time. I only gave each group one card, and I had another task ready for them if they finished early. They didn’t. Students chose whether they wanted to explore on paper or using technology.
Each card had a hint, which I held until I felt like the group might need it. While students were working, I monitored their progress.
The first group had Cutting Shapes.
When you cut a piece off a shape you reduce its area.
When you cut a piece off a shape you reduce its perimeter.
They thought Always for both statements.
Most of them were taking a quadrilateral and cutting off a triangle on the corner.
How could I get them to figure out it was sometimes besides just telling them? I also didn’t want to give this group the hint card because I felt like it gave too much away.
What if you cut off something besides a triangle? Someone cut off a rectangular corner.
What just happened to the area? It got smaller.
What just happened to the perimeter? It stayed the same!
How do you know?
What if you cut somewhere besides a corner?
I went to another group after I asked this question.
By the time I got back to them, they had a great explanation as to why both statements were not always.
I’m sure there was a better way to do this, which might include having students evaluate the statements by themselves before coming to class for the lesson. We could have spent a week on these six cards. But we didn’t.
Before each group presented their work, we sent out a Quick Poll to see what the rest of the class instinctively thought about the statements.
I showed the results, but I deselected Show Correct Answer before doing so. I wanted the group to know what their peers thought before they just told them the results.
The group presented their work, not just giving us their results, instead talking us through their thinking about the statements, and how they arrived at their conclusion.
And so the journey continues …