I am trying to de-unitize my grade 5 math curriculum this year. As we are reviewing subtraction, looking at visual patterns and exploring arrays, we also work on building vocabulary and precision in describing and classifying shapes. We started with a Which One Does Not Belong? board which is the permanent setup now in our hallway with regularly changing prompts.
Rope Polygons: Body-Scale Exploration
Last Friday, I decided to implement a Rope Polygons lesson from Whole-Body Math Lessons developed by Malke Rosenfeld. I was hoping that my students will have an opportunity to refine their understanding and to develop their vocabulary by working collaboratively; communicating with each other should create a need for more precision and justifications. Malke shared a very detailed lesson plan here.
After students investigated the ropes and noticed the knots, I asked them to create as many regular polygons as they could. Eventually, all the groups started using the knots and created squares, triangles, hexagons. I moved some students holding the vertices of a square apart, and they informed me that it is not a regular shape anymore but struggled to explain why. A few mentioned angles.
After half an hour of building, I asked my students to reflect on the activity. What strategies did they use? What helped them to be successful? What were the challenges? And how would they explain what regular polygon is to someone who doesn’t know? Give me the definition.
Definitions: Polygons Are Big
Here are the (non-exhaustive) list of definitions I was surprised to read after school.
A regular polygon is a shape that has edges.
A regular polygon is even.
A regular polygon is the shape whose angles are the same.
A regular polygon is straight line and symmetrical.
A regular polygon is like a square or triangle.
A regular polygon is the shape that has same perimeter and area.
Polygon is the shape with parallel lines.
Regular polygons have the same angles.
Polygon is the shape that is really big.
Students described all the properties that they noticed while building regular polygons with the rope, including the size. How do I zoom in on the defining ones?
Attack and Counter-Attack: Refining the Definition
I got the idea from the blog post Attacks and Counterattacks in Geometry by Sam Shah. There are still a lot of ideas in this post that I would like to try this year, like finding counterattacks for the altered textbook definitions. I made it into a whole class activity with students working on the small whiteboards.
We started with this example: “A circle is a shape that has curves. Counterattack! Draw a shape that fits this description, has curves, but is NOT a circle.”
Then we moved on to regular polygons. Here are some counter-attacks.
We made a list of properties on the board. After each counterattack we had a discussion if this property applies to all regular polygons and if it is essential. I think I overdid it a bit with circling and crossing, so I pretty much had the definition on the board by the time I asked my students to go back and to revise theirs.
Thoughts: What’s Next?
Something that naturally appeared in the discussion was “Never, Sometimes, Always” format. Regular polygons never have curves, sometimes are big and always have edges of equal length. I might pull a few statements for Talking Points (I learned about Talking Points here). I’ve been thinking about Van Hiele levels. How do I support my students in moving from the shapes as objects of investigation to the properties of shapes?