It was a great question and so today we started exploring it.
We reviewed together what we had discovered about finding the area of a rectangle and a triangle.
I then drew this type of trapezium on the board and the children had some time trying to figure out how we could measure its area. After hearing quite a few 'wow' moments flashing in the room, a student shared with us the strategy we can use:
Giving them a paper with images of regular and irregular polygons, types of quadrilaterals and types of triangles, they chose shapes and tried to create ways we could measure their area.
Some really creative ideas started emerging. They weren't necessarily the easiest way to measure the area, but in mathematical thinking creativity is important so we didn't dispel their strategies when we shared what we had discovered.
This student started discovering how we can find triangles inside regular polygons:
This student came up with a really creative way to measure the area of a regular octagon:
Here is another creative discovery made. We can split a decagon into a rectangle, 2 trapeziums and 2 triangles. Amazing!
Here a student discovered a way to measure the area of a kite, a parallelogram and a different way to measure the area of a square. She knew the easier way to measure the area of a square was to simply multiply its length and height, but wanted to challenge herself to see if there were other strategies:
We will continue exploring such strategies over the next few days.
All of this amazing mathematical thinking stemmed from a student wondering how can we find the area of a hexagon. When we value student questions, this is the type of authentic enquiries and mathematical thinking that can take place in our classrooms. This became an engaging and rewarding problem solving and mathematical reasoning learning experience which also created a lot of self-pride in the students when they started making their discoveries.