We investigated perimeter and area by thinking about objects in the classroom and then measuring their surfaces for perimeter. We then talked about area and what that represented in a 2-D shape and measured area of those classroom surfaces. Students began to understand that their completed teapot package would be a 3-D shape, and that we would measure the volume. Some students chose to measure rectangular objects like tables and cabinets. Keita and Haikal headed to the hallway to measure it in meters. Jesper and Caleb decided to find the area of a circular object and then work on volume of the box of tissues. They had to discover the formula for finding the area of a circle.
Students then drew out their ideas for the teapot package as a group. They measured their idea for a teapot package exactly, labeling dimensions with cm. For some, this meant connecting several pieces of paper together so that they could fit the entire package.
We then talked about scale or sizing the package so that it fit on a regular sheet of paper. Students used 1 cm graph paper to draw out a scaled version of their teapot. They chose the scale. For some, it was 2 cm, and for some it was 5 cm. Their new drawings reflected the scale.
One group, with a challenging design for their teapot package (a maple leaf) ran into problems trying to scale down their design. It wasn’t a rectangular prism or a trapezoid like some of the other shapes, and they couldn’t figure out how to scale it.
Even though they wanted to give up, through some collaboration, they began to figure it out. Yoshie said that she had to find the area of a complex shape in a past school but couldn’t quite figure out how to explain it. Eric came in and suggested dividing the shape into triangles and then finding the area of those triangles.
With some careful measurement, Yoshie, Eric and Kalea set to work trying to figure out the area of a variety of triangles: from acute triangles to right triangles. It’s taking a while, but they are engaged in the journey.
Others finished up their scaled drawings and set to work on designing their teapot package on Sketchup. There were some good engaging hours of Math this week.