Exploring Scale Models, Perimeter and Area

This past week students started to explore perimeter and area. I’ve observed that most students arrive into third grade with an understanding of perimeter. They can find the perimeter around polygons with a ruler or when measurements are given. When polled, the majority of students said perimeter is basically the measurement around something. After discussing perimeter, the class measured the distance around objects in the classroom. Once the class reviewed the perimeter the class moved on to area.  We used scale drawings to emphasize the concept of perimeter.

On Thursday students investigated how to create a rough sketch of a floor plan.

The class used the classroom as an example. Students started by creating a rough sketch of the dimensions of the classroom. Student teams were assigned walls of the classroom to measure. After around 15 minutes students came back and wrote their measurements on the board and in their math journals. Students then transferred that rough sketch data into a scale model. This took time.   We spent around 10 minutes deciding on what ¼ of an inch would represent on a grid. This was time consuming. The class had an amazing conversation on what could be an appropriate scale model that would actually fits paper. Students made the connection between a scale model and how to writer intervals on a graph. Although this was time consuming, it gave students an opportunity to use trial-and-error with different scales. Eventually the class decided on using ¼ of an inch to represent two feet in the classroom.

The class constructed the scale drawing and put in place the windows, doors and walls. The perimeter was found and then students counted the squares inside to find the area. This was a bit challenging for some as the concept of perimeter and area are different.  During this process students started to identify their own misconceptions about area.  Some of the squares were full while others were halves. Students had to combine the halves to find the total area. Students worked in groups to find different ways to find the area of the classroom. Besides counting the squares, students explored other strategies, such as multiplying the length and width or using some type of array model with squares.

The next day students were asked to find an object in the classroom with a rectangular face. Students found many different objects in the classroom (folder, journal, Kleenex box) while others picked objects that they couldn’t bring back to their desk (window panes, cabinet doors, desk face). Students measured the face uo the nearest inch or half-inch. They created a rough sketch and a scale drawing on grid paper. Students used the grid paper to find the perimeter and area of the item.

Next week students will be sharing their projects with the class. Each student will share their findings and the class will have a conversation about the similarities and differences between perimeter and area.