Measurement: Perimeter and Area in Grades 3 - 5
Session 4: Exploring the Relationship Between Perimeter and Area
Objectives
 In this session, you will: Explore what happens to two-dimensional shapes when the perimeters are held constant and the areas are changed; Explore what happens to two-dimensional shapes when the areas are held constant and the perimeters are changed; Examine the relationship between the perimeters and the areas of two-dimensional shapes by organizing the data from your observations into charts and tables; Apply your understanding of the relationship between the perimeters and areas of two-dimensional shapes to real-life problems.

The following reading is drawn from Knowing and Teaching Elementary Mathematics by Liping Ma. In the chapter entitled "Exploring New Knowledge: The Relationship Between Perimeter and Area," Ma investigates how teachers from the United States and China approached a scenario involving the relationship between the perimeter and area. Ma's investigation presents very interesting perspectives concerning both the teachers' content knowledge and the teachers' approaches with students. You will be asked to refer back to this reading during the discussion.

Activities
1.
2.

Do the "Using Shape Tiles to Explore Perimeter and Area" activity.

3.

Do the "Area Explorer" activity to examine the relationship between the areas and the perimeters of two-dimensional shapes when the perimeters remain constant.

4.

Do the "Perimeter Explorer" activity to examine the relationship between the areas and the perimeters of two-dimensional shapes when the areas remain constant.

5.

Do the "Rectangle Misconceptions" activity to explore the relationships between the dimensions of a rectangle and the effect of changing the dimensions on the rectangle's perimeter and area.

Discussion
After reviewing the reading "Exploring New Knowledge: The Relationship Between Perimeter and Area," use the Discussion Board to address the following:
1.
Consider the student scenario presented in the reading. How do you think the tools and activities explored in this session could assist the student in determining whether her theory was true?
2.
Read the responses in the Discussion Board and contribute to the conversation. If you like, you may review the expectations for contributing to the online discussion.