Investigating Perimeter and Area

Est. Class Sessions: 2

Developing the Lesson

Part 3: Design a Playground Problem

Check-in: Questions 5–6 in the Student Guide introduce an Antopolis playground design problem. To initiate a student discussion of the design constraints, ask student pairs to read Question 5 to each other and take turns stating the problem to each other in their own words. Tell students that you want to be sure they know the problem and that this strategy is often used to determine what is important in a problem.

After student pairs have had the opportunity to discuss the problem, ask:

What information from this question will you need in order to solve the problem? (We need to use inches as our unit of measurement. The area is 8 square inches. The perimeter is 14 inches. All of the parts of the playground need to be connected.)

You may want to record this information on a class display so students can refer to it as they complete their work.

Ask:

How would you have to place the square-inch tiles so that parts of the playground are connected? (The tiles need to all be touching each other.)

To clarify this, use square-inch tiles to display the shapes in Figure 3. The playground shape has to connect edge to edge.

Common convention says to use a period when abbreviating a word (e.g., inch becomes in. and square becomes sq.). Metric units generally do not follow this convention (e.g., centimeter becomes cm and kilogram becomes kg). Following that pattern, square centimeter is often abbreviated as sq cm instead of sq. cm. In Math Trailblazers, a variety of forms are used so students are exposed to the different conventions.

Provide each student with a sheet of Square-Inch Grid Paper and square-inch tiles to test their shapes while solving this problem. Figure 4 shows three samples of solutions to this problem.

In Check-in: Question 6, students are asked to write a paragraph explaining how they determined their playground design. Prepare students to write this paragraph by brainstorming ways to show Math Practices Expectations 4, 5, and 6 in this problem.

Check my calculations. If I make mistakes, I correct them.
Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.
Use labels. I use labels to show what numbers mean.

Display the Math Practices page in the Student Guide Reference section and ask pairs to read Expectations 4, 5, and 6 and to make a list of ideas to include in their paragraph. See Figure 5.

After student pairs have created a list of ideas, summarize those ideas on a class list. Display this summary list and remind students to use these ideas to write a paragraph for Check-In: Question 6.