Same Area, Same Perimeter?

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

3

Overview

This learning activity is designed to activate students thinking about perimeter and area. Students will work together to answer writing prompts about a rectangle that has an area of 36 inches.

Phase

Before/Engage
Mathematics (2019) Grade(s): 3

MA19.3.24

Construct rectangles with the same perimeter and different areas or the same area and different perimeters.

UP:MA19.3.24

Vocabulary

  • Perimeter
  • Area
  • Side length
  • Side measure

Knowledge

Students know:
  • Perimeter is a measurable attribute of rectangles.
  • Area is a measurable attribute of rectangles.

Skills

Students are able to:
  • Construct rectangles with a given perimeter.
  • Construct rectangles with a given area.
  • Construct rectangles with the same perimeters but differing areas.
  • Construct rectangles with the same areas but differing perimeters.

Understanding

Students understand that:
  • Perimeter and area are measurable attributes of rectangles.
  • Perimeter is the distance around a figure found by adding side lengths.
  • The area of a plane figure is measured by the number of square units that cover the interior space of the rectangle.

Learning Objectives

I can construct rectangles with the same perimeter and different areas or the same area and different perimeters.

Activity Details

In the engage activity, Same Area, Same Perimeter? the students will answer the following writing prompts.

  1. If a rectangle has an area of 36 square inches, what could the length and width be? 
  2. What would the length and width be if the shape were a square?

The students will record their thinking and drawings in a math journal or on blank paper.

The teacher will ask the following essential questions:

  1. How many different rectangles did you find?
  2. Were the perimeters the same? Why or why not?

These questions are in the notes section of the slideshow.

Assessment Strategies

Teachers will observe student responses to determine student understanding of the concept and skill. You can use the following guidelines to ensure students meet the learning objective and answer the essential questions.

Check that the student:

  1. can make multiple rectangles with an area of 36.
  2. can identify that squares have four equal sides, so the dimensions must be the same on each side.
  3. can identify that some of the rectangles have the same area, but different perimeters.
  4. can identify that some of the rectangles have the same area and same perimeters.

Variation Tips

Students may need a manipulative, such as color tiles, to build the rectangles. This would help students visually notice the different perimeters and configurations of the area.

Background / Preparation

The teacher will need a computer and projector to display the slideshow. The students will need a math journal or blank paper, pencils, and possibly color tiles.

Learning Activity (Before)

Same Area, Same Perimeter?

Learning Activity (During)

The Patio

Learning Activity (After)

Area and Perimeter Scavenger Hunt
Same Area, Same Perimeter? - slideshow
https://docs.google.com/presentation/d/1SPFxBb4TaRGb2eiU7Ono3CN34vGF7QU8nKjPq-B…

Approved Date

Owner (Author)

mfrye
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