The Patio

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

3

Overview

In this authentic learning task students are designing a rectangular patio using 40 patio stones. This task will have many answers, but students will choose the design they like best. Students will use that design to determine the perimeter in part two of the problem.

Phase

During/Explore/Explain
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 activity, The Patio, the students will actively use their knowledge of area and perimeter. The teacher will display the slideshow and give each student graph paper to record their designs. The students have 40 patio stones to arrange in a rectangle. The students will answer and complete the following:

  1. What are all the different ways they can arrange their stones?
  2. Record your solutions on your grid paper.

After sufficient time, the teacher will move to the second part of the task (slide 3). On this slide, students are given information to help them determine the perimeter of their patio. The students will complete the following:

  1. Choose your favorite layout and determine how much border they will need to complete the project.

Essential questions for teachers are included 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.

Check that the student:

1. can design a rectangular shape using 40 stones.

2. can find all the ways to arrange 40 stones.

3. can find the perimeter of their design.

4. can recognize that the definition of area and perimeter differ.

Variation Tips

Students may use color tiles to build the concrete model before recording their designs on graph paper.

Background / Preparation

The teacher will need a computer and projector to display the slideshow. Each student will need graph paper and a pencil. 

Learning Activity (Before)

Same Area, Same Perimeter?

Learning Activity (During)

The Patio

Learning Activity (After)

Area and Perimeter Scavenger Hunt
The Patio - slideshow
https://docs.google.com/presentation/d/1-NyFOImGb8WuvIpW32RHZqsbGGdeucHnSaoPvfy…

Approved Date

Owner (Author)

mfrye
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