Mathematics · 3rd Grade

Active learning ideas

Perimeter: Measuring Around Shapes

Perimeter shifts students from number crunching to visual and spatial thinking, which requires hands-on movement and concrete examples. Active learning lets third graders walk around shapes, draw boundaries, and test ideas with their bodies and tools, making the abstract measure of perimeter visible and real.

• Common Core State Standards
• CCSS.Math.Content.3.MD.D.8

• 20–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 25 min · Pairs

Gallery Walk: Polygon Perimeters

Post polygons of various types around the room, each with some side lengths labeled. Students rotate in pairs to calculate the perimeter and, where one side is missing, determine the unknown length. Each pair records their work on sticky notes placed next to the polygon.

Differentiate between area and perimeter in practical applications.

Facilitation Tip

During the Gallery Walk, place rulers and colored pencils at each station so students can trace and label sides as they move.

What to look for

Provide students with a drawing of a rectangle with one side length missing and the total perimeter labeled. Ask them to calculate the missing side length and then find the perimeter of a different given polygon.

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Same Perimeter, Different Shapes

Give each student a fixed perimeter (e.g., 24 units) and square tiles or grid paper. Students first build one rectangle independently, then compare with a partner who built a different rectangle. The pair records both configurations and describes how the areas differ.

Design a rectangle with a given perimeter but a different area than another rectangle.

Facilitation Tip

In the Think-Pair-Share, give each pair one set of grid paper rectangles with equal perimeters to compare and discuss differences.

What to look for

Present students with two different rectangles on grid paper. Ask them to calculate the perimeter of each and then determine which rectangle has a larger area. Discuss their findings as a class.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Inquiry Circle
• 30 min · Small Groups

Inquiry Circle: Garden Design Challenge

Small groups receive a scenario: they have a fixed amount of fencing and must design a rectangular garden plot on grid paper. Each group presents their design to the class, explaining their perimeter calculations and what they chose to optimize.

Explain how to find an unknown side length of a polygon given its perimeter and other side lengths.

Facilitation Tip

During the Garden Design Challenge, assign specific roles like measurer, recorder, and sketcher to keep all students engaged in the process.

What to look for

Pose the question: 'Imagine you have 20 feet of rope. Can you make a rectangle with a larger area using the rope as the perimeter than a square using the same rope? Explain your thinking and show your work.'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Teach perimeter by connecting it to real objects and student movement first, then move to drawn shapes on paper. Avoid starting with formulas; instead, build the concept through tracing, walking, and measuring. Research shows that students who physically outline shapes before calculating are less likely to confuse perimeter with area later.

Students will trace, measure, and calculate perimeter with accuracy, explain how perimeter differs from area, and justify their reasoning using evidence from their work. They will also recognize that shapes with the same perimeter can have different areas and explain why.

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Watch Out for These Misconceptions

• During Gallery Walk, watch for students who add only two sides of a rectangle when calculating perimeter.

  Have students place a finger on a starting corner and physically trace the entire boundary with a ruler or pencil while counting each side aloud before writing any numbers.

• During Think-Pair-Share, watch for students who confuse perimeter with area when comparing shapes.

  Give each pair two colored pencils: one for outlining the perimeter and one for shading the area, then ask them to explain which color represents which measure before sharing with the class.

• During Garden Design Challenge, watch for students who assume a longer perimeter always means more space inside.

  Prompt students to calculate both the perimeter and area of their designs and post them side by side to directly compare the two measures.

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Methods used in this brief

• Gallery Walk
• Think-Pair-Share
• Inquiry Circle