Perimeter of Polygons

Active learning turns abstract perimeter concepts into concrete experiences. When students move, measure, and build, they connect counting to physical space, which strengthens early spatial reasoning. Hands-on tasks also reduce anxiety about adding side lengths by making the process visual and tactile for young learners.

• Junior Infants
• Foundations of Mathematical Thinking
• 4 activities
• 25 min–40 min

Learning Objectives

1. Calculate the perimeter of various polygons using non-standard units.
2. Identify the outer boundary of a composite shape.
3. Explain the process of measuring the perimeter of a shape.
4. Design a simple composite shape and calculate its perimeter.

Problem-Based Learning

⏱ 30 min·Pairs

Block Fencing: Outline Shapes

Draw large polygons on the floor with chalk. Pairs use connecting blocks to form a fence around each shape, count the blocks per side, then add for total perimeter. Compare perimeters of different shapes and discuss why they vary.

Prepare & details

Explain how to calculate the perimeter of any polygon.

Facilitation Tip: During Block Fencing, circulate to ensure students place blocks end-to-end without gaps or overlaps along each side.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 35 min·Small Groups

String Measure: Composite Creations

Provide straws or string and tape. Small groups build composite shapes like a robot from rectangles and triangles. They measure the outer perimeter with string, lay it straight, and count units to find the total length.

Prepare & details

Analyze how perimeter is used in practical applications like fencing or framing.

Facilitation Tip: For String Measure, demonstrate how to hold one end of the string at a corner and trace the outer edge of the composite shape.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 25 min·Whole Class

Perimeter Hunt: Classroom Walk

Label classroom objects like tables or mats as polygons. Whole class walks around each, using footsteps or hand spans to measure sides and add for perimeter. Record findings on a shared chart and find the longest perimeter.

Prepare & details

Design a composite shape and calculate its perimeter.

Facilitation Tip: Set clear boundaries for the Perimeter Hunt by marking start and end points with tape on the floor to focus the walk.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 40 min·Individual

Design Challenge: Garden Fence

Individuals draw a garden as a composite shape on grid paper. They count squares along the outer edge for perimeter, then share designs and verify measurements with peers using rulers or blocks.

Prepare & details

Explain how to calculate the perimeter of any polygon.

Facilitation Tip: In the Design Challenge, provide a checklist with simple steps, such as 'draw your shape' and 'measure with string,' to guide students.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

Start with non-standard units like blocks or paper clips to build intuition about length and addition. Avoid introducing rulers too early, as they can distract from the concept of perimeter as a sum of sides. Use peer collaboration to let students compare measurements and resolve discrepancies together. Research shows that repeated, varied practice with physical materials solidifies understanding better than worksheets alone.

What to Expect

Success looks like students confidently outlining shapes, counting units accurately, and explaining how perimeter measures the outside edge. They should recognize that equal sides may have different lengths and that only outer edges matter in composite shapes. Peer comparisons and shared models help them articulate their understanding clearly.

Watch Out for These Misconceptions

Common Misconception

During Block Fencing, watch for students counting the number of blocks placed rather than the total distance around the shape.

What to Teach Instead

Prompt students to slide their finger along each side while counting blocks aloud, then ask, 'Does the number of blocks equal the length of this side?' Use a second shape with unequal sides to highlight that side length, not just count, matters.

Common Misconception

During String Measure, watch for students tracing all edges, including internal ones, when measuring composite shapes.

What to Teach Instead

Have students use a different color string to outline only the outer edges, then lift the string off the shape to count units. Ask, 'Why did we not use the string for the lines inside the shape?' to guide their thinking.

Common Misconception

During Perimeter Hunt, watch for students assuming all shapes with the same number of sides have the same perimeter.

What to Teach Instead

Pause the hunt to compare two shapes with equal side counts but different perimeters. Ask students to measure both and discuss why one shape needs more steps to walk around it.

Assessment Ideas

Quick Check

After Block Fencing, provide students with pre-drawn shapes (square, rectangle, triangle) on paper. Ask them to use paper clips to measure and record the perimeter of each shape. Observe their counting and addition skills.

Exit Ticket

After the Design Challenge, give each student a small card. Ask them to draw a simple composite shape made from two squares. Then, have them use blocks to measure and write down the perimeter of their composite shape.

Discussion Prompt

During Perimeter Hunt, show students a picture of a playground with a fence. Ask, 'How could we find out how much fencing is needed to go all the way around the playground?' Guide them to explain the idea of measuring the outside edge.

Extensions & Scaffolding

• Challenge early finishers to create a composite shape with a perimeter of exactly 12 blocks, then swap with a partner to verify.
• Scaffolding for struggling students: Provide shapes with pre-labeled side lengths using blocks or sticky notes to simplify addition.
• Deeper exploration: Ask students to design a shape with a perimeter larger than a given target, then measure and justify their choice in a class discussion.

Key Vocabulary

Perimeter	The total distance around the outside edge of a shape. It is the length of the boundary.
Polygon	A closed shape made up of straight line segments. Examples include squares, triangles, and rectangles.
Composite Shape	A shape made by joining two or more simpler shapes together. Only the outside edges are measured for its perimeter.
Non-standard unit	A measurement tool that is not a formal unit of length, such as blocks, paper clips, or string.