Mathematics · Grade 4

Active learning ideas

Perimeter of Rectangles and Composite Shapes

Active learning helps students build spatial reasoning through hands-on measurement, which is essential for understanding perimeter. Working with physical models and real-world contexts makes abstract formulas concrete and memorable.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.4.MD.A.3

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 30 min · Pairs

Geoboard Task: Rectangle Perimeters

Provide geoboards and rubber bands for students to build rectangles of varying lengths and widths. Pairs measure sides, calculate perimeters, and record in tables to identify patterns like how increasing length by one unit adds to the total. Discuss findings as a class.

Explain how two shapes can have the same perimeter but different areas.

Facilitation Tip

During the Geoboard Task, encourage students to stretch the rubber bands to form rectangles with the same perimeter but different dimensions to directly challenge the misconception.

What to look for

Provide students with a drawing of a composite rectilinear shape. Ask them to: 1. Write down the strategy they used to find the perimeter. 2. Calculate and write the perimeter in the correct linear units.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 40 min · Small Groups

Grid Paper Challenge: Composite Shapes

Students draw composite rectilinear shapes on centimetre grid paper, decompose into rectangles, and compute perimeters by tracing outer paths. Small groups verify by measuring string around outlines and compare results. Adjust for errors in shared edges.

Justify why perimeter is measured in linear units.

Facilitation Tip

For the Grid Paper Challenge, model how to highlight only the outer edges of composite shapes before calculating to prevent overcounting internal lines.

What to look for

Present two rectangles on the board: Rectangle A (4 cm x 6 cm) and Rectangle B (2 cm x 8 cm). Ask students: 'What is the perimeter of each rectangle? What do you notice about the dimensions and the perimeters? Can two rectangles have the same perimeter but different dimensions? Explain your thinking.'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 35 min · Small Groups

Design Relay: Same Perimeter Variations

In small groups, one student sketches a rectangle with a given perimeter, passes to partner to modify dimensions while keeping perimeter same but changing area. Groups calculate and share most extreme area differences. Whole class votes on creativity.

Design a strategy to find the perimeter of a composite rectilinear figure.

Facilitation Tip

In the Design Relay, set a timer for each round to keep the energy high and ensure teams rotate quickly to experience multiple perimeter variations.

What to look for

Give students a worksheet with several rectangles and composite shapes. Ask them to label the dimensions and calculate the perimeter for each. Circulate to observe their methods and provide immediate feedback on their calculations and strategies.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 45 min · Whole Class

Playground Perimeter Hunt: Whole Class

Measure perimeters of schoolyard rectangles like sandboxes or hopscotch grids using trundle wheels or string. Class compiles data, identifies composites like combined benches, and solves for missing dimensions. Create a perimeter map.

Explain how two shapes can have the same perimeter but different areas.

Facilitation Tip

For the Playground Perimeter Hunt, assign specific starting points so the entire class covers the space efficiently and groups can compare findings afterward.

What to look for

Provide students with a drawing of a composite rectilinear shape. Ask them to: 1. Write down the strategy they used to find the perimeter. 2. Calculate and write the perimeter in the correct linear units.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teach perimeter by connecting measurement to physical movement around shapes. Avoid starting with formulas; instead, let students discover the relationship between length, width, and perimeter through repeated hands-on trials. Research shows that students who measure with rulers or strings first develop stronger conceptual foundations than those who start with abstract equations.

Students will confidently measure and calculate perimeter for rectangles and composite shapes, explaining their methods with clear evidence. They will recognize that equal perimeters do not imply equal areas and adjust for shared edges in composite figures.

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Watch Out for These Misconceptions

• During the Geoboard Task, watch for students who assume any rectangle with the same perimeter must have the same area.

  Have them record the length, width, and area for each rectangle they create, then compare results as a class to show that same perimeter does not mean same area.

• During the Grid Paper Challenge, watch for students who add all edges of every rectangle in the composite shape without removing shared sides.

  Guide them to trace the outer boundary with a highlighter first, then count only those edges before calculating.

• During the Playground Perimeter Hunt, watch for students who measure perimeter in square units because they confuse it with area.

  Have them use a measuring tape to physically walk the perimeter, reinforcing that perimeter is a linear measure by counting steps or using a string marked in centimeters.

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Methods used in this brief

• Experiential Learning