Mathematics · Primary 4

Active learning ideas

Area and Perimeter of Composite Figures

Hands-on activities allow students to physically manipulate shapes, which helps them see how composite figures break apart into familiar components. This tactile approach builds intuition about area and perimeter in ways worksheets alone cannot replicate.

• MOE Syllabus Outcomes
• MOE: Geometry and Measurement - S1

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

Activity 01

• Collaborative Problem-Solving
• 35 min · Pairs

Geoboard Builds: Composite Creations

Supply geoboards, rubber bands, and grid paper. Students construct composite figures with two or three basic shapes, sketch the outline, then compute area by counting squares and perimeter by measuring edges. Pairs swap shapes to verify each other's work.

How do you read information from a table or a bar graph to answer questions?

Facilitation Tip

During Geoboard Builds, have students describe their shape’s decomposition to a partner before measuring to reinforce verbal reasoning alongside visual work.

What to look for

Provide students with a worksheet showing 2-3 composite figures made of rectangles. Ask them to calculate the area and perimeter of each figure, showing their work by drawing lines to decompose the shapes and labeling dimensions.

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

Activity 02

• Collaborative Problem-Solving
• 40 min · Small Groups

Paper Cutouts: Decompose and Measure

Provide grid paper templates of L-shapes or T-shapes. Students cut along decomposition lines into rectangles and triangles, label dimensions, calculate individual areas and total perimeter. Small groups reassemble and present findings.

What does the scale on a bar graph mean, and how do you use it to read values accurately?

Facilitation Tip

When students do Paper Cutouts, collect leftover scraps and ask them to prove their total area matches the original shape’s dimensions.

What to look for

Give each student a composite figure that includes a triangle and a rectangle. Ask them to write down the steps they would take to find the area and perimeter, and to calculate one of them (either area or perimeter) if all necessary dimensions are provided.

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

Activity 03

• Collaborative Problem-Solving
• 30 min · Small Groups

String Trace: Perimeter Hunt

Draw composite figures on large chart paper. Groups use string to trace outer perimeters, measure lengths, and compare to calculated values. Extend by designing their own shapes for classmates to solve.

Can you collect data, organise it in a table, and then draw a bar graph to display it?

Facilitation Tip

For String Trace, challenge groups to find the shortest possible perimeter path by adjusting their figure’s shape slightly.

What to look for

Present students with two different ways to decompose the same composite figure. Ask: 'Are both methods valid for calculating the total area? Why or why not? Which method do you find easier and why?'

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

Activity 04

• Collaborative Problem-Solving
• 45 min · Whole Class

Grid Puzzle: Area Challenges

Distribute puzzles where students fill grids to form composites matching given areas. They record decompositions and perimeters. Whole class shares strategies via gallery walk.

How do you read information from a table or a bar graph to answer questions?

Facilitation Tip

In Grid Puzzle, require students to trade solutions with another group and verify each other’s calculations before moving on.

What to look for

Provide students with a worksheet showing 2-3 composite figures made of rectangles. Ask them to calculate the area and perimeter of each figure, showing their work by drawing lines to decompose the shapes and labeling dimensions.

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

A few notes on teaching this unit

Start with concrete manipulatives like geoboards or paper shapes to establish the concept of breaking apart figures. Move to grid-based activities to reinforce decomposition and measurement, avoiding abstract formulas until students can explain why they add or ignore certain sides. Research shows students who draw decomposition lines before calculating make fewer errors in perimeter and area.

Students should confidently decompose composite figures into simpler shapes, apply area and perimeter formulas correctly, and justify their calculations by labeling dimensions. Peer collaboration ensures they internalize these steps through discussion and verification.

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Watch Out for These Misconceptions

• During String Trace, watch for students who include internal edges when measuring perimeter with string.

  Have students lay the string only along the outer edge and mark where it meets itself to show that internal sides do not count. Ask them to compare their string length to the sum of all sides to highlight the difference.

• During Paper Cutouts, watch for students who skip breaking the composite figure into parts before measuring area.

  Prompt them to rearrange the cut pieces into a single shape they can measure easily, like a rectangle, to demonstrate why summing parts works better than guessing.

• During Geoboard Builds, watch for students who use the triangle’s base and height incorrectly after combining it with other shapes.

  Ask them to test different base-height pairs on the geoboard to see which combination matches the figure’s actual dimensions, then discuss why only one pair is valid for area calculation.

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Methods used in this brief

• Collaborative Problem-Solving