Mathematics · Primary 5

Active learning ideas

Area of Composite Figures

Active learning lets students manipulate and visualize complex shapes, which strengthens their understanding of area beyond abstract formulas. When students cut, rearrange, and measure, they internalize how composite figures break down into simpler parts, making the concept tangible and memorable.

• MOE Syllabus Outcomes
• MOE: Measurement - P5

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Decomposition Stations

Prepare four stations with grid paper cutouts of composite figures. Students decompose each into rectangles, squares, and triangles, calculate areas, and record strategies. Rotate groups every 10 minutes, then share efficient methods as a class.

Analyze different strategies for decomposing complex shapes into simpler ones to find their area.

Facilitation Tip

During Decomposition Stations, provide scissors and grid paper so students physically separate shapes and verify measurements by counting squares.

What to look for

Provide students with a worksheet showing 2-3 composite figures made of rectangles and triangles. Ask them to draw lines to decompose each figure, label the dimensions of each smaller shape, and calculate the total area for each composite figure.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 30 min · Pairs

Pairs: Shape Designer Challenge

Partners sketch a composite figure using at least three basic shapes, label dimensions, and compute total area. They swap designs with another pair, verify calculations, and discuss improvements. Present one design to the class.

Design a composite figure and calculate its total area.

Facilitation Tip

For the Shape Designer Challenge, remind pairs to trade their designs and calculate areas to check each other’s work before presenting.

What to look for

Present two different methods of decomposing the same composite figure on the board. Ask students: 'Which method do you think is more efficient and why? What makes one strategy better than another for this specific shape?'

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

Activity 03

• Problem-Based Learning
• 35 min · Small Groups

Small Groups: Tangram Composites

Provide tangram sets on grid mats. Groups form composite figures, decompose them back into pieces, calculate areas using grid squares, and justify their method. Compare group results for the same figure.

Evaluate the most efficient method for finding the area of a given composite figure.

Facilitation Tip

In Tangram Composites, circulate to ensure groups rotate cutouts to test different decompositions, not just the first solution they see.

What to look for

Give each student a card with a composite figure. Ask them to write down the formulas they used for each component shape and show the final calculation for the total area. They should also write one sentence about a strategy they used.

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

Activity 04

• Problem-Based Learning
• 25 min · Whole Class

Whole Class: Classroom Floor Plan

Project a simple floor plan divided into rectangles and triangles. Class votes on decomposition strategies, calculates total area step-by-step on shared whiteboard, and adjusts for overlaps.

Analyze different strategies for decomposing complex shapes into simpler ones to find their area.

Facilitation Tip

With the Classroom Floor Plan, assign roles so every student measures and records dimensions, then collaboratively calculates the total area.

What to look for

Provide students with a worksheet showing 2-3 composite figures made of rectangles and triangles. Ask them to draw lines to decompose each figure, label the dimensions of each smaller shape, and calculate the total area for each composite figure.

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

A few notes on teaching this unit

Start with hands-on materials before moving to abstract problems, as research shows concrete experiences build stronger spatial reasoning. Avoid rushing to formulas; instead, let students discover that triangles can form rectangles or that overlapping regions require subtraction. Encourage multiple strategies, as flexibility in decomposition leads to deeper understanding and fewer errors.

Successful learning looks like students confidently decomposing composite figures, accurately calculating areas of individual shapes, and correctly combining them for a total. They should explain their process clearly and recognize when to add or subtract overlapping regions without prompting.

---

Watch Out for These Misconceptions

• During Decomposition Stations, watch for students who add all visible areas without considering overlaps or cutouts.

  Have them physically rearrange their paper shapes to see duplicate regions, then erase or cross out the overlapping parts before calculating.

• During the Shape Designer Challenge, watch for students who confuse perimeter with area by tracing outlines instead of shading interiors.

  Ask them to outline the figure in one color and shade the interior in another, then compare the string length (perimeter) to the shaded area (total).

• During Tangram Composites, watch for students who mislabel the base or height of triangles by choosing non-perpendicular sides.

  Provide right-angle templates for students to test their measurements against, adjusting until the triangle fits perfectly into a rectangle formed by the grid.

---

Methods used in this brief

• Stations Rotation
• Problem-Based Learning