Mathematics · 6th Grade

Active learning ideas

Area of Composite Figures

Active learning helps students grasp the concept of area for composite figures because they must physically manipulate shapes and visualize decompositions. Breaking down complex problems into simpler parts is a skill that improves with hands-on practice. This topic benefits from collaborative work where students articulate their reasoning and learn from peers.

• Common Core State Standards
• CCSS.Math.Content.6.G.A.1

• 20–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inquiry Circle
• 50 min · Small Groups

Inquiry Circle: Floor Plan Challenge

Each group receives an irregular floor plan sketch (L-shape, T-shape, or U-shape) and must decompose it at least two different ways. They calculate the total area using each decomposition and confirm both methods give the same result, then present their strategies to the class.

Analyze how any polygon can be broken down into triangles and rectangles.

Facilitation Tip

During the Floor Plan Challenge, circulate and ask groups to explain how they chose their decomposition lines.

What to look for

Provide students with a diagram of a composite figure made of 2-3 rectangles and/or triangles. Ask them to draw lines showing one possible decomposition and calculate the total area, showing all steps.

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

Activity 02

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Add or Subtract?

Present two composite figures: one where students add areas and one where a shape has been removed (e.g., a rectangle with a triangular corner cut out). Pairs decide for each which strategy is more efficient and justify their reasoning before sharing with the class.

Design a strategy to find the area of an irregular shape.

Facilitation Tip

In the Think-Pair-Share, provide a figure where both addition and subtraction are possible so students see the value of both approaches.

What to look for

Give students a composite figure with dimensions labeled. Ask them to write down two different ways to decompose the figure and calculate the area for one of the methods. Then, ask them to explain which method they found easier and why.

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

Activity 03

• Gallery Walk
• 40 min · Individual

Gallery Walk: Strategy Comparison

Post five composite figures around the room, each already solved using one decomposition method. Students must find and draw a different valid decomposition for each figure and verify that both methods give the same area.

Justify the process of decomposing a complex figure to calculate its area.

Facilitation Tip

For the Gallery Walk, ask students to compare strategies by writing one sentence on each poster about what they learned.

What to look for

Present students with a composite figure that can be solved using subtraction (e.g., a rectangle with a smaller rectangle removed from a corner). Ask: 'How can we find the area of the shaded region? What are the steps involved in using subtraction to find the area?'

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

Activity 04

• Simulation Game
• 45 min · Individual

Simulation Game: Design Your Own Floor Plan

Students design an irregular polygon floor plan for an imaginary room on grid paper, add labeled measurements, and find its area by decomposing. They write a brief explanation of their decomposition strategy that another student could follow independently.

Analyze how any polygon can be broken down into triangles and rectangles.

Facilitation Tip

During the Design Your Own Floor Plan, remind students to label all dimensions and include at least two different shapes in their composite figure.

What to look for

Provide students with a diagram of a composite figure made of 2-3 rectangles and/or triangles. Ask them to draw lines showing one possible decomposition and calculate the total area, showing all steps.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

A few notes on teaching this unit

Start with simple composite figures made of two shapes and gradually increase complexity. Model decomposition by thinking aloud as you decide where to draw lines. Avoid moving too quickly to advanced figures before students are comfortable with basic decompositions. Research shows that students benefit from seeing multiple solutions to the same problem, so present figures that can be solved using different methods.

Students will confidently decompose composite figures into familiar shapes, choose appropriate area formulas, and combine results accurately. They will also recognize when subtraction is more efficient than addition. Group discussions should include clear explanations of strategies and justifications for chosen methods.

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Watch Out for These Misconceptions

• During Collaborative Investigation: Floor Plan Challenge, watch for students who draw decomposition lines that overlap or leave gaps.

  Ask students to use colored pencils to shade each sub-region a different color and check that no area is double-shaded before calculating. Have them present their shaded sketches to the group before moving to calculations.

• During Think-Pair-Share: Add or Subtract?, watch for students who always use addition even when subtraction is more efficient.

  Provide figures where subtraction is clearly the better method, such as a rectangle with a corner cut out. After students share their solutions, show both addition and subtraction methods for the same figure to demonstrate equivalence and build confidence in subtraction.

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Methods used in this brief

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