Mathematics · Class 1

Active learning ideas

Area of Composite Figures

Active learning works well for composite figures because students often struggle to visualise complex shapes on paper. When they cut, draw, or build shapes, their understanding of decomposition becomes clearer. This hands-on approach also helps them connect abstract formulas to real objects they can touch and measure.

• CBSE Learning Outcomes
• NCERT: Class 7, Chapter 11, Perimeter and Area

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Outdoor Investigation Session
• 25 min · Pairs

Shape Decomposition Puzzle

Students receive cut-out composite shapes on grid paper and decompose them into rectangles or triangles. They calculate the area of each part and find the total. This builds confidence in breaking down complex figures.

Analyze how to decompose complex shapes into simpler geometric figures.

Facilitation Tip

During Shape Decomposition Puzzle, provide scissors and coloured paper so students can physically separate shapes; this makes overlaps easier to see and correct.

What to look for

Provide students with a worksheet showing 2-3 composite figures. Ask them to draw lines to decompose each figure into simpler shapes and write the total area for each figure. Collect these to check their decomposition and calculation skills.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 02

• Outdoor Investigation Session
• 30 min · Small Groups

Room Design Challenge

In pairs, students design a classroom floor plan using rectangles and triangles on grid paper. They label dimensions, calculate areas of sections, and find the total carpet needed. Discuss real measurements next.

Evaluate different strategies for finding the area of a composite figure.

Facilitation Tip

For the Room Design Challenge, give students graph paper with a fixed scale so they practise measuring realistically and not just counting squares.

What to look for

Display a composite figure on the board. Ask students to write down on a small piece of paper: 1. The simpler shapes they see. 2. The formula they would use for each shape. This checks their ability to identify components and recall formulas.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 03

• Outdoor Investigation Session
• 20 min · Whole Class

Area Hunt Game

Students search the classroom or school ground for objects made of composite shapes, like windows or desks. They sketch, decompose, and estimate areas using string or paper grids. Share findings in class.

Construct a composite figure and calculate its total area.

Facilitation Tip

In Area Hunt Game, walk around with a checklist to note which students are missing overlaps or using wrong formulas, so you can redirect them immediately.

What to look for

Present two different ways to decompose the same composite figure. Ask students: 'Which method is easier for you and why? Are both methods correct? What could happen if we don't subtract overlapping areas?' This encourages strategic thinking and understanding of overlaps.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 15 min · Individual

Custom Figure Creator

Individually, students create their own composite figure using geometric stencils on grid paper. They swap with a partner to decompose and calculate the area, then compare results.

Analyze how to decompose complex shapes into simpler geometric figures.

Facilitation Tip

While using Custom Figure Creator, ask students to swap their figures with peers to verify calculations; this builds accountability and peer learning.

What to look for

Provide students with a worksheet showing 2-3 composite figures. Ask them to draw lines to decompose each figure into simpler shapes and write the total area for each figure. Collect these to check their decomposition and calculation skills.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Start with concrete objects like tiles or cardboard cutouts to show how composite shapes appear in daily life. Teach students to label each part clearly before calculating to avoid formula mix-ups. Avoid rushing to abstract formulas; let students struggle a little with decomposition first, as research shows this deepens understanding. Use right-angled triangles often in examples, since students find it easier to identify base and height there.

By the end of these activities, students should confidently break composite figures into known shapes, calculate each area correctly, and add or subtract parts as needed. They should explain their steps clearly and choose efficient decomposition methods without confusion between area and perimeter.

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Watch Out for These Misconceptions

• During Shape Decomposition Puzzle, watch for students who add all areas without checking for overlaps. Redirect them by asking, 'Does this part appear in more than one shape? How can you show the overlap?'

  Have them colour the overlapping region with a different pen and subtract its area once from the total.

• During Room Design Challenge, watch for students who confuse area with perimeter when measuring walls and floors. Redirect them by asking, 'Are you measuring the space inside the room or the length of the walls? What units will you use?'

  Ask them to measure one wall’s length for perimeter and one floor section’s area separately to clarify the difference.

• During Custom Figure Creator, watch for students who use the wrong formula for triangles, especially non-right-angled ones. Redirect them by asking, 'How do you identify the base and height in this triangle? Should you use the same method as before?'

  Provide right-angled triangles initially, then gradually introduce other types with formula charts for reference.

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Methods used in this brief

• Outdoor Investigation Session