Mathematics · Primary 1

Active learning ideas

Composing and Decomposing Shapes

Active learning works for composing and decomposing shapes because young learners build spatial reasoning through touch and visual trials rather than abstract rules. Hands-on manipulation helps students internalize how shapes relate to one another, which supports later geometry skills and problem solving.

• MOE Syllabus Outcomes
• MOE: G(v).1
• MOE: G(v).2

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 30 min · Pairs

Pattern Block Challenges: Compose a Robot

Provide pattern blocks in pairs. Students select a robot outline card and cover it exactly using triangles, squares, and hexagons without overlaps or gaps. They then draw their robot and label the shapes used. Pairs swap cards to compose a different robot.

Which shapes can we put together to make a new shape?

Facilitation Tip

During Pattern Block Challenges, circulate while students work and ask them to explain how the edges of the blocks meet to form new shapes.

What to look for

Provide students with pattern blocks. Ask them to use two triangles to make a rhombus. Then, ask them to use two squares to make a rectangle. Observe if they can successfully compose the new shapes.

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

Activity 02

• Stations Rotation
• 40 min · Small Groups

Tangram Decomposition Stations

Set up stations with tangram sets. At each, students decompose a large square into seven pieces, then recompose into animal silhouettes provided on cards. They record two ways to make the same silhouette. Groups rotate every 10 minutes.

How can we split a shape into two smaller shapes?

Facilitation Tip

At Tangram Decomposition Stations, encourage students to trace each piece before rearranging to reinforce conservation of area.

What to look for

Give each student a picture of a simple composite shape (e.g., a train made of rectangles and circles). Ask them to draw lines to show how they could decompose the shape into its basic parts and label the parts.

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

Activity 03

• Gallery Walk
• 35 min · Pairs

Shape Split Gallery Walk

Give each pair a large shape cutout like a rectangle or trapezoid. Students draw lines to split it into two smaller shapes, naming them, then post on walls. Class walks around, votes on creative splits, and discusses multiples ways.

How many different ways can we make the same shape from smaller shapes?

Facilitation Tip

For the Shape Split Gallery Walk, post a simple rule at each station: 'Find at least two ways to split this shape.'

What to look for

Show students a large rectangle made from two smaller squares. Ask: 'How many ways can we decompose this rectangle into two smaller shapes? What shapes do we get?' Encourage them to share their ideas and demonstrate with blocks.

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

Activity 04

• Stations Rotation
• 25 min · Small Groups

Whole Class Shape Build Relay

Divide class into teams. Call out a target shape; teams race to compose it from shared shape bins using squares and triangles. Correct compositions stay built; incorrect ones rebuild. Discuss strategies after each round.

Which shapes can we put together to make a new shape?

Facilitation Tip

During the Whole Class Shape Build Relay, pause after each round to ask the group to describe the successful combination aloud.

What to look for

Provide students with pattern blocks. Ask them to use two triangles to make a rhombus. Then, ask them to use two squares to make a rectangle. Observe if they can successfully compose the new shapes.

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

A few notes on teaching this unit

Teach this topic by letting students explore freely first, then guiding them to articulate their discoveries through questioning. Avoid correcting mistakes immediately; instead, let peers share solutions so students learn from one another. Research shows that open-ended play followed by structured reflection strengthens spatial reasoning more than step-by-step instructions.

Successful learning looks like students freely experimenting with shape combinations, explaining why certain parts fit together, and confidently separating shapes into equal or varied parts. They should show curiosity by trying multiple solutions and discussing their findings with peers.

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Watch Out for These Misconceptions

• During Pattern Block Challenges, watch for students who only combine identical shapes because they believe mixed sizes won’t fit.

  Prompt them to test mismatched blocks side-by-side and describe how the edges align, then ask peers to share their successful mixed-size combinations.

• During Tangram Decomposition Stations, watch for students who think the total area changes when a shape is split.

  Have them trace the original shape’s outline on paper, then trace each piece separately to visibly confirm the area remains the same before reassembling.

• During Whole Class Shape Build Relay, watch for students who believe only one solution exists for each target shape.

  Stop the relay after two rounds and ask groups to share their different solutions, then list all possibilities on the board for comparison.

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Methods used in this brief

• Stations Rotation
• Gallery Walk