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.

• Primary 1
• Mathematics
• 4 activities
• 25 min–40 min

Learning Objectives

1. Combine two or more 2D shapes to create a new composite shape, such as a house or a boat.
2. Decompose a given 2D shape into two smaller, congruent shapes, identifying the smaller shapes formed.
3. Identify different combinations of smaller 2D shapes that can compose a larger, target shape.
4. Explain how a larger shape can be divided into smaller shapes, naming the shapes created.

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

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.

Prepare & details

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.'

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

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

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.

Prepare & details

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.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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

Assessment Ideas

Quick Check

After Pattern Block Challenges, provide students with two triangles and two squares. Ask them to compose a rhombus using the triangles, then a rectangle using the squares, and observe their ability to match edges and angles.

Exit Ticket

After Tangram Decomposition Stations, give each student a picture of a composite train made of rectangles and circles. Ask them to draw lines to show how to decompose the shape and label each part with its name.

Discussion Prompt

During Whole Class Shape Build Relay, show students a large rectangle made from two squares. Ask them to name all the ways they can decompose it into two smaller shapes and demonstrate their solutions using the blocks.

Extensions & Scaffolding

• Challenge students to compose a given shape using the fewest number of pattern blocks during Pattern Block Challenges.
• Scaffolding for students struggling with Tangram Decomposition: provide pre-cut shapes with dotted lines showing possible splits.
• Deeper exploration: Have students measure and compare the perimeters of their composed shapes to see how different combinations can yield the same area but different edge lengths.

Key Vocabulary

Compose	To put together or join shapes to make a new, larger shape. Think of building with blocks.
Decompose	To break apart a shape into smaller shapes. This is like taking apart a puzzle.
Composite Shape	A shape made by putting together two or more smaller shapes. A house made from a square and a triangle is a composite shape.
Congruent	Shapes that are exactly the same size and shape. If you can place one exactly on top of the other, they are congruent.