Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

Building with 3D Shapes

Hands-on construction with 3D shapes turns abstract geometry into something concrete for students. When children manipulate blocks to build towers or bridges, they connect mathematical properties like faces and edges to real-world stability and design.

• NCCA Curriculum Specifications
• NCCA: Primary - Shape and Space
• NCCA: Primary - Problem solving

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Project-Based Learning
• 35 min · Small Groups

Tower Challenge: Stable Builds

Provide 3D blocks including cubes, cylinders, and prisms. Students build the tallest tower that stands for 30 seconds, identifying shapes used and explaining base choices. Groups test and redesign after collapses.

What 3D shapes did you use to build your structure?

Facilitation Tip

During Tower Challenge, have students work in pairs to test which shapes stack highest without toppling by recording the number of blocks added each time.

What to look for

Provide students with a small, pre-built structure made of 2-3 blocks. Ask them to draw the structure, label at least two different 3D shapes used, and write one sentence explaining why the bottom block made a good base.

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

Activity 02

• Project-Based Learning
• 30 min · Pairs

Bridge Construction: Shape Selection

Challenge pairs to span a 20cm gap with blocks, using at least three shapes. They record which shapes work best for supports and why, then share with the class.

Which shape made the best base for your building? Why?

Facilitation Tip

For Bridge Construction, provide a limited set of shapes and ask students to sketch their bridge before building to focus on purposeful selection.

What to look for

After students have built their structures, ask: 'Imagine you need to build a very tall tower. Which shape block would you choose for the very bottom, and why? How would using cylinders instead of cubes change your building?'

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

Activity 03

• Project-Based Learning
• 40 min · Small Groups

Structure Sort and Rebuild: Property Focus

Students sort blocks by properties like rolling or stacking, then rebuild a teacher model using specific shapes. Discuss differences in building with cubes versus cylinders.

How are a cube and a cylinder different when you try to build with them?

Facilitation Tip

In Structure Sort and Rebuild, provide a tray of mixed blocks and ask students to group them by properties before rebuilding a structure, using labeled cards for support.

What to look for

As students build, circulate and ask them to point to a specific shape in their structure and name it. Ask follow-up questions like, 'What do you call the flat sides of that shape?' or 'How many corners does that shape have?'

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

Activity 04

• Project-Based Learning
• 45 min · Whole Class

Classroom City: Collaborative Design

Whole class plans a cityscape on large mats, assigning roles for buildings. Each group builds one structure, labels shapes, and presents stability features.

What 3D shapes did you use to build your structure?

Facilitation Tip

In Classroom City, assign roles like architect and builder to encourage clear communication about shape choices and design plans.

What to look for

Provide students with a small, pre-built structure made of 2-3 blocks. Ask them to draw the structure, label at least two different 3D shapes used, and write one sentence explaining why the bottom block made a good base.

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

A few notes on teaching this unit

Start with free exploration using a variety of 3D blocks to build familiarity with their properties. Encourage students to test shape stability by gently pushing their structures, then redirect their observations toward the role of flat versus curved surfaces. Avoid rushing to definitions; instead, let students articulate their own insights first through guided questions like, 'What makes this tower stay up?'

Students will confidently select and name 3D shapes based on their properties, explain their building choices, and reflect on how shape affects stability. Successful learning shows in their ability to discuss trade-offs between different solids and adjust designs based on testing.

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Watch Out for These Misconceptions

• During Tower Challenge, watch for students who assume all blocks can roll equally well.

  Ask students to test each block’s rolling ability on a gentle slope, then have them group the blocks into 'rollers' and 'stackers' before continuing their builds.

• During Bridge Construction, watch for students who confuse cubes and cuboids as the same shape.

  Provide a set of cubes and cuboids side by side and ask students to measure each face with a ruler, noting that only cubes have equal sides.

• During Classroom City, watch for students who believe larger blocks are always more stable.

  Have students build two identical towers, one using large cubes and one using small cubes, then ask them to explain why the smaller blocks tower remains upright after gentle shaking.

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Methods used in this brief

• Project-Based Learning