Mastering Mathematical Thinking: 4th Class · 4th Class

Active learning ideas

Tessellations

Active learning lets students feel the fit of shapes as they test, fail, and revise. When students rotate through stations with hands-on pieces, they experience the angle rule in real time rather than memorize it abstractly. The tactile work turns abstract geometry into something they can see and adjust immediately.

• NCCA Curriculum Specifications
• NCCA: Primary - Shape and Space
• NCCA: Primary - Symmetry

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Polygon Tessellation Tests

Prepare stations with cutouts of equilateral triangles, squares, hexagons, and pentagons. Groups test each shape by arranging them around a point and extending to cover paper, noting gaps or overlaps in journals. Rotate every 10 minutes and share findings with the class.

Why do some shapes tessellate perfectly while others leave gaps?

Facilitation Tip

In Personal Tessellation Design, prompt students to outline their final pattern in marker so the tessellating units stand out clearly.

What to look for

Provide students with cut-out shapes of equilateral triangles, squares, and regular hexagons. Ask them to select one shape and demonstrate how it tessellates by arranging it on grid paper. On the back, they should write one sentence explaining why their chosen shape works.

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

Activity 02

• Stations Rotation
• 30 min · Pairs

Pairs Challenge: Mixed Shape Tessellations

Partners receive assorted regular polygons and try combining two or more types to cover a worksheet without gaps. They sketch successful patterns and explain the angle sums verbally. Switch partners midway to compare strategies.

Analyze the properties of shapes that allow them to tessellate.

What to look for

Show students images of a regular pentagon pattern with gaps and a regular hexagon tessellation. Ask: 'What is the key difference in the angles at the points where the shapes meet? How does this difference affect whether the shapes can cover the entire surface?'

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

Activity 03

• Stations Rotation
• 35 min · Whole Class

Whole Class: Collaborative Floor Tessellation

Project a large grid on the floor with tape. Class works together to fill it using shape cutouts, adjusting as needed. Discuss properties that made it work and photograph the final design.

Construct a tessellating pattern using a regular polygon.

What to look for

Observe students as they work in small groups to create a tessellating pattern using at least two different regular polygons. Note which groups successfully achieve a gap-free pattern and which students can articulate the angle sum rule (360 degrees) at the vertices.

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

Activity 04

• Stations Rotation
• 25 min · Individual

Individual: Personal Tessellation Design

Each student selects a tessellating shape, colors it, and repeats it to fill A4 paper, adding symmetry elements. They label angles and present one unique feature to peers.

Why do some shapes tessellate perfectly while others leave gaps?

What to look for

Provide students with cut-out shapes of equilateral triangles, squares, and regular hexagons. Ask them to select one shape and demonstrate how it tessellates by arranging it on grid paper. On the back, they should write one sentence explaining why their chosen shape works.

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

A few notes on teaching this unit

Teachers should avoid telling students the angle rule up front; instead, let the materials reveal it through repeated trials. Move between groups asking guiding questions like 'Where are the vertices meeting?' and 'Can you rotate that piece to close the gap?' to steer thinking without giving answers. Research shows that self-discovery of the 360-degree rule sticks better than direct instruction.

Successful learning looks like students confidently selecting, rotating, and matching shapes to cover paper without gaps or overlaps. They should explain why only certain regular polygons work by pointing to the angles at a vertex. Groups should also create mixed-shape patterns and defend their choices with angle sums.

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Watch Out for These Misconceptions

• During Station Rotation: watch for students who believe scaling a regular pentagon down will make it tessellate.

  Hand them a set of pentagons in three sizes and ask them to test each one on grid paper, then compare vertex gaps with the hexagon set to see that size does not fix the angle problem.

• During Pairs Challenge: watch for students who assume only squares can tessellate when mixed with other shapes.

  Have them rotate through mixed sets and compare their mixed patterns to the single-shape stations, asking them to list all successful combinations and explain why those angles fit.

• During Collaborative Floor Tessellation: watch for students who think tessellations must have straight edges.

  Place curved puzzle pieces at the station and ask groups to match edges precisely, then compare straight-edge and curved-edge tessellations side by side.

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Methods used in this brief

• Stations Rotation