Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Tessellating Patterns

Active learning works because tessellations require spatial reasoning and hands-on trial and error, which concrete materials provide. Students need to physically manipulate shapes to see how angles and edges fit together, making abstract concepts visible. This approach builds confidence as students observe immediate feedback from their arrangements.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Statistics and Probability - S.2.1

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Shape Tessellation Stations

Prepare stations with triangles, squares, rectangles, and hexagons on cardstock. Students cut and arrange shapes to cover paper without gaps. Rotate groups every 10 minutes, then share successful patterns with the class.

What does it mean for a shape to tessellate?

Facilitation Tip

During Shape Tessellation Stations, circulate with guiding questions like 'What do you notice about how these edges meet?' to prompt reflection.

What to look for

Provide students with a collection of pre-cut regular polygons (squares, triangles, hexagons). Ask them to select shapes that can tessellate and arrange them on a piece of paper to demonstrate a pattern. Observe which shapes they choose and how they attempt to fit them together.

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

Activity 02

• Experiential Learning
• 30 min · Pairs

Pairs: Custom Tessellation Design

Partners select one shape and create a repeating pattern on large paper, rotating and flipping as needed. They trace outlines and colour the design. Pairs present, explaining their choices.

How can you use a shape to make a repeating pattern with no gaps or overlaps?

Facilitation Tip

For Custom Tessellation Design, provide grid paper with pre-drawn shapes to scaffold students who struggle with freehand drawing.

What to look for

Give each student a card with a picture of a shape. Ask them to write one sentence explaining whether the shape can tessellate and why or why not. For example, 'A square can tessellate because its corners fit together perfectly around a point.'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 35 min · Whole Class

Whole Class: Tessellation Floor Mat

Distribute shape tiles to the class. Students collaborate to cover a floor outline, adjusting placements collectively. Discuss challenges and solutions as a group.

Can you create your own tessellating pattern using squares, rectangles, or triangles?

Facilitation Tip

When using the Tessellation Floor Mat, stand back to observe peer discussions, listening for geometric vocabulary like 'vertex' or 'edge'.

What to look for

Present students with two different tessellating patterns, one made with squares and one with triangles. Ask: 'What do you notice about how the shapes fit together at the corners in each pattern?' Guide them to discuss the angles meeting at the vertices.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 20 min · Individual

Individual: Pattern Extension Challenge

Give each student a starter tessellation strip. They extend it across a page, trying different orientations. Collect and display for peer feedback.

What does it mean for a shape to tessellate?

Facilitation Tip

In the Pattern Extension Challenge, encourage students to rotate their page to see if the pattern still tessellates, reinforcing flexibility in thinking.

What to look for

Provide students with a collection of pre-cut regular polygons (squares, triangles, hexagons). Ask them to select shapes that can tessellate and arrange them on a piece of paper to demonstrate a pattern. Observe which shapes they choose and how they attempt to fit them together.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teach tessellations by starting with simple shapes students already know, like squares, before introducing triangles or hexagons. Avoid rushing to abstract rules; let students discover patterns through repeated trials. Research shows that manipulatives and visual models are essential for young learners to grasp spatial relationships. Emphasize that tessellations are about relationships between shapes, not just the shapes themselves.

Successful learning looks like students confidently selecting shapes that tessellate, arranging them without gaps or overlaps, and explaining their choices using geometric terms. They should discuss why certain shapes fit and others do not, showing evidence-based reasoning. Patterns should repeat predictably, demonstrating understanding of edge-to-edge alignment.

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Watch Out for These Misconceptions

• During Shape Tessellation Stations, watch for students assuming all shapes tessellate equally. Correction: Direct them to trial different shapes on their station table, comparing gaps when they arrange circles versus squares, then ask, 'What do you observe about the edges that fit perfectly?'

  During Custom Tessellation Design, watch for students rotating shapes rigidly. Correction: Remind them to flip or turn pieces, demonstrating with a triangle turned 180 degrees to show how it still fits, then ask, 'How did changing the orientation help?'

• During Tessellation Floor Mat, watch for students believing only squares tessellate. Correction: Place a pentagon cutout nearby and ask, 'Can this shape tessellate? Try arranging it with the squares.' Prompt them to notice angles meeting at vertices.

  During Pattern Extension Challenge, watch for students thinking curved shapes cannot tessellate. Correction: Provide a curved pentagon template and ask, 'How can you adjust this shape to fit without gaps?' Encourage them to trim edges if needed.

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Methods used in this brief

• Stations Rotation
• Experiential Learning