Mathematics · 1st Class

Active learning ideas

Patterns and Repeating Designs

Active learning lets students test rules with their hands and eyes, not just listen to explanations. For patterns and tessellations, movement and trial build spatial logic faster than worksheets alone.

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

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 20 min · Pairs

Pairs: Pattern Extension Relay

Partners take turns extending a teacher's starter pattern with coloured blocks or beads, saying the rule aloud before passing. Switch roles after three extensions. Pairs compare final patterns and explain differences.

What comes next in this shape or colour pattern?

Facilitation Tip

In the Pattern Extension Relay, circulate with a timer and call out the next step only after pairs have shown their answer to you.

What to look for

Provide students with a worksheet showing three incomplete patterns. Ask them to draw the next three elements for each pattern and write the rule for one of them (e.g., 'blue circle, red square, blue circle, red square').

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 30 min · Small Groups

Small Groups: Tessellation Challenge

Provide paper, scissors, and shape templates like equilateral triangles, squares, and hexagons. Groups cut and arrange shapes to cover surfaces without gaps, rotating or flipping as needed. Record successful combinations on charts.

How can you make your own repeating pattern using shapes or colours?

Facilitation Tip

During the Tessellation Challenge, provide scissors so groups can trim shapes to test fits on grid paper before gluing.

What to look for

Hold up a set of 2D shape cut-outs (squares, triangles, hexagons). Ask students to select shapes that can tessellate and demonstrate how they fit together on their desks. Ask: 'Which shapes fit together without any spaces?'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 25 min · Whole Class

Whole Class: Repeating Pattern Chain

Teacher models a simple shape or colour pattern on the board. Each student adds one element following the rule, standing to share. Class votes on accuracy and extends collectively.

Can you describe the rule in a pattern and continue it correctly for three more items?

Facilitation Tip

For the Repeating Pattern Chain, hand each student a single card so the whole class must decide order together.

What to look for

Show students images of tiled floors or patterned wallpaper. Ask: 'What patterns do you see? Can you describe the repeating part? What shapes are used? Do the shapes fit together perfectly?'

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 15 min · Individual

Individual: Design Your Tessellation

Students select 2-3 shapes from a kit and create a personal repeating design on grid paper. Label the tiling rule and colour for display. Share one discovery with the class.

What comes next in this shape or colour pattern?

Facilitation Tip

With Design Your Tessellation, give colored pencils and dot paper so students can rotate shapes before drawing final lines.

What to look for

Provide students with a worksheet showing three incomplete patterns. Ask them to draw the next three elements for each pattern and write the rule for one of them (e.g., 'blue circle, red square, blue circle, red square').

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Teach by doing first: let students extend a pattern with real objects before they draw or write rules. Avoid showing finished answers early; instead, ask, 'What could come next?' to keep thinking open. Research shows physical pattern blocks reduce guessing and build stronger reasoning than screen-based drills.

Successful learners will speak in rules, spot errors in sequences, and adjust shapes until they fit together without gaps. They will explain their thinking clearly to peers during each task.

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Watch Out for These Misconceptions

• During Tessellation Challenge, watch for students assuming all shapes can tile without testing.

  Hand each group circles and irregular pentagons alongside squares; ask them to try fitting them on grid paper and observe the gaps before moving to regular shapes.

• During Repeating Pattern Chain, watch for students describing patterns as random or just pretty.

  Pause the chain after three turns and ask a student to state the rule aloud; if unclear, have the class test predictions using the next card to reveal the pattern's consistency.

• During Design Your Tessellation, watch for students arranging shapes only in straight rows.

  Provide curved templates or let students rotate triangles to form spirals; display finished designs to show that tessellations can curve and shift while still covering the surface.

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Methods used in this brief

• Plan-Do-Review