Mathematics · 2nd Year

Active learning ideas

Repeating and Growing Patterns

Active learning helps students grasp repeating and growing patterns by making the abstract concrete. Moving, building, and discussing with peers turns pattern rules into something they can see and test right away. This hands-on work builds confidence before moving to abstract notation or symbols.

• NCCA Curriculum Specifications
• NCCA: Primary - Algebra
• NCCA: Primary - Reasoning

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Inside-Outside Circle
• 25 min · Pairs

Partner Chain: Repeating Patterns

Pairs build paper chains with repeating units of two colors or shapes, like red-blue-red-blue. One student starts a five-link chain, the partner extends it by four links following the rule. Partners switch, describe the rule to each other, and compare chains.

What comes next in this pattern: circle, triangle, square, circle, triangle, ...?

Facilitation Tip

During Partner Chain: Repeating Patterns, circulate and listen for students naming the core unit aloud before they add the next element.

What to look for

Present students with a sequence of 5-7 shapes (e.g., red circle, blue square, red circle, blue square, red circle). Ask: 'What shape comes next?' and 'What is the rule for this pattern?'

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

Activity 02

• Inside-Outside Circle
• 35 min · Small Groups

Group Build: Growing Shape Towers

Small groups use linking cubes to construct towers where each level adds one more shape, alternating colors. They extend the pattern to five levels, sketch it, and write the rule. Groups share towers and predict the tenth level.

How would you describe the rule of a repeating pattern?

Facilitation Tip

During Group Build: Growing Shape Towers, ask guiding questions like 'How many cubes will you add next?' to focus attention on the growth rule.

What to look for

Give students a card with a growing pattern (e.g., 1 apple, 3 apples, 5 apples). Ask them to write the next number in the sequence and explain the rule in one sentence.

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

Activity 03

• Inside-Outside Circle
• 30 min · Pairs

Class Hunt: Pattern Spotters

Whole class brainstorms pattern categories, then pairs search classroom and school for examples like window arrangements or number lines. They photograph or draw three patterns, note the rule, and share in a class gallery walk.

Where can you find a pattern in your classroom or school?

Facilitation Tip

During Class Hunt: Pattern Spotters, carry a clipboard to model recording a rule immediately after students describe their findings.

What to look for

Ask students: 'Find a pattern in our classroom. Describe its rule and explain if it is a repeating or growing pattern.' Encourage them to share their findings with a partner.

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

Activity 04

• Inside-Outside Circle
• 20 min · Individual

Individual Create: Number Necklaces

Students string beads into growing patterns, starting with one bead, then two of another color, three of the first. They extend to six beads, label the rule on paper, and wear necklaces for peer review.

What comes next in this pattern: circle, triangle, square, circle, triangle, ...?

Facilitation Tip

During Individual Create: Number Necklaces, provide number cards in advance so students focus on the necklace design rather than writing numbers.

What to look for

Present students with a sequence of 5-7 shapes (e.g., red circle, blue square, red circle, blue square, red circle). Ask: 'What shape comes next?' and 'What is the rule for this pattern?'

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

A few notes on teaching this unit

Teach patterns by starting with visuals and movement before symbols. Use multiple representations—shapes, colors, and numbers—so students connect the rule across formats. Avoid rushing to written rules; let students verbalize their thinking first. Research shows that students who describe patterns aloud before writing are more accurate and flexible in their rule application.

Successful learning looks like students confidently describing the core unit in repeating patterns, explaining how each step grows in growing patterns, and creating new examples with clear rules. Look for students using precise vocabulary and justifying their answers with evidence from the materials.

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Watch Out for These Misconceptions

• During Partner Chain: Repeating Patterns, watch for students who insist patterns must involve numbers and ignore shape or color sequences.

  Use mixed materials like colored tiles and pattern blocks during Partner Chain. Ask partners to sort their core unit by shape, color, and number to show that rules can apply across types.

• During Group Build: Growing Shape Towers, watch for students who assume towers always add one cube each step.

  Provide towers with varied growth rules (add one, add two, skip count by twos) and have groups sort them by rule type. Ask, 'How did your tower change from step to step?' to highlight different growth patterns.

• During Class Hunt: Pattern Spotters, watch for students who claim classroom patterns are random with no describable rule.

  Ask students to sketch the pattern they find and label the core unit or growth step. Require them to share the rule with a partner before recording it, ensuring every pattern has a clear description.

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Methods used in this brief

• Inside-Outside Circle