Mathematics · Year 7

Active learning ideas

Identifying and Describing Patterns

Active learning helps students move beyond noticing what comes next in a pattern to understanding why it happens. Hands-on tasks like building matchstick shapes or sketching tile designs let students see the structure of patterns, making abstract rules concrete and memorable.

• ACARA Content Descriptions
• AC9M7A01

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

Activity 01

• Inquiry Circle
• 45 min · Small Groups

Inquiry Circle: Matchstick Patterns

Students use matchsticks (or toothpicks) to build a growing geometric pattern. They record the number of sticks for each step in a table and work together to find a rule that predicts the number of sticks needed for the 100th step.

Analyze how different patterns can be represented visually and numerically.

Facilitation Tip

During Matchstick Patterns, ask each group to sketch their Stage 4 shape on the board before comparing their counts to uncover inconsistencies in their recursive rules.

What to look for

Present students with a visual pattern (e.g., growing squares made of dots). Ask them to draw the next two stages and write a sentence describing how the pattern grows. Then, provide a numerical sequence like 3, 6, 9, 12 and ask for the next two numbers and the rule in words.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Pattern Detectives

Provide students with a sequence of numbers. Individually, they write a rule in words, then pair up to translate that rule into an algebraic expression (e.g., 'double the number and add one' becomes 2n + 1).

Construct a rule in words for a given sequence of numbers.

Facilitation Tip

During Pattern Detectives, circulate and listen for students using phrases like 'each time' versus 'for any stage', which signals their shift from recursive to functional thinking.

What to look for

Give each student a card with a different numerical sequence (e.g., 10, 8, 6, 4 or 5, 10, 15, 20). Ask them to write the next two terms and the rule in words. Also, ask them to identify if the pattern is increasing or decreasing.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Gallery Walk
• 35 min · Small Groups

Gallery Walk: Visual to Variable

Groups create a visual pattern on a poster but leave the algebraic rule hidden under a flap. Other groups rotate through, try to determine the rule, and write their guess on a sticky note before checking the answer.

Differentiate between increasing and decreasing patterns.

Facilitation Tip

During Gallery Walk, provide sticky notes for peers to leave comments on posters, asking questions like 'How did you find the 50th term?' to push students to articulate their methods.

What to look for

Display two sequences: one increasing (e.g., 2, 4, 6, 8) and one decreasing (e.g., 15, 12, 9, 6). Ask students: 'How are these patterns different? What words can we use to describe the rule for each sequence? Can you create your own increasing and decreasing pattern?'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Start with visual patterns to ground the concept in concrete examples before moving to abstract rules. Avoid rushing to algebra; instead, let students grapple with inefficiency of recursive methods to motivate the need for a general rule. Research shows that students who discover patterns themselves retain understanding longer than those who are told the rule upfront.

Students will describe patterns using both words and symbols, moving from recursive descriptions ('add 3 each time') to functional rules ('3n + 1'). They will connect visual growth to numerical sequences and justify their reasoning in small groups and written work.

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Watch Out for These Misconceptions

• During Collaborative Investigation: Matchstick Patterns, watch for students who count matchsticks only for the next stage instead of generalizing a rule for any stage.

  Ask each group to calculate the number of matchsticks for Stage 100. When they realize counting one-by-one is impractical, prompt them to find a direct relationship between the stage number and matchstick count.

• During Think-Pair-Share: Pattern Detectives, watch for students who treat the variable 'n' as a fixed unknown rather than a placeholder for any position in the sequence.

  Have students physically stand in a line labeled with stage numbers. As they move forward, ask them to describe their output value, emphasizing that 'n' represents their position, not a hidden number.

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Methods used in this brief

• Inquiry Circle
• Think-Pair-Share
• Gallery Walk