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.

• Year 7
• Mathematics
• 3 activities
• 20 min–45 min

Learning Objectives

1. Identify visual and numerical patterns in sequences.
2. Describe identified patterns using clear, concise language.
3. Construct a rule in words to represent a given numerical sequence.
4. Differentiate between increasing and decreasing numerical patterns.
5. Analyze how visual patterns can be translated into numerical sequences.

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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).

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

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.

Prepare & details

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.

Setup: Wall space or tables arranged around room perimeter

Materials: Large paper/poster boards, Markers, Sticky notes for feedback

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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.

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Collaborative Investigation: Matchstick Patterns, ask students to present their rule for the 100th stage and explain how the visual pattern supports their equation. Note whether they use recursive or functional language.

Exit Ticket

After Think-Pair-Share: Pattern Detectives, collect students’ cards with their sequence rules. Check if they describe the pattern in terms of the position (e.g., 'multiply stage number by 4') rather than just the change (e.g., 'it goes up by 4').

Discussion Prompt

During Gallery Walk: Visual to Variable, display a mix of increasing and decreasing patterns on the walls. Ask students to identify which patterns have rules written as 'add' versus 'subtract' and justify their choices in pairs.

Extensions & Scaffolding

• Challenge: Ask students to create their own matchstick pattern where the rule involves two operations (e.g., multiply by 2 then add 1) and predict the 20th stage.
• Scaffolding: Provide a partially completed table for students to fill in, with some values pre-calculated to help them see the relationship between stage number and matchsticks.
• Deeper: Introduce a non-linear pattern (e.g., triangular numbers) and ask students to compare its growth to the linear patterns they’ve studied.

Key Vocabulary

Pattern	A sequence of numbers or shapes that repeat or follow a specific rule.
Sequence	An ordered set of numbers or shapes that follow a specific rule or pattern.
Rule	The specific instruction or relationship that determines how each term in a sequence is generated from the previous term.
Term	Each individual number or shape within a sequence.