Creating Our Own Patterns

Active learning transforms abstract pattern concepts into tangible experiences. When students handle materials like beads or blocks, they build spatial reasoning and logical connections that static worksheets cannot provide. These hands-on activities encourage collaboration, which strengthens both pattern design and verbal explanation skills.

• 2nd Year
• Foundations of Mathematical Thinking
• 4 activities
• 20 min–45 min

Learning Objectives

1. Design repeating patterns using at least two different attributes (e.g., color, shape, size).
2. Describe the rule of a created repeating pattern using precise mathematical language.
3. Compare and contrast their own created patterns with those of their peers, identifying similarities and differences in rules and attributes.
4. Create a growing pattern where the number of elements increases by a consistent amount.
5. Explain the rule governing a growing pattern, articulating the consistent change between steps.

Project-Based Learning

⏱ 30 min·Pairs

Pairs: Shape Swap Patterns

Partners take turns creating a repeating pattern with two shapes on a strip of paper, then describe the rule without showing it. The listener recreates the pattern and checks accuracy. Switch roles after 10 minutes.

Prepare & details

Can you create your own repeating pattern using two different shapes?

Facilitation Tip: During Shape Swap Patterns, circulate and listen for students to name their rules aloud before swapping, ensuring clarity before they trade designs.

Setup: Flexible workspace with access to materials and technology

Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials

• Apply
• Analyze
• Evaluate
• Create
• Self-Management
• Relationship Skills
• Decision-Making

Project-Based Learning

⏱ 45 min·Small Groups

Small Groups: Growing Bead Chains

Each group uses string and beads to build a growing pattern, starting with one bead type and adding more each time per the rule. Groups extend each other's chains and present the final rule to the class.

Prepare & details

How is your pattern the same or different from your partner's?

Facilitation Tip: For Growing Bead Chains, ask guiding questions like, 'How did you decide to add two beads this time?' to push students to verbalize their growing rule.

Setup: Flexible workspace with access to materials and technology

Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials

• Apply
• Analyze
• Evaluate
• Create
• Self-Management
• Relationship Skills
• Decision-Making

Project-Based Learning

⏱ 25 min·Whole Class

Whole Class: Pattern Prediction Game

Display student patterns on the board. Class predicts the next three elements as a group, with creator confirming the rule. Vote on predictions to build consensus.

Prepare & details

What rule did you use to make your pattern?

Facilitation Tip: In the Pattern Prediction Game, pause after each round to have students explain their reasoning before revealing the next step.

Setup: Flexible workspace with access to materials and technology

Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials

• Apply
• Analyze
• Evaluate
• Create
• Self-Management
• Relationship Skills
• Decision-Making

Project-Based Learning

⏱ 20 min·Individual

Individual: Material Mix Patterns

Students select from a tray of objects to create one repeating and one growing pattern on paper. Label the rule and share one with a neighbor for feedback.

Prepare & details

Can you create your own repeating pattern using two different shapes?

Setup: Flexible workspace with access to materials and technology

Materials: Project brief with driving question, Planning template and timeline, Rubric with milestones, Presentation materials

• Apply
• Analyze
• Evaluate
• Create
• Self-Management
• Relationship Skills
• Decision-Making

Teaching This Topic

Teach patterns by starting with simple repeating structures before introducing growth, as reversing this order often leads to confusion. Use consistent language like 'core unit' for repeating patterns and 'step size' for growing ones to avoid mixing concepts. Research shows that students grasp patterns best when they create, describe, and refine their ideas in real time with immediate peer interaction.

What to Expect

Successful learning shows when students can create clear patterns, articulate their rules, and predict next steps without hesitation. They should confidently explain their reasoning and adjust their designs based on feedback from peers. Observing students describe and replicate patterns reveals their true understanding of the underlying structure.

Watch Out for These Misconceptions

Common Misconception

During Shape Swap Patterns, watch for students who assume all patterns must repeat the same sequence forever.

What to Teach Instead

Have partners review each other's swaps and point to the core unit, then challenge them to add one more element to their partner’s pattern to introduce growth.

Common Misconception

During Material Mix Patterns, watch for students who treat any arrangement as a valid pattern.

What to Teach Instead

Ask pairs to describe their pattern to each other using precise language like 'after each red square, there is a blue triangle,' which highlights the need for a clear rule.

Common Misconception

During Growing Bead Chains, watch for students who confuse growing patterns with repeating ones.

What to Teach Instead

Ask students to build their chains while saying the step numbers aloud, such as 'one bead, two beads, three beads,' to emphasize the increasing quantity rather than a fixed sequence.

Assessment Ideas

Quick Check

After Material Mix Patterns, provide manipulatives and ask students to create a repeating pattern using two attributes (e.g., color and shape). Observe their creations and listen for them to state the rule aloud, such as 'yellow circle, green square, yellow circle, green square.'

Discussion Prompt

During Growing Bead Chains, have students share their patterns in pairs. Ask: 'How many beads are in your first step? How many in your second? What is the rule that makes your pattern grow?' Then prompt them to compare patterns: 'What is the same about your patterns? What is different?'

Peer Assessment

After Shape Swap Patterns, have students exchange their written rules and try to replicate their partner’s pattern. The classmate provides one specific piece of feedback, such as 'Your rule clearly explains how to make the next step.'

Extensions & Scaffolding

• Challenge: Ask students to create a pattern that combines both repeating and growing elements, such as a core unit that itself grows each cycle.
• Scaffolding: Provide a partially completed pattern for students to extend, using one attribute (e.g., color) so they focus on the rule first.
• Deeper exploration: Have students document their pattern on graph paper, then write a short story where the pattern represents a repeating event in their story's world.

Key Vocabulary

Repeating Pattern	A pattern that follows a sequence that repeats itself exactly, such as ABAB or ABCABC.
Growing Pattern	A pattern where the number of elements increases or decreases by a consistent amount at each step.
Attribute	A characteristic or feature of an object, such as its color, shape, or size, used to create patterns.
Rule	The specific instruction or logic that defines how a pattern is made or extended.