Mathematics · 2nd Year

Active learning ideas

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.

• NCCA Curriculum Specifications
• NCCA: Primary - Algebra
• NCCA: Primary - Communicating and expressing

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

Activity 01

• Hundred Languages
• 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.

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.

What to look for

Provide students with a collection of manipulatives (e.g., colored blocks, buttons). Ask them to create a repeating pattern using two different attributes, like color and shape. Observe their creations and ask them to state the rule aloud, for example, 'Red square, blue circle, red square, blue circle.'

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Hundred Languages
• 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.

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.

What to look for

Have students work in pairs to create a growing pattern. After they have designed it, ask: 'How many items are in your first step? How many in your second? What is the rule that makes your pattern grow?' Then, prompt them to compare their pattern to their partner's: 'What is the same about your patterns? What is different?'

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Hundred Languages
• 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.

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.

What to look for

Students create a visual representation of their repeating or growing pattern on paper, including a written rule. They then exchange their work with a classmate. The classmate's task is to try and replicate the pattern based on the rule and then provide one specific piece of feedback, such as 'Your rule clearly explains how to make the next step.'

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Hundred Languages
• 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.

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

What to look for

Provide students with a collection of manipulatives (e.g., colored blocks, buttons). Ask them to create a repeating pattern using two different attributes, like color and shape. Observe their creations and ask them to state the rule aloud, for example, 'Red square, blue circle, red square, blue circle.'

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Hundred Languages