Mathematics · Year 1

Active learning ideas

Growing Patterns

Active learning works well for growing patterns because students need to see and build the steady increase themselves, not just hear about it. When children manipulate objects, the jump from 3 to 5 blocks or from 1 to 2 beads becomes clear in their hands before it appears on paper.

ACARA Content DescriptionsAC9M1A01
15–30 minPairs → Whole Class4 activities

Activity 01

Placemat Activity20 min · Pairs

Pairs: Block Chain Builder

Partners take turns adding to a chain of unifix cubes following a rule like 'add two each time.' They describe the rule after five steps and predict the tenth step. Switch roles and compare predictions.

Differentiate between a pattern that repeats and one that grows.

Facilitation TipDuring Block Chain Builder, circulate with a chart that lists possible growth rules so you can nudge pairs who are stuck on ‘What comes next?’

What to look forProvide students with a visual growing pattern (e.g., squares arranged in increasing rows). Ask them to draw the next two steps and write the growth rule in a sentence, such as 'This pattern adds one square each time'.

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Activity 02

Placemat Activity30 min · Small Groups

Small Groups: Shape Garden Growth

Each group gets pattern cards with growing flower shapes. They copy the first three terms on grid paper, identify the rule, and draw the next two. Discuss as a class what rules they found.

Analyze the 'growth rule' in a numerical or visual pattern.

Facilitation TipShape Garden Growth runs best when you limit each group to two colors and one shape so the growth in quantity stands out against the constant visual elements.

What to look forPresent students with a numerical growing pattern like 2, 4, 6, 8. Ask: 'What is the rule for this pattern?' and 'What would be the next number in the pattern?' Observe student responses for understanding of the growth rule and extension.

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Activity 03

Placemat Activity25 min · Whole Class

Whole Class: Human Number Line

Students line up to form a growing pattern by adding one more child each round, such as groups of 2, 3, 4. The class calls out the rule and predicts the next group size before adding.

Construct the next two steps in a given growing pattern.

Facilitation TipFor the Human Number Line, place a large number line on the floor and have students physically step forward by the agreed amount to feel the increase in their bodies.

What to look forShow students two patterns: one repeating (e.g., circle, square, circle, square) and one growing (e.g., 1 block, 2 blocks, 3 blocks). Ask: 'How are these patterns different?' and 'Which one is a growing pattern, and how do you know?'

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Activity 04

Placemat Activity15 min · Individual

Individual: Bead Necklace Extension

Students string beads in a growing pattern provided on cards, like 1 bead, 2 beads, 4 beads. They continue independently and write the rule in words.

Differentiate between a pattern that repeats and one that grows.

What to look forProvide students with a visual growing pattern (e.g., squares arranged in increasing rows). Ask them to draw the next two steps and write the growth rule in a sentence, such as 'This pattern adds one square each time'.

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Templates

Templates that pair with these Mathematics activities

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A few notes on teaching this unit

Start with repeating patterns for contrast, then introduce growing patterns using the same vocabulary: ‘This one adds two more each time.’ Avoid calling any pattern ‘easy’ or ‘hard’; instead, praise clear descriptions of the rule. Research shows that when students articulate the rule themselves, their transfer to new contexts improves.

Successful learning looks like students describing the rule aloud, building or drawing the next two steps, and using the same rule when the materials change. Expect them to explain why the pattern grows rather than repeats, and to compare a growing pattern to a repeating one in their own words.

Watch Out for These Misconceptions

  • During Block Chain Builder, watch for students who loop back to the first shape instead of adding more.

    Hand them a second strip of paper labeled ‘Step 1, Step 2, Step 3’ and ask them to rebuild the chain exactly before drawing the next two steps.

  • During Shape Garden Growth, watch for students who change the amount added each step without noticing.

    Have them rebuild the garden with color-coded sticks and ask them to count the new pieces only; the consistency will become visible.

  • During Bead Necklace Extension, watch for students who treat the visual picture as a repeating pattern.

    Cover all but the first two beads with paper, then slowly reveal each new bead while saying ‘Now we have one more than before,’ to highlight growth.

Methods used in this brief

More in Patterns and Algebraic Logic

Repeating Patterns

Recognizing the core of a repeating pattern and predicting what comes next in various forms (visual, auditory, movement).

2 methodologies

Skip Counting by 2s, 5s, and 10s

Using patterns in sequences of 2s, 5s, and 10s to build multiplication readiness and number fluency.

2 methodologies

Missing Elements in Patterns

Using logic to find missing numbers or shapes in a sequence, applying pattern rules.

2 methodologies