Mathematics · Year 1 · Patterns and Algebraic Logic · Term 3

Growing Patterns

Identifying the rule of a growing pattern and extending it, understanding how elements increase or decrease.

• ACARA Content Descriptions
• AC9M1A01

About This Topic

Growing patterns show sequences where the number of elements increases or decreases by a consistent amount each step, such as a chain of blocks that adds two more each time: three blocks, five blocks, seven blocks. Year 1 students learn to spot the difference between repeating patterns, like red-blue-red-blue, and growing ones. They describe the rule, such as 'add three,' and draw or build the next two terms. This aligns with AC9M1A01, where students recognise, describe and continue everyday patterns.

In the Patterns and Algebraic Logic unit, this topic strengthens number sense and prediction skills. Students explore visual patterns with shapes or objects alongside simple numerical ones like 1, 3, 5, 7. These activities foster logical reasoning, a foundation for algebra, and connect to real-life examples like planting seeds in rows that grow longer each week.

Active learning suits growing patterns because students manipulate concrete materials to test rules themselves. Building patterns with linking cubes or beads lets them see and feel the growth, correct errors through trial, and explain their thinking to peers, which solidifies understanding and builds confidence in abstract concepts.

Key Questions

1. Differentiate between a pattern that repeats and one that grows.
2. Analyze the 'growth rule' in a numerical or visual pattern.
3. Construct the next two steps in a given growing pattern.

Learning Objectives

• Identify the growth rule in a given visual or numerical growing pattern.
• Compare and contrast repeating patterns with growing patterns.
• Construct the next two steps of a growing pattern based on its identified rule.
• Explain the rule of a growing pattern using clear mathematical language.

Before You Start

Repeating Patterns

Why: Students need to have experience recognizing and extending patterns to differentiate between repeating and growing sequences.

Counting and Number Recognition

Why: Understanding how numbers change and the concept of addition is fundamental to identifying and applying a growth rule.

Key Vocabulary

Growing Pattern	A sequence where the number of items or the value increases or decreases by a consistent amount at each step.
Repeating Pattern	A sequence where a specific unit or set of items is repeated over and over again.
Growth Rule	The specific instruction that describes how the pattern changes from one step to the next, for example, 'add 2' or 'take away 1'.
Term	A single element or step within a pattern sequence.

Watch Out for These Misconceptions

Common Misconception

All patterns just repeat the same sequence.

What to Teach Instead

Students often expect growth patterns to loop back, like ABAB. Hands-on building shows steady increase instead. Pair discussions help them articulate why it grows and compare to repeating examples.

Common Misconception

The growth amount changes randomly each step.

What to Teach Instead

Children may add varying numbers without seeing the rule. Concrete manipulatives reveal consistency when they rebuild steps. Group challenges to match a partner's pattern reinforce rule-finding.

Common Misconception

Growing patterns only work with numbers, not shapes.

What to Teach Instead

Visual patterns confuse some as 'pictures.' Using shapes in stations lets students transfer rules across types. Peer teaching clarifies the shared logic of growth.

Active Learning Ideas

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.

20 min·Pairs

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.

30 min·Small Groups

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.

25 min·Whole Class

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.

15 min·Individual

Real-World Connections

• Construction workers use growing patterns when laying bricks or tiles, where each row might increase by a set number of bricks to create a specific design or angle.
• Gardeners observe growing patterns in plant development, such as a sunflower stalk adding a consistent number of leaves or a row of vegetables extending longer each week.

Assessment Ideas

Exit Ticket

Provide 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'.

Quick Check

Present 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.

Discussion Prompt

Show 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?'

Frequently Asked Questions

How to teach growing patterns in Year 1 Australian Curriculum?

Start with concrete visuals like block towers that add one each time. Use AC9M1A01 to guide describing rules and extending two steps. Daily routines, such as calendar patterns growing by days, embed practice. Progress from copying to creating patterns independently.

What are examples of growing patterns for Year 1?

Simple additions work best: 2,4,6,8 (add 2) or triangle shapes: 1, then 3, then 6 (add next row). Real-life ties include stairs with increasing steps or apple slices doubling. Always pair with repeating patterns for contrast.

How can active learning help students understand growing patterns?

Manipulatives like cubes or beads make rules visible and testable. Students build, predict, and verify in pairs, which corrects misconceptions through action. Whole-class human patterns engage kinesthetically, while discussions build language for rules, leading to deeper retention than worksheets alone.

Common mistakes in growing patterns Year 1?

Mixing repeating and growing, or irregular growth. Address with side-by-side charts and hands-on trials. Rules stated simply, like 'add three stars,' prevent overload. Regular low-stakes checks ensure early correction.