Mathematics · Year 3 · Data and Chance in Action · Term 4

Growing Patterns

Describing the rule for a growing pattern (e.g., add 2 each time) and predicting subsequent terms.

• ACARA Content Descriptions
• AC9M3A01

About This Topic

Growing patterns introduce Year 3 students to sequences that increase by a fixed amount each step, such as 4, 7, 10, 13 where the rule is 'add 3'. Students describe these rules using everyday language or symbols like +2, predict subsequent terms, and create their own patterns. This content matches AC9M3A01 in the Australian Curriculum, strengthening number fluency and laying groundwork for algebraic thinking within the Data and Chance unit.

Students connect growing patterns to real contexts, like rows of seats expanding by two each time or plant heights increasing steadily. They explain rules to justify predictions for the next three terms and design patterns with constant growth, which sharpens logical reasoning and precise communication. These skills support data analysis by showing how patterns appear in collected measurements.

Active learning suits this topic well. Hands-on tools like counters or beads let students build and extend patterns physically, revealing the rule through touch and sight. Group challenges to predict and verify terms spark discussions that clarify thinking and correct errors on the spot.

Key Questions

1. Explain the rule that governs a given growing pattern.
2. Design a growing pattern that increases by a constant amount each step.
3. Predict the next three terms in a growing pattern based on its rule.

Learning Objectives

• Explain the constant difference that defines a given growing pattern.
• Predict the next three terms in a growing pattern by applying its identified rule.
• Design a growing pattern with a constant increase, specifying its rule.
• Identify the rule for a growing pattern presented visually or numerically.

Before You Start

Skip Counting

Why: Students need to be proficient at counting by a constant amount (e.g., by 2s, 5s, 10s) to easily identify and extend growing patterns.

Addition Facts

Why: Understanding how to add a constant number repeatedly is fundamental to identifying and applying the rule in growing patterns.

Key Vocabulary

Growing Pattern	A sequence of numbers or objects that increases by the same amount each step.
Rule	The instruction that describes how to get from one step in a pattern to the next, often involving addition.
Term	Each individual number or object in a sequence or pattern.
Predict	To state what you think will happen next in a pattern based on the established rule.

Watch Out for These Misconceptions

Common Misconception

Growing patterns always double or multiply.

What to Teach Instead

Many grow by simple addition, like +2 each time. Building with manipulatives shows the steady increase step by step. Group sharing lets students compare rules and see addition patterns match their constructions.

Common Misconception

The rule changes partway through a pattern.

What to Teach Instead

Rules stay constant for growing patterns. Predicting with physical models tests consistency over many terms. Peer verification in pairs helps students spot and correct assumed changes through evidence.

Common Misconception

Growing patterns repeat shapes without numbers.

What to Teach Instead

These focus on numerical growth by a constant. Visualizing with counters links shapes to numbers clearly. Collaborative drawings reinforce that numbers drive the predictable increase.

Active Learning Ideas

Manipulative Build: Linking Cube Patterns

Provide unifix cubes or linking blocks. Students start with a given first term and rule, such as 3 then add 2, to build the first four terms. They predict and add the next three terms, then explain the rule to their group. Groups share one pattern with the class for predictions.

30 min·Small Groups

Human Number Line: Growing Steps

Mark a floor number line. Select students to stand at positions representing pattern terms, like 5, 8, 11. The class calls out the rule and directs the next three positions. Switch roles so all students participate in moving and predicting.

25 min·Whole Class

Prediction Cards: Pattern Challenges

Prepare cards showing partial patterns, such as 1, 4, __, __. In pairs, students write the rule, fill gaps, and predict three more terms. Pairs swap cards to check predictions and discuss rule differences.

20 min·Pairs

Design Station: Custom Pattern Art

At stations with beads, paper, or tiles, students design a growing pattern artwork that increases by a constant, like adding one shape per step. Label the rule and next terms. Rotate to extend a peer's pattern.

35 min·Individual

Real-World Connections

• Construction workers use growing patterns to calculate the number of bricks needed for walls that increase in height by a set number of courses with each layer.
• Gardeners might plan plant spacing in rows where each subsequent row has one more plant than the last, creating a predictable increase in the total number of plants needed for a garden bed.

Assessment Ideas

Quick Check

Present students with a pattern like 5, 10, 15, 20. Ask: 'What is the rule for this pattern?' and 'What are the next two numbers in the pattern?'

Exit Ticket

Give each student a card with a different growing pattern (e.g., add 4, add 1). Ask them to write down the rule and the next three terms for their specific pattern.

Discussion Prompt

Show a visual pattern of dots increasing by 3 each time. Ask: 'How can you describe the rule in words?' and 'If this pattern continued for 5 more steps, how many dots would there be in total?'

Frequently Asked Questions

What are growing patterns in Year 3 Australian Curriculum maths?

Growing patterns are number sequences that increase by a fixed amount each step, like 3, 6, 9, 12 with 'add 3'. Per AC9M3A01, students describe rules, predict terms, and create patterns. This builds number sense for data units and future algebra by emphasizing consistent change.

How do you teach students to explain rules for growing patterns?

Model rules with words and symbols, such as 'start at 5, add 4'. Use visuals like arrow diagrams. Have students build patterns with blocks, then state rules to partners. Practice predicting next terms reinforces clear explanations through trial and justification.

How can active learning help students master growing patterns?

Active approaches make rules tangible: students stack cubes to see +2 growth or line up for human patterns to feel steps. Group predictions and verifications build confidence via discussion. These methods turn abstract rules into observable actions, reducing errors and deepening understanding of constant increase.

What activities predict next terms in growing patterns Year 3?

Use prediction cards for pairs to fill sequences and justify rules. Human number lines let the class extend patterns physically. Cube builds challenge groups to forecast and test three more terms. These keep engagement high while practicing AC9M3A01 skills in context.