Mathematics · Year 4

Active learning ideas

Investigating Increasing Number Patterns

Active, hands-on tasks help Year 4 students notice how repeated addition or multiplication changes a sequence. When children build, move, and talk about patterns, they connect abstract rules to concrete growth they can see and feel, which strengthens their ability to predict and explain.

• ACARA Content Descriptions
• AC9M4A01

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Carousel Brainstorm
• 30 min · Pairs

Pairs: Pattern Prediction Relay

Pairs take turns predicting the next three terms in a given sequence, writing them on mini whiteboards before passing to their partner for verification. Switch sequences every two minutes, focusing first on additive then multiplicative patterns. End with pairs creating and sharing one original pattern.

Analyze the rule governing a given increasing number pattern.

Facilitation Tip

During Pattern Prediction Relay, stand at the finish line with answer strips so pairs immediately check their next term against the correct rule.

What to look for

Present students with three different number patterns on a worksheet (e.g., 5, 10, 15, 20; 2, 4, 8, 16; 1, 3, 9, 27). Ask them to write the rule for each pattern and predict the next two terms for each.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 02

• Carousel Brainstorm
• 45 min · Small Groups

Small Groups: Cube Pattern Builds

Provide linking cubes for groups to build additive patterns (e.g., add 4 cubes each step) and multiplicative ones (double the cubes). Groups record terms, sketch the pattern, and describe rules on chart paper. Rotate materials to try peers' patterns.

Predict the next terms in a complex number sequence.

Facilitation Tip

In Cube Pattern Builds, ask each group to photograph their finished tower and label the add or multiply rule on a sticky note before sharing.

What to look for

Give each student a card with a sequence like 3, 9, 27, ___, ___. Ask them to write the rule used to create the pattern and then fill in the missing two terms. On the back, they should create their own increasing pattern with an additive rule and write its rule.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 03

• Carousel Brainstorm
• 35 min · Whole Class

Whole Class: Number Pattern Hunt

Display sequences around the room; students circulate, noting the rule for each and predicting two more terms on sticky notes. Gather as a class to vote on predictions and reveal correct extensions, discussing variations.

Construct a new increasing number pattern and describe its rule.

Facilitation Tip

Start the Number Pattern Hunt by modelling how to trace a sequence with your finger while saying the rule aloud so students hear the connection between movement and operation.

What to look for

Pose two patterns: Pattern A: 4, 8, 12, 16... and Pattern B: 4, 8, 16, 32... Ask students: 'Which pattern grows faster? How do you know?' Encourage them to explain their reasoning using the pattern rules.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

Activity 04

• Carousel Brainstorm
• 25 min · Individual

Individual: Pattern Creator Cards

Students draw five cards with starting numbers and operations (add 2, multiply by 3), then generate sequences on worksheets. They swap with a neighbour to predict and check the next terms.

Analyze the rule governing a given increasing number pattern.

Facilitation Tip

Hand Pattern Creator Cards to early finishers with a blank grid to design a new pattern for a partner to solve after your next lesson.

What to look for

Present students with three different number patterns on a worksheet (e.g., 5, 10, 15, 20; 2, 4, 8, 16; 1, 3, 9, 27). Ask them to write the rule for each pattern and predict the next two terms for each.

• Remember
• Understand
• Analyze
• Relationship Skills
• Social Awareness

A few notes on teaching this unit

Teach this topic by letting students experience the difference between additive and multiplicative growth firsthand rather than naming rules too soon. Use manipulatives to build sequences so children notice how adding the same amount feels different from multiplying by the same amount. Avoid rushing to formal notation; instead, focus on spoken explanations that students can later connect to symbols.

Students will confidently state the rule behind a pattern, use it to extend the sequence, and justify their next terms. They will also compare patterns and explain why some grow faster than others using clear language about the operation and starting amount.

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Watch Out for These Misconceptions

• During Pattern Prediction Relay, watch for students who extend any sequence by adding 1 regardless of the starter pattern.

  Hand them the cube chain for that pattern and ask them to rebuild the first five cubes, counting aloud as they add the correct amount each time—this physical check reveals the true step size.

• During Cube Pattern Builds, watch for students who assume every multiplicative pattern is ‘just doubling’ and miss triples or larger factors.

  Challenge them to build a 2, 6, 18, 54 sequence with cubes, forcing them to test multiplication by 3 rather than defaulting to doubling.

• During Number Pattern Hunt, watch for students who claim the rule changes halfway through a pattern.

  Have them walk the full visual path of the pattern with their finger while you ask, ‘Does the step size stay the same all the way?’ and prompt them to verify before inventing a new rule.

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Methods used in this brief

• Carousel Brainstorm