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.

• Year 4
• Mathematics
• 4 activities
• 25 min–45 min

Learning Objectives

1. Analyze the additive or multiplicative rule governing a given increasing number pattern.
2. Predict the next three terms in a complex increasing number sequence with at least three steps in the rule.
3. Construct a new increasing number pattern with a clear additive or multiplicative rule and describe its rule accurately.
4. Compare and contrast two different increasing number patterns based on their rules and rates of growth.

Ready-to-Use Activities

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

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.

Prepare & details

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.

Setup: Charts posted on walls with space for groups to stand

Materials: Large chart paper (one per prompt), Markers (different color per group), Timer

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Pattern Prediction Relay, collect the final rule strips from each pair and check that their next two terms match the stated rule; flag any mismatches for follow-up.

Exit Ticket

After Cube Pattern Builds, collect the labelled photos and sticky notes; look for accurate rules and matching tower heights to confirm understanding of additive versus multiplicative growth.

Discussion Prompt

During Number Pattern Hunt, circulate and listen to how students explain which pattern grows faster; use Pattern A and Pattern B examples to prompt reasoning about common differences and multipliers in whole-class share time.

Extensions & Scaffolding

• Challenge students who finish early to invent a pattern that mixes two different rules (e.g., add 2, then multiply by 3) and write a short explanation of the combined effect.
• Scaffolding: Provide a partially completed grid with some numbers missing and a choice of two rules so students can test their ideas before committing.
• Deeper exploration: Ask pairs to create a pattern that grows faster than a peer’s pattern and explain why it outpaces the other using terms like ‘multiplier’ or ‘common difference’ in their reasoning.

Key Vocabulary

Pattern Rule	The specific instruction that explains how to get from one number to the next in a sequence. This can involve adding, subtracting, multiplying, or dividing.
Increasing Pattern	A sequence of numbers where each subsequent term is larger than the previous term. This growth is typically due to addition or multiplication.
Additive Rule	A pattern rule where a constant number is added to each term to find the next term. For example, add 5 each time.
Multiplicative Rule	A pattern rule where each term is multiplied by a constant number to find the next term. For example, multiply by 3 each time.
Term	An individual number within a number pattern or sequence.