Mathematics · Year 3

Active learning ideas

Number Patterns and Rules

Active learning lets students physically manipulate numbers and rules, making abstract sequences concrete. When children move, discuss, and test patterns together, they build shared language to describe how numbers change and why. This hands-on approach moves pattern recognition from guesswork to clear, repeatable thinking.

• ACARA Content Descriptions
• AC9M3A01

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Outdoor Investigation Session
• 25 min · Pairs

Pairs Activity: Pattern Pairs Challenge

Partners draw a starting number and rule card, then build the sequence using linking cubes up to the 10th term. They swap cards, predict the next three numbers, and check partner's work. Discuss why the rule fits or fails.

Analyze the rule for a number pattern that involves both addition and subtraction.

Facilitation Tip

During Pattern Pairs Challenge, circulate and listen for students to verbalize the rule before writing it down, ensuring the spoken language matches the written form.

What to look for

Present students with a sequence like 15, 12, 9, 6. Ask them to write down the rule and predict the next two numbers in the sequence. Check for correct identification of the subtraction rule and accurate continuation.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 02

• Outdoor Investigation Session
• 30 min · Small Groups

Small Groups: Sequence Relay Race

Divide into teams. One student writes the first three terms of a pattern, passes to next who adds two more using the group rule, continues around. Teams race to 12 terms, then present rule to class.

Construct a number pattern that starts with 5 and increases by 3 each time.

Facilitation Tip

In Sequence Relay Race, stand at the finish line to watch students’ final terms and listen to their team’s rule explanation before they record it.

What to look for

Give each student a card with a starting number and a rule (e.g., 'Start at 7, add 4'). Ask them to write the first four numbers of the sequence and then predict the 6th number. Collect these to assess understanding of rule application and prediction.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 03

• Outdoor Investigation Session
• 35 min · Whole Class

Whole Class: Interactive Pattern Wall

Project a growing pattern on board. Students call out next terms or rules, vote on predictions, add sticky notes with their sequences. Teacher reveals correct rule, discusses errors as class.

Predict the 7th number in a sequence that decreases by 4 each time.

Facilitation Tip

At the Interactive Pattern Wall, model how to test a rule by pointing to terms and asking the class to confirm or challenge the pattern’s consistency.

What to look for

Display two number patterns on the board, one with only addition (e.g., 3, 6, 9) and one with mixed addition/subtraction (e.g., 10, 13, 10, 13). Ask students to describe the rule for each pattern and explain why one is simpler to analyze than the other.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

Activity 04

• Outdoor Investigation Session
• 20 min · Individual

Individual: Personal Pattern Journal

Students choose start number and operation, create 10-term sequence, write rule, predict 15th term. Draw real-life example, like plant growth. Share one with neighbor for verification.

Analyze the rule for a number pattern that involves both addition and subtraction.

Facilitation Tip

Have each student in Personal Pattern Journal sketch one concrete object (like cubes or counters) next to each number to anchor the abstract sequence in visual form.

What to look for

Present students with a sequence like 15, 12, 9, 6. Ask them to write down the rule and predict the next two numbers in the sequence. Check for correct identification of the subtraction rule and accurate continuation.

• Remember
• Understand
• Analyze
• Social Awareness
• Self-Awareness
• Decision-Making

A few notes on teaching this unit

Teach this topic by moving from concrete to abstract, using physical objects first and then transitioning to symbols. Avoid telling students the rule too quickly; instead, let them test hunches using materials like bead strings or cubes. Research shows that students who construct rules themselves retain understanding longer and apply them more flexibly than those who memorize steps. Encourage students to verbalize their ideas even when unsure, normalizing mistakes as part of the learning process.

Students will confidently state the rule for any sequence, predict terms both forward and backward, and create their own patterns with accurate rules. They will explain their reasoning to peers and adjust ideas when presented with counterexamples, showing flexible number sense.

---

Watch Out for These Misconceptions

• During Pattern Pairs Challenge, watch for students who assume every sequence increases.

  Give each pair one increasing and one decreasing sequence using bead strings. Ask them to describe how the bead strings change in length and to write rules that match both types of patterns.

• During Pattern Pairs Challenge, watch for students who think the rule is based only on the difference between the first two numbers.

  Have students test their rule starting at the third term by covering the first two numbers with paper. If the rule changes, they must revise it, reinforcing that the rule applies consistently along the whole sequence.

• During Sequence Relay Race, watch for students who resist predicting backward terms.

  Ask teams to extend their sequence backward from the last term before writing the rule. Provide a second set of cards with reversed operations to prompt flexible thinking about subtraction and division as reverse operations of addition and multiplication.

---

Methods used in this brief

• Outdoor Investigation Session