Mathematics · Year 7

Active learning ideas

Multiplying and Dividing Integers

Active learning helps students move beyond memorizing rules by letting them physically model integer operations. Working with counters, number lines, and real-world scenarios makes abstract sign rules visible and discussable for all learners.

• ACARA Content Descriptions
• AC9M7N02
• AC9M7N03

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Stations Rotation
• 35 min · Small Groups

Number Line Relay: Multiplication Rules

Mark a floor number line from -20 to 20 with tape. In small groups, one student starts at zero and jumps according to the multiplier (e.g., -2 × 3: jump left 2, three times). Group records the endpoint and sign pattern. Rotate roles for five problems.

Justify why the product of two negative integers is positive.

Facilitation Tip

During Number Line Relay, place masking tape number lines on the floor so students can physically step through multiplication as repeated jumps.

What to look for

Provide students with three problems: 1. Calculate -7 x 8. 2. Calculate -45 ÷ -5. 3. Explain in one sentence why -3 x -4 = 12.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 25 min · Pairs

Two-Colour Counters: Sign Exploration

Provide red chips for negatives, yellow for positives. Pairs model products like (-2) × 3 by making pairs of chips and removing opposites. Discuss why (-2) × (-3) leaves positives. Record rules in journals.

Analyze how integer multiplication relates to repeated addition or subtraction.

Facilitation Tip

For Two-Colour Counters, have students pair negative counters to model cancellation before recording results in a sign chart.

What to look for

Display a number line. Ask students to show how repeated addition of -3, five times, results in -15. Then, ask them to write the corresponding multiplication sentence.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 40 min · Small Groups

Debt Division Cards: Real-World Problems

Distribute scenario cards (e.g., share -24 debt among 4 people). Small groups solve, draw models, and create their own problems. Share one per group with class justifications.

Construct a real-world problem that requires division of negative integers.

Facilitation Tip

Use Debt Division Cards with play money so students can physically exchange bills to see how division reverses multiplication in real contexts.

What to look for

Pose the question: 'Imagine you owe three friends $10 each. How can you represent this debt using integers? If you then found $30, how would you represent paying them all back using division?'

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 30 min · Whole Class

Integer Pattern Tables: Whole Class Build

Project a partially filled multiplication table for integers -5 to 5. Students suggest entries in turns, justifying with repeated addition. Class votes and corrects using number lines.

Justify why the product of two negative integers is positive.

Facilitation Tip

In Integer Pattern Tables, ask students to pause after each row to predict the next sign before completing calculations.

What to look for

Provide students with three problems: 1. Calculate -7 x 8. 2. Calculate -45 ÷ -5. 3. Explain in one sentence why -3 x -4 = 12.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach this topic by starting with concrete models before moving to abstract rules. Avoid rushing to the sign rules—instead, let students discover patterns through repeated addition and subtraction. Research shows that students who build their own rules through modeling retain concepts longer and make fewer sign errors. Emphasize peer discussion to resolve contradictions during modeling phases.

Students will confidently apply sign rules to multiply and divide integers, explain why rules work using models, and connect operations to real-life contexts like debt and temperature changes. Look for clear explanations and correct calculations in both individual and group work.

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Watch Out for These Misconceptions

• During Two-Colour Counters: Sign Exploration, watch for students who pair negative counters but then miscount the remaining counters as negative.

  Have students circle each pair of negative counters and label the leftover counters with a different-colored marker before recording the total sign. Ask them to explain why the leftover positives make sense in a debt scenario.

• During Number Line Relay: Multiplication Rules, watch for students who reverse the direction of jumps when multiplying by a negative number.

  Pause the relay and have students act out the jumps together, starting at zero and stepping backward for negative multipliers. Ask them to compare -3 x 4 with 3 x -4 to see the sign flip in action.

• During Integer Pattern Tables: Whole Class Build, watch for students who fill in the table without noticing the pattern in the signs.

  Have students pause after each row to predict the next sign based on the previous row. Ask them to explain their prediction using the counters or number lines they’ve used in other activities.

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Methods used in this brief

• Stations Rotation