Mathematics · Year 7

Active learning ideas

Adding and Subtracting Integers

Active learning works well for adding and subtracting integers because students need to see and feel the movement of values on a number line or counters. These concrete models turn abstract rules like 'double negatives' into visible actions, making misunderstandings easier to spot and correct.

• ACARA Content Descriptions
• AC9M7N02
• AC9M7N03

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

Activity 01

• Collaborative Problem-Solving
• 25 min · Pairs

Pairs: Two-Color Counter Drills

Provide red counters for negatives and yellow for positives. Pairs take turns posing integer problems; the other models the operation by adding or removing counters, then states the result. Switch roles after five problems and discuss any sign prediction errors.

Explain why subtracting a negative integer is equivalent to adding a positive integer.

Facilitation Tip

During the Two-Color Counter Drills, circulate and ask pairs to explain their setup before and after each problem to ensure they’re modeling cancellation correctly.

What to look for

Provide students with three problems: 1) -5 + 3, 2) 7 - (-2), 3) -4 + (-6). Ask them to solve each problem using a number line and write one sentence explaining their strategy for problem 2.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 35 min · Small Groups

Small Groups: Human Number Line Challenges

Mark a floor number line from -20 to 20 with tape. Groups of four solve addition/subtraction problems by having one student start at zero and jump left or right while others predict and verify the landing spot. Rotate roles and record results on mini-whiteboards.

Predict the sign of the result when adding integers with different signs.

Facilitation Tip

For Human Number Line Challenges, assign roles like ‘marker’ and ‘timer’ to keep students engaged and accountable during the movement activities.

What to look for

Display a scenario: 'A submarine is at -50 meters. It ascends 20 meters, then descends 30 meters. What is its final depth?' Have students write the integer expression and solve it on mini-whiteboards.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 30 min · Whole Class

Whole Class: Real-World Integer Stories

Project scenarios like temperature changes or debt payments. Class votes on operation signs, then volunteers demonstrate on a shared number line. Discuss predictions as a group and adjust based on collective evidence.

Design a visual model to demonstrate the sum of two negative integers.

Facilitation Tip

In the Real-World Integer Stories, pause after each story to let students sketch their own quick number line before sharing solutions as a class.

What to look for

Pose the question: 'If you have $10 and spend $15, what is your balance? Explain how this relates to adding integers with different signs.' Facilitate a class discussion where students share their reasoning and connect it to the concept of owing money.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 20 min · Individual

Individual: Model Design Task

Students design and draw a visual model for a given problem, such as -3 + (-5), using number lines or counters. They label steps and explain the result in writing, then share one with a partner for feedback.

Explain why subtracting a negative integer is equivalent to adding a positive integer.

What to look for

Provide students with three problems: 1) -5 + 3, 2) 7 - (-2), 3) -4 + (-6). Ask them to solve each problem using a number line and write one sentence explaining their strategy for problem 2.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Experienced teachers approach this topic by prioritizing visual and tactile models before moving to abstract rules. Use number lines and counters to build intuition, then gradually shift students toward mental calculations. Avoid rushing to memorize rules—let students verbalize patterns first. Research shows that students who physically move on a number line or manipulate counters retain the concepts longer than those who only hear explanations.

Successful learning looks like students confidently explaining why subtracting a negative is the same as adding a positive, using number lines or counters to model problems, and predicting the correct sign for mixed operations without guessing. They should also be able to design their own models to represent two negative integers.

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Watch Out for These Misconceptions

• During Two-Color Counter Drills, watch for students who treat subtracting a negative counter as adding a positive counter on the same side.

  Have students verbally walk through the process: ‘When I subtract a negative counter, I remove one from the negative side, which shifts the total to the positive side.’ Encourage them to physically move the counter to the neutral pile and recount the remaining positives.

• During Human Number Line Challenges, watch for students who move left when adding a negative integer.

  Stop the group and ask them to act out the problem together: ‘If you start at 3 and add -4, which direction do you face? Walk the step together as a group and count the jumps aloud.’ Use peer modeling to rebuild the correct movement.

• During Real-World Integer Stories, watch for students who assume the sum of two negative integers is always positive.

  Pause the story and ask students to draw a quick sketch on the board. Prompt them with: ‘If you lose $3 and then lose $5 more, where are you on the number line?’ Let the class correct the misconception by rebuilding the scenario step-by-step.

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Methods used in this brief

• Collaborative Problem-Solving