Mathematics · Year 7

Active learning ideas

Introduction to Integers

Active learning works well for introducing integers because students must physically and visually experience the shift from counting objects to understanding directed numbers. Moving bodies and handling temperature or debt scenarios make abstract concepts concrete, which reduces confusion about negative values versus positive ones.

• ACARA Content Descriptions
• AC9M7N02

• 15–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 30 min · Whole Class

Simulation Game: The Human Number Line

Create a large number line on the floor using masking tape. Students take turns acting as a 'human counter,' physically stepping forward for addition and backward for subtraction, or turning around to face the negative direction when subtracting a negative integer.

Analyze how negative numbers extend the number system beyond whole numbers.

Facilitation Tip

During the Human Number Line activity, ensure students stand far enough apart to show the relative distance between integers like -5 and 3.

What to look for

Give students a card with a number (e.g., -7, 3, 0). Ask them to write one sentence explaining what this number might represent in the real world and to draw its position on a mini number line.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Inquiry Circle
• 45 min · Small Groups

Inquiry Circle: Global Temperatures

In small groups, students research the record high and low temperatures of various cities across the Asia-Pacific region and the world. They must calculate the total temperature range for each city and present their findings on a vertical number line poster.

Compare the representation of positive and negative integers on a number line.

Facilitation Tip

In the Global Temperatures investigation, provide printed maps with marked cities so students can physically annotate temperature changes with positive and negative integers.

What to look for

Display a number line with several points labeled A, B, C, D. Ask students to write down the integer represented by each point and then to order them from least to greatest. Review answers as a class.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: The Debt Dilemma

Provide a scenario where a person has a bank balance of -$20 and receives a bill for $15. Students individually determine the new balance, discuss their reasoning with a partner to check for direction errors, and then share their strategies with the class.

Construct real-world examples where negative integers are essential for description.

Facilitation Tip

For The Debt Dilemma think-pair-share, assign roles so one student explains the debt amount while the other explains the balance after payment.

What to look for

Pose the question: 'Why do we need negative numbers in mathematics? Can you think of a situation where only positive numbers or whole numbers would not be enough to describe what is happening?' Facilitate a brief class discussion, guiding students to articulate the necessity of integers.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach integers by connecting them to lived experiences, not just rules. Use vertical number lines to show that 'lower' means 'less' in value, and avoid phrases like 'bigger negative' that reinforce misconceptions. Research shows that two-colour counters and number lines build stronger mental models than abstract algorithms alone.

Students will confidently place integers on a number line, explain their real-world meaning, and perform addition or subtraction using counters or mental models. They will also articulate why negative numbers are necessary in contexts like finance or weather.

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Watch Out for These Misconceptions

• During Simulation: The Human Number Line, watch for students who place -10 to the right of -2 because they think the larger digit means a larger value.

  Have students stand in place and ask, 'Who owes more money: someone with a $10 debt or a $2 debt?' Then adjust their positions on the number line to show -10 is to the left of -2.

• During Collaborative Investigation: Global Temperatures, watch for students who believe subtracting a negative temperature always makes it warmer.

  Use two-colour counters to model subtracting negative temperatures as 'removing cold.' Ask, 'If we have -3 degrees and remove -2 degrees of cold, what is the new temperature?'

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Methods used in this brief

• Simulation Game
• Inquiry Circle
• Think-Pair-Share