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.

• Year 7
• Mathematics
• 3 activities
• 15 min–45 min

Learning Objectives

1. Identify integers on a number line, distinguishing between positive, negative, and zero.
2. Compare and order sets of integers, justifying their positions relative to zero.
3. Construct real-world scenarios that require the use of negative integers for accurate representation.
4. Explain the concept of 'opposite numbers' in the context of integers and their position on a number line.

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.

Prepare & details

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.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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?'

Assessment Ideas

Exit Ticket

After Simulation: The Human Number Line, give each student a card with an integer. Ask them to write one real-world example and draw it on a mini number line as they exit the room.

Quick Check

During Collaborative Investigation: Global Temperatures, display a number line with points labeled A (-4), B (2), C (-1), D (0). Ask students to write the integers in order from least to greatest and hold up their answers to check for understanding.

Discussion Prompt

After Think-Pair-Share: The Debt Dilemma, ask students to share why only positive numbers would not be enough to describe a bank account balance after a withdrawal. Facilitate a class discussion to capture their reasoning.

Extensions & Scaffolding

• Challenge students to create a real-world scenario involving two negative integers and one positive integer, then solve an addition or subtraction problem using the number line or counters.
• Scaffolding: Provide a partially completed number line with labeled points for students to fill in missing integers between -10 and 10.
• Deeper exploration: Ask students to research sea level changes in millimeters over a year and represent the data using integers on a line graph.

Key Vocabulary

Integer	A whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples include -3, 0, and 5.
Positive Integer	An integer greater than zero. These are the whole numbers we commonly use for counting.
Negative Integer	An integer less than zero. These numbers represent values below zero on a number line.
Number Line	A visual representation of numbers, typically a straight line with markings for integers. It helps in comparing and ordering numbers.
Opposite Numbers	Two numbers that are the same distance from zero on the number line but in opposite directions. For example, 5 and -5 are opposite numbers.