Adding and Subtracting Integers

Active learning works because integer operations require visual and kinesthetic understanding of direction and magnitude. Students need to move, see, and discuss before rules feel intuitive. These activities let them experience the logic behind signs and operations before formalizing steps.

• Primary 6
• Mathematics
• 4 activities
• 30 min–45 min

Learning Objectives

1. Calculate the sum of two or more integers using number line models and established rules.
2. Calculate the difference between two integers, including subtracting negative integers, using number line models and established rules.
3. Explain the equivalence between subtracting a negative integer and adding its positive counterpart.
4. Predict the sign and approximate magnitude of the result when adding or subtracting multiple integers.
5. Construct a rule for adding integers with different signs based on observed patterns.

Ready-to-Use Activities

Stations Rotation

⏱ 35 min·Pairs

Number Line Hopscotch: Adding Integers

Draw a large number line on the floor with tape. Pairs take turns calling out problems like +3 or -2, then hop the correct distance while classmates verify with mini number lines. Discuss patterns after 10 rounds to form addition rules.

Prepare & details

Construct a rule for adding integers with different signs.

Facilitation Tip: During Number Line Hopscotch, have students call out each jump aloud to reinforce the connection between verbal steps and written symbols.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 40 min·Small Groups

Integer Chip Sort: Mixed Operations

Provide red and white chips for negatives and positives. Small groups model problems like -4 + 6 by pairing opposites, then count leftovers for the result. Extend to subtraction by removing pairs. Groups share strategies on whiteboard.

Prepare & details

Explain how subtracting a negative number is equivalent to adding a positive number.

Facilitation Tip: For Integer Chip Sort, require groups to present their final arrangement and explain the zero pairs they created before moving to mixed operations.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 30 min·Small Groups

Temperature Plunge Relay: Subtracting Negatives

Teams race to solve temperature problems on cards, like 5°C - (-3°C), using personal number lines or apps. First correct answer passes baton. Debrief equivalents like subtracting negative as adding positive.

Prepare & details

Predict the outcome of adding or subtracting multiple integers.

Facilitation Tip: In Temperature Plunge Relay, pause after each sequence to ask students to predict the next jump before revealing the correct answer.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 45 min·Pairs

Debt Dash Board Game: Multi-Step Problems

Students play in pairs with a board tracking debts and credits. Roll dice for integers, add or subtract to move, predicting outcomes first. Winner explains final position with rules.

Prepare & details

Construct a rule for adding integers with different signs.

Facilitation Tip: Set a 5-minute timer for Debt Dash Board Game to keep the energy high and push students to apply rules under time pressure.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

Start with hands-on movement to build intuition before introducing formal rules. Avoid teaching mnemonics like 'keep, change, flip' without visual proof, as they can confuse students later. Research shows that physical models and collaborative discussions help pupils internalize the meaning behind signs and operations more deeply than abstract explanations alone.

What to Expect

Successful learning looks like students using number lines or chips to justify their answers with clear, rule-based reasoning. They should explain why a negative sign appears using movement or pairing, not just recall a procedure. Watch for students who can generalize patterns across different problems in mixed operations.

Watch Out for These Misconceptions

Common Misconception

During Temperature Plunge Relay, watch for students who assume subtracting a negative always results in a negative value.

What to Teach Instead

Have them act out -(-3) on the relay course: standing at -2, subtract a -3 by moving right three spaces to +1, then ask the group to compare this result to the original rule they stated.

Common Misconception

During Integer Chip Sort, watch for students who add a positive and negative by simply combining magnitudes and keeping the negative sign.

What to Teach Instead

Ask them to model 5 + (-3) with chips, pairing three positives and three negatives to see two positives remain, then repeat with -4 + 2 to reinforce the pattern.

Common Misconception

During Number Line Hopscotch, watch for students who confuse the order of operations when multiple signs appear.

What to Teach Instead

Give them a sequence like 3 + (-2) - (-1) and have them jump step-by-step, describing each move aloud before writing the equation to clarify the sequence.

Assessment Ideas

Quick Check

After Number Line Hopscotch, present the following problems: 1. 5 + (-3) = ? 2. -4 - 2 = ? 3. -7 + (-1) = ? 4. 6 - (-2) = ? Ask students to solve each problem and then write one sentence explaining the rule they used for problem 4.

Discussion Prompt

During Temperature Plunge Relay, ask students: 'Imagine you are a diver. You start at sea level (0 meters). You descend 10 meters, then ascend 5 meters, then descend 8 meters. What is your final depth?' Have students explain their steps and the integer operations used to find the answer.

Exit Ticket

After Debt Dash Board Game, give each student a card with two integer addition or subtraction problems, for example: '-9 + 4 = ?' and '3 - 7 = ?'. On the back, ask them to write a rule for adding integers with different signs.

Extensions & Scaffolding

• Challenge: Ask students to create three new problems where subtracting a negative equals adding its positive, then trade with a partner to solve.
• Scaffolding: For students struggling with direction, provide pre-labeled number lines with 0 in the center and let them trace each step with a finger before writing the equation.
• Deeper exploration: Have students research real-world contexts where negative numbers appear, such as elevations or temperatures, and present one example with an integer equation to the class.

Key Vocabulary

Integer	A whole number that can be positive, negative, or zero. Examples include -3, 0, and 5.
Positive Integer	An integer greater than zero. These are the numbers we commonly know as counting numbers.
Negative Integer	An integer less than zero. These numbers are represented with a minus sign.
Number Line	A visual representation of numbers, with integers arranged in order. It helps model addition and subtraction by moving left or right.