Operations with Integers: Addition and Subtraction

Active learning works for integer operations because students need to physically move and see the direction of change to grasp how positives and negatives interact. When students walk on a floor number line or manipulate counters, they build intuitive understanding that rules alone cannot provide. Movement and touch turn abstract signs into concrete experiences that stick.

• 4th Class
• Mastering Mathematical Thinking: 4th Class
• 4 activities
• 25 min–40 min

Learning Objectives

1. Calculate the sum and difference of two integers using a number line.
2. Explain the rule for adding a negative integer to another integer.
3. Differentiate between subtracting a positive integer and subtracting a negative integer.
4. Construct a word problem involving the addition or subtraction of integers.
5. Analyze the result of adding or subtracting integers in a given real-world context.

Experiential Learning

⏱ 30 min·Pairs

Floor Number Line: Operation Walks

Tape a number line across the floor from -10 to 10. Pairs start at zero; call problems like -3 + 5 or 4 - (-2). Students walk steps, land, and explain moves to partners. Debrief as a class on patterns noticed.

Prepare & details

Explain how a number line can be used to visualise addition and subtraction of integers.

Facilitation Tip: During Operation Walks, have pairs call out each step aloud to reinforce the connection between movement and operation symbols.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 25 min·Small Groups

Two-Colour Counters: Model and Solve

Provide red counters for negatives, black for positives. In small groups, students model equations like -4 + (-3) by placing counters and making zero pairs. They record solutions and share one group strategy with the class.

Prepare & details

Differentiate between adding a negative number and subtracting a positive number.

Facilitation Tip: For Two-Colour Counters, insist students verbalise each step: 'We see three red counters, so we remove zero pairs by adding three yellows.'

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 35 min·Whole Class

Temperature Scenarios: Line Plots

Give cards with weather changes, like 'drops 2 degrees from -1'. Whole class plots starting points on personal number lines, solves, and plots endpoints. Discuss real Irish weather data to connect operations.

Prepare & details

Construct a real-world scenario that involves adding or subtracting negative numbers.

Facilitation Tip: In Temperature Scenarios, ask students to plot daily changes on a shared line graph to make patterns visible to the whole class.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 40 min·Small Groups

Debt Cards: Real-World Match

Small groups get scenario cards like 'owe €5 more'. They match to operations, solve with chips or lines, and create their own card. Groups present one to the class for verification.

Prepare & details

Explain how a number line can be used to visualise addition and subtraction of integers.

Facilitation Tip: With Debt Cards, have students explain their matching process to a peer before recording the equation.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Teaching This Topic

Experienced teachers approach integer operations by prioritising visual and kinaesthetic models before abstract rules. They avoid rushing to the algorithm and instead let students discover patterns through movement and manipulation. Research shows that students who construct meaning from models rather than memorise rules retain understanding longer and apply it more flexibly.

What to Expect

By the end of these activities, students will confidently explain why adding a negative moves left on a number line and why subtracting a negative turns into addition. They will also use models to justify their answers and apply rules accurately in real-world contexts like temperature changes and bank balances.

Watch Out for These Misconceptions

Common Misconception

During Operation Walks, watch for students who move right after adding a negative because they default to positive addition habits.

What to Teach Instead

Pause the walk and ask the pair to re-read the operation aloud: 'Add negative 3 means move left three spaces.' Have them trace the path with their finger on the line to correct the movement.

Common Misconception

During Two-Colour Counters, watch for students who remove red counters without adding yellow zero pairs when subtracting a negative.

What to Teach Instead

Ask the student to recount their steps using the phrase 'removing a negative is like adding a positive.' Demonstrate by adding zero pairs first, then removing the red counters to show the positive result.

Common Misconception

During Operation Walks, watch for students who start their walks only from positive numbers and ignore the negative side of the line.

What to Teach Instead

Have the student begin at zero and move left first to demonstrate symmetry. Ask them to explain how moving left from zero feels different from moving right, then repeat the original problem.

Assessment Ideas

Exit Ticket

After Operation Walks, ask students to draw a number line and show the steps for calculating -4 + 6. Collect their diagrams to check if they moved right for the positive and left for the negative correctly.

Quick Check

During Temperature Scenarios, have students plot a 5-degree drop followed by a 7-degree rise on a shared line. Ask each student to write the integer expression that matches the final temperature relative to the start.

Discussion Prompt

After Debt Cards, pose this question: 'If you owe €12 and then someone cancels €8 of your debt, what happens to your balance?' Facilitate a discussion comparing subtraction of a negative to adding a positive, using the cards as visual evidence.

Extensions & Scaffolding

• Challenge students to create their own real-world scenario cards that require adding or subtracting integers, then trade with peers to solve.
• Scaffolding: Provide pre-printed number lines with marked intervals and counters for students to focus on the operation rather than drawing.
• Deeper exploration: Introduce multi-step problems where students combine temperature changes over several days or calculate total balance changes over a week.

Key Vocabulary

Integer	A whole number that can be positive, negative, or zero. Examples include -3, 0, and 5.
Number Line	A visual representation of numbers where positive numbers increase to the right and negative numbers decrease to the left. It helps show addition and subtraction.
Additive Inverse	A number that, when added to another number, results in zero. For example, the additive inverse of 5 is -5.
Opposite Integers	Two integers that are the same distance from zero on the number line but in opposite directions. For example, 7 and -7 are opposite integers.