Addition and Subtraction of Integers

Active learning works for integer addition and subtraction because these operations rely on spatial reasoning and concrete modeling. Students need to see and feel the difference between positive and negative movement, which physical activities like number lines and elevators provide. Movement-based tasks build lasting intuition that paper-and-pencil drills alone cannot.

• 3rd Class
• Mathematical Explorers: Building Number and Space
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the sum and difference of two integers using a number line model.
2. Explain the relationship between adding a negative integer and subtracting a positive integer.
3. Analyze the effect of adding or subtracting zero on an integer's value.
4. Design a real-world problem that requires the addition or subtraction of integers to solve.
5. Compare the results of adding and subtracting integers with different signs.

Collaborative Problem-Solving

⏱ 30 min·Pairs

Number Line Walk: Integer Moves

Mark a large floor number line from -10 to 10. Pairs take turns calling problems like 4 + (-3) or -2 - (-5); the other walks from start to solution and states the result. Switch roles after five problems, then discuss patterns observed.

Prepare & details

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

Facilitation Tip: During the Number Line Walk, have students take turns calling out moves aloud while the whole class follows along with their fingers on their own number lines to build shared accountability.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 25 min·Whole Class

Temperature Tracker: Daily Changes

Whole class records morning temperature as starting integer. Add simulated changes like +2 or -4 throughout lesson using a shared chart. Students predict endpoints before updating, then verify with number lines.

Prepare & details

Analyze the effect of adding or subtracting zero from an integer.

Facilitation Tip: For the Temperature Tracker, assign each pair a city to track for a week, then ask them to present their data using addition and subtraction of integers to show change.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 35 min·Small Groups

Elevator Challenge: Floor Operations

Small groups use mini number lines as elevators. Draw cards with problems like start at 3, +(-2), -1; move token and record sequence. Groups share one real-world elevator story matching their path.

Prepare & details

Design a real-world scenario that requires the addition or subtraction of integers.

Facilitation Tip: In the Elevator Challenge, require each group to record their token moves on a whiteboard equation so you can see their reasoning before they announce the final floor.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 20 min·Pairs

Zero Effect Relay: Sign Rules

Pairs line up; teacher calls integer plus zero variant like 5 + 0 or -3 - 0. First student computes and tags partner who verifies on personal number line. Rotate problems to cover all rules.

Prepare & details

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

Facilitation Tip: During the Zero Effect Relay, time the race and have students reflect afterward on why zero never changes the starting value in their equations.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Teaching This Topic

Teach integer operations by pairing abstract symbols with physical movement first, then connect to real-world contexts like temperature or finance. Avoid teaching rules like 'two negatives make a positive' as a standalone chant. Instead, let students discover the pattern through repeated, guided trials with number lines or tokens. Research shows that students who generate their own rules through movement retain understanding longer than those given rules to memorize.

What to Expect

At the end of these activities, students should confidently explain integer operations using movement, signs, and real contexts. They should model equations with number lines or tokens, justify their steps aloud, and correct peers’ misapplications of sign rules. Success looks like students debating solutions in groups and adjusting their models based on feedback.

Watch Out for These Misconceptions

Common Misconception

During Number Line Walk, watch for students who assume adding a negative always makes the result smaller than any starting number.

What to Teach Instead

Pause the walk and ask the student to model -3 + (-2) on the line. Have them explain why the result is more negative, and ask the class to compare this to -3 + 2 to highlight the difference in direction.

Common Misconception

During Elevator Challenge, listen for groups that claim subtracting a negative always makes the result negative.

What to Teach Instead

Ask the group to act out -2 - (-3) using tokens, then have them discuss why the floor moves up to +1. Require them to explain their path to another group before they record the answer.

Common Misconception

During Zero Effect Relay, notice students who think adding or subtracting zero changes the starting number.

What to Teach Instead

Have the student race to confirm that zero tokens do not move the marker. Ask them to explain why zero leaves the position unchanged, and have peers verify with their own relays.

Assessment Ideas

Quick Check

After Number Line Walk, present -7 + 3 = ?. Ask students to solve it by drawing the steps on their lines, then write one sentence explaining their answer in terms of movement direction.

Discussion Prompt

After Temperature Tracker, pose: 'Is adding -5 the same as subtracting 5?' Have students pair up, use their number lines to test both operations, and prepare to share their justification with the class using their data.

Exit Ticket

After Elevator Challenge, give each student the submarine scenario: 'A submarine is at a depth of 50 meters. It ascends 20 meters.' Ask them to write the integer addition or subtraction problem and calculate the final depth.

Extensions & Scaffolding

• Challenge students to create a new scenario (e.g., scuba diving, stock market) that uses three operations with integers, then swap with a partner to solve.
• For students who struggle, provide a partially completed number line with the first move already marked and ask them to finish the sequence and write the equation.
• Deeper exploration: Ask students to compare integer addition to vector addition on a coordinate plane, discussing how direction and magnitude relate to positive and negative values.

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. On a number line, these are to the right of zero.
Negative Integer	An integer less than zero. On a number line, these are to the left of zero.
Number Line	A visual representation of numbers, including positive and negative integers, used to model addition and subtraction.