Adding and Subtracting Integers

Active learning helps students connect abstract integer rules to concrete movement and visual models. Students who physically step on number lines or manipulate counters build stronger mental images of positive and negative direction. This kinesthetic link reduces reliance on memorized rules and deepens conceptual understanding.

• 5th Class
• Mathematical Mastery: Exploring Patterns and Logic
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the sum and difference of integers using concrete models and number lines.
2. Analyze the effect of subtracting a negative integer on the value of an expression.
3. Identify and explain common errors made when performing operations with integers.
4. Construct a number line model to demonstrate the addition of two integers, including negative numbers.
5. Compare the results of adding a positive integer versus adding a negative integer to a given number.

Stations Rotation

⏱ 25 min·Pairs

Pairs: Number Line Walks

Create a large floor number line marked from -10 to 10 with tape. Partners take turns: one states a starting point and operation, like 'start at -5, subtract -2'; the other walks it out and states the end. Switch roles after five problems, then record three examples on mini-whiteboards.

Prepare & details

Analyze the effect of subtracting a negative number on the overall value.

Facilitation Tip: In Pairs: Number Line Walks, have students take turns calling out moves and modeling them on the floor line to build shared understanding.

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

⏱ 35 min·Small Groups

Small Groups: Two-Color Counter Challenges

Provide each group with red and black counters. Assign problems like 3 + (-4): students make zero pairs first, then add leftovers. For subtraction, model as adding opposites. Groups race to solve five cards, then share one solution with the class.

Prepare & details

Construct a number line model to demonstrate the sum of -3 and 5.

Facilitation Tip: In Small Groups: Two-Color Counter Challenges, circulate to prompt groups when counters and written equations don’t match.

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·Whole Class

Whole Class: Integer Operation Relay

Divide class into teams lined up. Teacher calls an operation; first student from each team runs to board, writes starting number, next adds the move with arrow notation. Continue until complete. Discuss results as a class.

Prepare & details

Evaluate the common errors made when adding and subtracting integers.

Facilitation Tip: During Whole Class: Integer Operation Relay, keep the pace brisk to hold attention but pause after mistakes so the team corrects together.

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

⏱ 20 min·Individual

Individual: Error Fix Journals

Give students five common error examples, like -2 - (-3) = -5. They draw number lines or counters to correct each, explain the mistake in writing, then create their own tricky problem.

Prepare & details

Analyze the effect of subtracting a negative number on the overall value.

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

Teach by having students act out operations first, then record the steps. Avoid rushing to symbols before concrete experiences. Research shows that students who move along number lines before writing equations make fewer sign errors. Always link the physical action to the abstract rule.

What to Expect

Successful learning shows when students explain why -3 - (-5) equals 2, not just calculate the answer. They use number lines or counters to justify steps and spot patterns across problems. Peer conversations reveal clear reasoning and corrected misconceptions.

Watch Out for These Misconceptions

Common Misconception

During Pairs: Number Line Walks, watch for students who move left when subtracting a negative, treating it like subtracting a positive.

What to Teach Instead

Ask the pair to re-enact -3 - (-5) step by step on the floor line, saying each move aloud and testing if the landing point makes sense as a larger number.

Common Misconception

During Small Groups: Two-Color Counter Challenges, watch for students who treat two negatives as positive because of whole-number habits.

What to Teach Instead

Have the group recount the red and black counters, then rephrase the equation as repeated addition of negatives to reveal the combined negativity.

Common Misconception

During Whole Class: Integer Operation Relay, watch for students who assume the first number’s sign determines the answer’s sign without checking the operation.

What to Teach Instead

Pause the relay at -1 + 4 and ask the team to model it together on the board, then compare to 1 + (-4) to highlight that the operation, not the first number, drives the direction.

Assessment Ideas

Exit Ticket

After Pairs: Number Line Walks, give students -7 + 4 to calculate and -12 - (-8) to explain. Collect answers to check if they used number line movement correctly and justified the sign of the result.

Quick Check

During Small Groups: Two-Color Counter Challenges, present a problem like -5 + (-3) and ask students to show the counter arrangement on their desks, then write the sum. Scan for correct placement of red counters and accurate totals.

Discussion Prompt

After Whole Class: Integer Operation Relay, pose the prompt 'Is subtracting a negative number always the same as adding a positive number?' Have students use their relay models or counters to justify their answers in pairs before sharing with the class.

Extensions & Scaffolding

• Challenge: Ask students to write a word problem for -8 - (-12) and model it on a number line for a partner to solve.
• Scaffolding: Provide pre-drawn number lines with only the starting point marked for students who need clearer visual anchors.
• Deeper: Introduce triple-digit integers like -125 + 89 and ask students to justify their steps using both number lines and counters.

Key Vocabulary

Integer	A whole number, including positive numbers, negative numbers, and zero. Examples include -5, 0, and 12.
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 arranged in order. It is used to model addition and subtraction of integers by moving left or right.
Opposite	A number that is the same distance from zero as another number but in the opposite direction. The opposite of 5 is -5, and the opposite of -3 is 3.