Subtracting Integers

Active learning works for subtracting integers because this concept demands students move beyond memorizing rules to truly visualizing movement on the number line. When students physically act out subtraction or manipulate cards, they connect abstract symbols to concrete experiences, reducing confusion between operation and sign.

• 7th Grade
• Mathematics
• 4 activities
• 15 min–25 min

Learning Objectives

1. Calculate the difference between two integers, including negative integers, using the additive inverse.
2. Explain the equivalence of subtracting a negative integer and adding a positive integer, referencing a number line model.
3. Analyze the relationship between the distance between two integers on a number line and the absolute value of their difference.
4. Construct a word problem requiring the subtraction of negative integers that models a real-world scenario.

Think-Pair-Share

⏱ 20 min·Whole Class

Kinesthetic Number Line: Walk the Subtraction

Create a large number line on the floor with tape. One student is the "starting number" and another holds a card showing the integer being subtracted. The class decides: do we face forward or backward? Do we add the opposite? Students physically step to the answer, then verify using the rule a - b = a + (-b).

Prepare & details

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

Facilitation Tip: During the Kinesthetic Number Line activity, have students verbally narrate their steps as they move to reinforce the connection between subtraction and adding the opposite.

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

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: Why Does Subtracting a Negative Add?

Present the statement: "5 - (-3) = 8" and ask students to individually write an explanation in words, then pair with a partner to compare explanations. Partners must produce one combined explanation that uses a real-world analogy, such as removing a debt. Selected pairs share with the class.

Prepare & details

Analyze how the distance between two integers on a number line relates to their difference.

Facilitation Tip: In the Think-Pair-Share, circulate to listen for misconceptions about subtracting negatives and address them immediately in small groups.

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

Think-Pair-Share

⏱ 25 min·Small Groups

Collaborative Card Sort: Equivalent Expressions

Groups receive a set of cards showing subtraction expressions (e.g., -4 - 7) and equivalent addition expressions (e.g., -4 + (-7)). Students match pairs, then order results on a number line from least to greatest. Groups compare their sorted lines and resolve any disagreements through discussion.

Prepare & details

Construct a real-world problem that requires subtracting negative integers.

Facilitation Tip: For the Collaborative Card Sort, provide a reference sheet with examples to scaffold students who struggle to see the equivalence between subtraction and addition expressions.

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

Think-Pair-Share

⏱ 20 min·Pairs

Problem Construction: Real-World Challenges

Students individually write a word problem that requires subtracting a negative integer, such as one involving elevation changes or account balances. Partners swap problems, solve each other's, and provide written feedback on whether the context makes mathematical sense.

Prepare & details

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

Facilitation Tip: During Problem Construction, ask students to include a written explanation of how their real-world scenario connects to the mathematical operation they chose.

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

Approach this topic by starting with number lines to build intuition, then move to symbolic representations once students grasp the movement. Avoid rushing to the rule 'change the sign and add' without first establishing why it works. Research shows that students who can visualize the number line retain the concept longer than those who rely solely on memorized steps.

What to Expect

Successful learning looks like students confidently explaining why subtracting an integer is the same as adding its opposite and correctly modeling this on a number line. They should also recognize and correct common sign errors when working with expressions like -4 - (-3).

Watch Out for These Misconceptions

Common Misconception

During the Kinesthetic Number Line activity, watch for students who still believe subtracting always makes a number smaller.

What to Teach Instead

Have students annotate their number line walks with real-world examples, such as removing a debt (subtracting a negative) to increase a bank balance. Use these annotations in a gallery walk so students see the pattern across different scenarios.

Common Misconception

During the Collaborative Card Sort, watch for students who confuse the operation sign with the integer's sign.

What to Teach Instead

Ask students to color-code the operation symbol (e.g., a red minus sign) and the integer's sign (e.g., a blue negative) on their cards. Then, have partners narrate each step aloud, pointing to the colors as they explain, before writing the final expression.

Common Misconception

During the Think-Pair-Share, watch for students who think the distance between two numbers is always the larger minus the smaller.

What to Teach Instead

Provide a number line template where students plot both integers and physically measure the gap between them with a ruler. Ask them to calculate the distance using absolute value and compare it to their initial assumption.

Assessment Ideas

Exit Ticket

After the Collaborative Card Sort, provide students with the expression 8 - (-3). Ask them to rewrite this as an addition problem and calculate the answer. On the back, have them explain why 8 - (-3) is the same as 8 + 3.

Quick Check

During the Problem Construction activity, present students with three subtraction problems such as -5 - 2, 4 - (-6), and -7 - (-1). Ask them to solve each and indicate on their paper whether the operation is equivalent to adding a positive or adding a negative number.

Discussion Prompt

After the Kinesthetic Number Line activity, pose this question: 'Imagine you are on a number line at -4. If you subtract -5, where do you end up? Explain your reasoning using the concept of adding the opposite and the direction of movement on the number line.' Use student responses to assess their understanding of subtracting negatives.

Extensions & Scaffolding

• Challenge: Ask students to create a mini-lesson video explaining why subtracting a negative is the same as adding a positive, using a real-world example they design.
• Scaffolding: Provide a partially completed number line template where students fill in the missing steps for expressions like 5 - (-2).
• Deeper exploration: Have students research how subtracting integers applies in contexts like temperature changes or financial transactions, then present their findings to the class.

Key Vocabulary

Integer	A whole number (not a fractional number) that can be positive, negative, or zero. Examples include -3, 0, and 5.
Additive Inverse	A number that, when added to a given number, results in zero. For example, the additive inverse of 5 is -5, and the additive inverse of -3 is 3.
Opposite	A number that is the same distance from zero on the number line but in the opposite direction. The opposite of a number is its additive inverse.
Number Line	A visual representation of numbers as points on a straight line, used to model operations and relationships between numbers.