Mathematics · 7th Grade

Active learning ideas

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.

• Common Core State Standards
• CCSS.Math.Content.7.NS.A.1b

• 15–25 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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).

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.

What to look for

Provide students with the expression 8 - (-3). Ask them to rewrite this expression as an addition problem and then calculate the final answer. On the back, ask them to briefly explain why 8 - (-3) is the same as 8 + 3.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• 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.

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.

What to look for

Present students with three subtraction problems involving integers, such as -5 - 2, 4 - (-6), and -7 - (-1). Have students solve each problem and indicate on their paper whether the operation is equivalent to adding a positive or adding a negative number.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• 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.

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.

What to look for

Pose the 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.'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• 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.

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.

What to look for

Provide students with the expression 8 - (-3). Ask them to rewrite this expression as an addition problem and then calculate the final answer. On the back, ask them to briefly explain why 8 - (-3) is the same as 8 + 3.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

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.

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).

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Watch Out for These Misconceptions

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

  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.

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

  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.

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

  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.

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Methods used in this brief

• Think-Pair-Share