Mathematics · 7th Grade

Active learning ideas

Integers and Absolute Value

Active learning helps students grasp the abstract nature of integers by making their movement on the number line visible and concrete. When students physically step along a number line or manipulate chips, they build an intuitive sense of how positive and negative values combine, which is essential for mastering this foundational topic.

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

• 15–30 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Simulation Game
• 30 min · Whole Class

Simulation Game: Human Number Line

Create a large number line on the floor. Students stand at a starting integer and 'walk' the addition or subtraction of another integer. For subtraction, they must physically turn around to face the opposite direction before moving, modeling the 'adding the opposite' rule.

Differentiate between natural numbers, whole numbers, and integers.

Facilitation Tip

During the Human Number Line, have students call out their step counts aloud to reinforce the connection between movement and arithmetic operations.

What to look for

Provide students with a list of numbers: -8, 5, 0, -3, 12. Ask them to: 1. Identify which numbers are integers. 2. Write the absolute value of -8 and 5. 3. Order the numbers from least to greatest.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 02

• Inquiry Circle
• 25 min · Pairs

Inquiry Circle: Integer Chips Battle

Pairs use two-colored counters (one color for positive, one for negative) to model expressions. They practice 'zeroing out' pairs to find the final sum. They then create their own 'puzzles' for other pairs to solve using only the chips.

Analyze how absolute value represents distance from zero on a number line.

Facilitation Tip

For Integer Chips Battle, remind students to record each move as an equation to connect the visual with symbolic representation.

What to look for

Draw a number line from -10 to 10. Ask students to place five integer cards on the line. Then, pose questions like: 'Which number is farthest from zero?' or 'Which two numbers have the same absolute value?'

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 03

• Think-Pair-Share
• 15 min · Pairs

Think-Pair-Share: Real World Negatives

Students are given scenarios like 'a bird 20 feet up and a fish 5 feet down.' They independently write an expression to find the distance between them, pair up to compare if they used addition or subtraction, and share why 'distance' always results in a positive value.

Construct a number line to represent and order a given set of integers.

Facilitation Tip

In the Think-Pair-Share, circulate and listen for students to use terms like 'debt,' 'opposite,' or 'distance from zero' when explaining their reasoning.

What to look for

Pose the scenario: 'A submarine is at -50 meters, and then it ascends 20 meters. What is its new depth? How does absolute value help us understand the submarine's position relative to sea level?' Facilitate a brief class discussion.

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

A few notes on teaching this unit

Teach this topic by starting with the number line as a visual anchor, then transitioning to integer chips to model the concept of additive inverses. Avoid rushing to rules like 'two negatives make a positive'; instead, let students discover patterns through guided exploration. Research shows that students who connect movement and visual models to symbolic operations retain these concepts longer.

Successful learning looks like students confidently using number lines and absolute value to explain why adding a negative moves left and subtracting a negative moves right. They should also justify their answers by referring to the magnitude and sign of the numbers involved.

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Watch Out for These Misconceptions

• During Human Number Line, watch for students who assume subtraction always moves them left on the number line, regardless of the sign of the subtrahend.

  Pause the simulation after a few steps and ask the student to explain why subtracting a negative number (e.g., 5 - (-3)) moves them to the right. Have them act it out again, emphasizing the direction of movement based on the sign of the number being subtracted.

• During Integer Chips Battle, watch for students who think the first number in an equation always determines the sign of the result.

  After teams record their final chip combinations, ask them to compare the absolute values of their totals. Guide them to notice that the team with the greater absolute value determines the sign, and have them adjust their equations accordingly.

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Methods used in this brief

• Simulation Game
• Inquiry Circle
• Think-Pair-Share