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.

• 7th Grade
• Mathematics
• 3 activities
• 15 min–30 min

Learning Objectives

1. Classify numbers as natural, whole, or integers.
2. Compare and order a given set of integers on a number line.
3. Calculate the absolute value of any integer.
4. Explain the relationship between an integer and its absolute value as distance from zero.
5. Construct a number line to represent and order a given set of integers.

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.

Prepare & details

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.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

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

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.

Prepare & details

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.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

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.

Prepare & details

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.

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

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After the Human Number Line, 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.

Quick Check

During Integer Chips Battle, draw a quick number line on the board and ask teams to place their final chip totals on it. Then pose questions like: 'Which number is farthest from zero?' or 'Which two numbers have the same absolute value?' Listen for students to explain their placements using absolute value.

Discussion Prompt

After Think-Pair-Share, pose the scenario: 'A submarine is at -50 meters, and then it ascends 20 meters. What is its new depth?' Have pairs discuss how absolute value helps them understand the submarine's position relative to sea level, then facilitate a brief class discussion to clarify any lingering misconceptions.

Extensions & Scaffolding

• Challenge students to create their own real-world scenarios involving integer operations and present them to the class.
• For students who struggle, provide partially completed number lines or pre-sorted integer chips to scaffold their first few attempts.
• Deeper exploration: Ask students to research historical contexts where negative numbers were first used, such as in ancient China or India, and discuss how these ideas evolved over time.

Key Vocabulary

Integer	A whole number or its opposite, including zero. Examples are -3, 0, 5.
Natural Numbers	The counting numbers starting from 1. Examples are 1, 2, 3, 4.
Whole Numbers	The counting numbers including zero. Examples are 0, 1, 2, 3.
Absolute Value	The distance of a number from zero on the number line, always a non-negative value. It is written with two vertical bars, for example, |–5|.
Additive Inverse	A number that, when added to another number, results in zero. For example, the additive inverse of 7 is -7.