Introduction

Opposites and Absolute Value is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.

In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with opposites and absolute value.

What Is Opposites and Absolute Value?

Opposites and Absolute Value means choosing a model, naming what each number means, and explaining the strategy.

The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.

Understanding Opposites and Absolute Value

Before solving, students should slow down and decide what each number, shape, unit, or label represents.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.

Visual Models

Visual Model 1

Question: The opposite of the opposite of \(-5\) is:

Visual Model 1

  • A. \(5\)
  • B. \(10\)
  • C. \(0\)
  • D. \(-5\)

Why it works: The opposite of \(-5\) is \(5\). The opposite of \(5\) is \(-5\). So the opposite of the opposite returns to the original number.

Answer: \(-5\)

Visual Model 2

Question: Which pair of numbers are opposites?

Visual Model 2

  • A. \(3\) and \(\frac{1}{3}\)
  • B. \(-4\) and \(4\)
  • C. \(6\) and \(12\)
  • D. \(-2\) and \(-2\)

Why it works: Opposites are numbers equidistant from zero on opposite sides of the number line. \(-4\) and \(4\) are opposites.

Answer: \(-4\) and \(4\)

Worked Examples

Example 1

Question: On a number line, which number is farthest from zero?

Example 1

  • A. \(|-3|\)
  • B. \(|5|\)
  • C. \(|-2|\)
  • D. \(|1|\)
  1. We compare absolute values: \(|-3|=3\), \(|5|=5\), \(|-2|=2\), \(|1|=1\).
  2. The largest is \(5\).

Answer: \(|5|\)

Example 2

Question: A submarine is \(650\) feet below sea level. Which expression represents this depth using absolute value?

Example 2

  • A. \(|-650|\)
  • B. \(|650|\)
  • C. \(-650\)
  • D. \(650\)
  1. Below sea level is represented by a negative number: \(-650\).
  2. The absolute value \(|-650|=650\) represents the magnitude of the depth.

Answer: \(|-650|\)

Example 3

Question: A bank account has a balance of \(-$45\). What does this represent in terms of absolute value?

Example 3

  • A. The account has \($45\) owed
  • B. The account has \($45\) deposited
  • C. The account has \($45\) in savings
  • D. The account is zero
  1. The absolute value \(|-45|=45\) represents the magnitude.
  2. A negative balance means a debt or overdraft of \($45\).

Answer: The account has \($45\) owed

Real-World Word Problems

Problem 1

Question: A stock price decreased by \($18\). How much did it decrease in absolute value?

  • A. \(-18\) dollars
  • B. \(0\) dollars
  • C. \(36\) dollars
  • D. \(18\) dollars

Why it works: A decrease of \($18\) is represented as \(-18\). The absolute value \(|-18|=18\) dollars represents the magnitude of the change.

Answer: \(18\) dollars

Problem 2

Question: If a diver is at \(-45\) feet relative to sea level, what is \(|-45|\)?

  • A. \(-45\) feet
  • B. \(90\) feet
  • C. \(0\) feet
  • D. \(45\) feet

Why it works: The absolute value \(|-45|=45\) feet represents the magnitude of depth below sea level.

Answer: \(45\) feet

Common Mistakes

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.

Strategy Tips

  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.

Practice Questions

Question 1

What is the value of \(|-12|\)?

  • A. \(12\)
  • B. \(0\)
  • C. \(-12\)
  • D. \(24\)

Question 2

Which number is the opposite of \(7\)?

  • A. \(-7\)
  • B. \(\frac{1}{7}\)
  • C. \(0\)
  • D. \(7\)

Question 3

What is \(|-8|\)?

  • A. \(-8\)
  • B. \(8\)
  • C. \(0\)
  • D. \(16\)

Question 4

What is the opposite of \(-15\)?

  • A. \(15\)
  • B. \(-15\)
  • C. \(0\)
  • D. \(\frac{1}{15}\)

Question 5

Find \(|0|\).

  • A. \(0\)
  • B. \(-1\)
  • C. \(1\)
  • D. Undefined

Question 6

Which expression with a negative number equals \(10\)?

  • A. \(|-10|\)
  • B. The opposite of \(10\)
  • C. \(|10|\)
  • D. \(-10\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(12\)

The absolute value of a number is its distance from zero on a number line, always non-negative. \(|-12|=12\).

Question 2

Answer: \(-7\)

The opposite of a positive number is its negative. The opposite of \(7\) is \(-7\), equidistant from zero on the other side.

Question 3

Answer: \(8\)

Absolute value measures distance from zero. Distance is always positive or zero, so \(|-8|=8\).

Question 4

Answer: \(15\)

The opposite of a negative number is its positive version. The opposite of \(-15\) is \(15\).

Question 5

Answer: \(0\)

The absolute value of zero is zero. Zero is its own distance from zero on the number line.

Question 6

Answer: \(|-10|\)

\(|-10|=10\) because absolute value is distance from zero.

Timed practice quizzes

Related Quizzes

After studying Opposites and Absolute Value, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.

Summary

Opposites and Absolute Value becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.