Introduction

Adding Integers is an important Grade 7 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 adding integers.

What Is Adding Integers?

Adding Integers means using place value, operations, and equations to reason accurately with numbers.

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 Adding Integers

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: Which number line correctly shows \(-3 + 7\)?

Visual Model 1

Why it works: Start at \(-3\) and move \(7\) units to the right to reach \(4\). Options B, C, and D either move in the wrong direction or start at the wrong point.

Answer: Number line A

Visual Model 2

Question: A chip model shows \(-2 + (-3)\). Which diagram is correct?

Visual Model 2

Why it works: For \(-2 + (-3)\), we combine \(2\) negative chips with \(3\) negative chips for a total of \(5\) negative chips, representing \(-5\). Option A shows this correctly.

Answer: Two negative chips and three negative chips

Worked Examples

Example 1

Question: A thermometer starts at \(20 ° \text{F}\). After adding \(-12 ° \text{F}\), which temperature is reached? Which shows the result of \(20 + (-12)\)?

Example 1

  • A. \(20 ° \text{F}\)
  • B. \(-20 ° \text{F}\)
  • C. \(-4 ° \text{F}\)
  • D. \(8 ° \text{F}\)
  1. \(20 + (-12) = 8\).
  2. Starting at 20° and decreasing by 12° gives 8°.

Answer: \(8 ° \text{F}\)

Example 2

Question: A student computed \(-7 + 4\) and got \(-11\). What error did the student make?

Example 2

  • A. Added the absolute values instead of subtracting them
  • B. Flipped the signs
  • C. Subtracted in the wrong order
  • D. Forgot to use a number line
  1. The student added \(|{-7}| + |4| = 7 + 4 = 11\) and kept the negative sign.
  2. For opposite signs, subtract: \(|{-7}| - |4| = 7 - 4 = 3\), so the correct answer is \(-3\).

Answer: Added the absolute values

Example 3

Question: Which chip model represents \(3 + (-5)\)?

Example 3

  1. We have 3 positive and 5 negative chips.
  2. The 3 positive chips pair with 3 of the negative chips and cancel.
  3. This leaves \(5 - 3 = 2\) negative chips (representing \(-2\)).
  4. Thus \(3 + (-5) = -2\).

Answer: 2 negative chips remain

Real-World Word Problems

Problem 1

Question: A plane descends \(2000\) feet from its cruising altitude of \(35000\) feet. What is its new altitude? (Model as \(-2000\) for descent.)

  • A. \(37000\) feet
  • B. \(70000\) feet
  • C. \(-33000\) feet
  • D. \(33000\) feet

Why it works: New altitude = \(35000 + (-2000) = 33000\) feet. The plane's altitude decreased by \(2000\) feet.

Answer: \(33000\) feet

Problem 2

Question: A stock started the day at \($50\). It fell \($12\) and then rose \($8\). What was its closing price?

  • A. \($30\)
  • B. \($70\)
  • C. \($54\)
  • D. \($46\)

Why it works: Model as \(50 + (-12) + 8 = 50 - 12 + 8 = 46\). The stock fell \($12\) then rose \($8\) for a net change of \(-$4\).

Answer: \($46\)

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 \(-8+5\)?

  • A. \(-13\)
  • B. \(13\)
  • C. \(3\)
  • D. \(-3\)

Question 2

Compute \(-6 + (-4)\).

  • A. \(-10\)
  • B. \(-2\)
  • C. \(2\)
  • D. \(10\)

Question 3

What is \(7 + 9\)?

  • A. \(2\)
  • B. \(-2\)
  • C. \(63\)
  • D. \(16\)

Question 4

Evaluate \(-13 + (-7)\).

  • A. \(-20\)
  • B. \(-6\)
  • C. \(6\)
  • D. \(20\)

Question 5

What is \(12 + (-5)\)?

  • A. \(7\)
  • B. \(-7\)
  • C. \(17\)
  • D. \(-17\)

Question 6

Compute \(3 + (-11)\).

  • A. \(14\)
  • B. \(8\)
  • C. \(-8\)
  • D. \(-14\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(-3\)

Start at \(-8\) on a number line and move \(5\) units right: \(-8+5=-3\).

Question 2

Answer: \(-10\)

When adding two negative numbers, add their absolute values and keep the negative sign: \(|{-6}| + |{-4}| = 10\), so \(-6 + (-4) = -10\).

Question 3

Answer: \(16\)

Both numbers are positive, so add them directly: \(7 + 9 = 16\).

Question 4

Answer: \(-20\)

Both numbers are negative. Add their absolute values: \(|{-13}| + |{-7}| = 13 + 7 = 20\). Since both are negative, the sum is \(-20\).

Question 5

Answer: \(7\)

Subtract the smaller absolute value from the larger: \(|12| - |{-5}| = 12 - 5 = 7\). The larger absolute value is positive, so the answer is \(7\).

Question 6

Answer: \(-8\)

The absolute value of \(-11\) is larger than \(3\), so subtract: \(|{-11}| - |3| = 11 - 3 = 8\). Since the larger absolute value is negative, the answer is \(-8\).

Timed practice quizzes

Related Quizzes

After studying Adding Integers, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 7 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

Adding Integers 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.