Adding and subtracting integers

Here you will learn strategies on how to add and subtract integers, including using visual models as well as the number line.

Students will first learn about integers in 6th grade math as part of their work with the number system and expand that knowledge to operations with integers in the 7th grade.

Every week, we teach lessons on adding and subtracting integers to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What are adding and subtracting integers?

Adding and subtracting integers is when you add or subtract two or more positive or negative numbers together.

You can add and subtract integers using visual models or a number line.

Adding Integers \hspace{2cm}

Visual model with counters: 3 + 2 = \, ? There are no zero-pairs. There are 5 positive pieces. Answer: 5	Number line: 3 + 2 = \, ? Start at 3 and move 2 places in the positive direction. You land at 5. Answer: 5
Visual model with counters: -5 + 3 = \, ? There are 3 zero pairs There are two negative counters left. Answer: -5 + 3 = -2	Number line: -5 + 3 = \, ? Start at -5 and move three places in the positive direction. You land at -2. Answer: -5 + 3 = -2
Visual model with counters: 6 + (-2) = \, ? There are two zero pairs with four positive counters left. Answer: 6 + (-2) = 4	Number line: 6 + (-2) = \, ? Start at 6 and move two places in the negative directions. You land at 4. Answer: 6 + (-2) = 4
Visual model with counters: -3 + (-4) = \, ? There are no zero pairs. There are 7 negative counters all together. Answer: -3 + (-4) = -7	Number line: -3 + (-4)= \, ? Start at -3 and move 4 places in the negative direction. You land on -7. Answer: -3 + (-4) = -7

Subtracting Integers \hspace{2cm}

Visual model with counters: -3 - (-2) = \, ? -3 take away -2 There are three negative counters. Taking away two of them, leaves you with 1 negative counter. Answer: -3-(-2) = -1	Number line: -3-(-2) means from -2 to -3 on the number line. From -2 move left one unit to -3, which is -1 unit. Answer: -3-(-2) = -1
Visual model with counters: -3-(+2) = \, ? -3 take away +2. Add two zero pairs in order to remove +2. There are five negative counters left. Answer: -3-(+2) = -5	Number line: -3-(+2) means from +2 to -3 on the number line. From +2 move left 5 units to -3, which is -5 units. Answer: -3-(+2) = -5
Visual model with counters: 2-(+5) = \, ? 2 take away +5. Add three zero pairs in order to remove +5. There are three negative counters left. Answer: 2-(+5) = -3	Number line: 2-(+5) = ? 2-(+5) means from +5 to +2 on the number line. From +5 move left three units to +2, which is -3 units. Answer: 2-(+5) = -3

What are adding and subtracting integers?

Common Core State Standards

How does this apply to 6th grade math and 7th grade math?

• Grade 6: Number System (6.NS.C.6)
  Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

• Grade 7: Number System (7.NS.A.1)
  Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

How to add and subtract integers?

In order to add and subtract integers using counters:

1. Represent the problem with counters identifying zero pairs with addition or adding zero pairs when necessary for subtraction.
2. The answer is the leftover counters.

In order to add and subtract integers using a number line:

1. To add, start at the first number and move to the second number; to subtract, start from the second number and move to the first number.
2. Write your answer.

Adding and subtracting integers examples

Example 1: adding integers with different signs using counters

Add: -2 + 7 = \, ?

1. Represent the problem with counters, identifying zero pairs with addition or adding zero pairs when necessary for subtraction.

There are two zero pairs with 5 positive counters left.

2The answer is the leftover counters.

Answer: -2 + 7 = 5

Example 2: subtracting integers with counters

Subtract: -4-(-5) = \, ?

Represent the problem with counters, identifying zero pairs with addition or adding zero pairs when necessary for subtraction.

-4 remove -5. Add 1 zero pair in order to remove -5.

Example 3: adding integers with a number line

Add: -8 + (-5) = \, ?

To add, start at the first number and move to the second number; to subtract, start from the second number and move to the first number.

-8 + (-5) is addition. Start at -8 and move in the negative direction (left) 5 places. You land at -13.

Example 4: subtracting integers with a number line

Solve: 7-(+9) = \, ?

To add, start at the first number and move to the second number; to subtract, start from the second number and move to the first number.

From positive 9 move in the negative direction until you get to 7. You move 2 places to the left, which is -2.

Teaching tips for adding and subtracting integers

• Adding and subtracting integers is a foundational skill for Algebra 1. Using counters and/or a number line helps students formulate conceptual understanding of the concept.

• Using actual hand-held counters help students to manipulate the zero pairs instead of using digital counters.

• Have students try and identify the patterns with adding and subtracting integers so that they can figure out the rules on their own.

• Although practice integer worksheets have their place, have students practice problems through digital games or scavenger hunts around the room to make it engaging.

Easy mistakes to make

• Mixing up the signs when adding and subtracting integers
  For example, using the rule for subtracting integers to add integers.
  
  

  

• Mixing up the positive and negative direction on the number line
  Left is negative, and right is positive.
  
  

  

Related addition and subtraction lessons

This adding and subtracting integers topic guide is part of our series on adding and subtracting. You may find it helpful to start with the main adding and subtracting topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:

• Addition and subtraction
• Standard algorithm addition
• Adding and subtracting negative numbers
• Adding and subtracting rational numbers
• Add and subtract within 100

The next lessons are

• Multiplication and division
• Multiplying and dividing integers
• Types of numbers
• Rounding numbers
• Solving one step equations
• Order of operations

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