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Natural numbers Whole numbers Integers Absolute valueHere 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.

**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:
There are no zero-pairs.
| Number line:
Start at 3 and move 2 places in the |

Visual model with counters:
There are two negative counters left.
| Number line:
Start at -5 and move three places in |

Visual model with counters:
There are two zero pairs with four | Number line:
Start at 6 and move two places in |

Visual model with counters:
There are no zero pairs. There are | Number line:
Start at -3 and move 4 places in the |

**Subtracting Integers** \hspace{2cm}

Visual model with counters:
There are three negative counters.
| Number line:
From -2 move left one unit to -3, |

Visual model with counters:
There are five negative counters left.
| Number line:
From +2 move left 5 units to -3, |

Visual model with counters:
There are three negative counters left.
| Number line:
From +5 move left three units to +2, |

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.

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents. 40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

DOWNLOAD FREEPrepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents. 40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

DOWNLOAD FREEIn order to add and subtract integers using counters:

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

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

**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.****Write your answer.**

Add: -2 + 7 = \, ?

**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.

2**The answer is the leftover counters.**

Answer: -2 + 7 = 5

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.

**The answer is the leftover counters.**

-4-(-5) = 1

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.

**Write your answer.**

-8 + (-5) = -13

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

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

**Write your answer.**

7-(+9) = -2

- 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.

**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.

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
- Add and subtract with the algorithm
- Add and subtract within 1,000
- Adding and subtracting rational numbers
- Add and subtract within 100

1. Look at the model below to add -7 + 6.

-13

-1

1

13

There are 6 zero pairs with one negative counter leftover.

-7 + 6 = -1

2. Subtract: -15-(9) = \, ?

-6

6

24

-24

Using the rule, change the sign of the second number, +9 becomes -9.

Then add the two numbers together.

-15 + (-9) = -24

From 9 move left 24 units, you get to -15.

So, -15-(9) = -24

3. Add: 8 + (-19) = \, ?

11

27

-11

-27

Using the rule, since the signs of the numbers are different, the difference between 8 and 19 is 11.

19 is the larger number, and it is negative, so the sum will be negative.

8 + (-19) = -11

You can also check your answer using a number line.

Start at 8 and move 19 places in the negative direction. You land at -11.

4. Subtract: -14-(-8) = \, ?

6

-22

22

-6

Using the rule for subtracting integers, change the sign of the second number.

-8 will become +8.

Then add the number to the first one, -14 + 8 = -6

You can also use a number line to check your answer.

From -8 move left 6 places until you get to -14.

So, -14-(-8) = -6

5. Add: -13 + (-12) = \, ?

-25

1

-1

25

Using the rule, the signs of the numbers are both negative, so add the numbers.

The sum is negative too.

-12 + (-13) = -25

6. On a February day in Chicago, the morning temperature was -3 degrees Fahrenheit. Later that day, the temperature increased by 4 degrees. What is the new temperature in degrees?

-1 degree

1 degree

7 degree

-7 degree

-3 increased by 4 degrees is -3 + 4.

The signs of the numbers are different.

The difference between 3 and 4 is 1.

4 is the larger number, so the sum is positive.

-3 + 4 = 1

Yes, there are negative fractions and decimals. Numbers to the left of 0 on the number line are negative.

Yes, using the number line when adding and subtracting integers will always work. However, it might not always be the fastest way to get the answer.

A zero pair is a number and its opposite. For example, 5 and -5 are a zero pair. The opposite of positive integers is negative integers.

The sum of zero pairs is an additive inverse because the sum is 0.

Addition of integers and subtraction of integers help when simplifying algebraic expressions and also when factoring algebraic expressions.

The positive sign does not necessarily need to be written in front of a number. For example, +5 is the same as 5. The positive sign is understood.

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

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[FREE] Common Core Practice Tests (Grades 3 to 6)

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Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!