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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.

7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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By the end of this lesson, students will be able to:
- Identify positive and negative integers on a number line
- Add and subtract positive and negative integers
- Multiply and divide positive and negative integers
- Apply integer operations to real-world situations

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How do positive and negative integers help us represent and solve real-world problems?

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Take 5 minutes to complete these questions:
1. Draw a number line from -10 to 10
2. Mark and label 5 integers on your number line
3. Where do you see positive and negative numbers in everyday life?

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Teacher will introduce the concept of integers, explaining that integers include positive numbers, negative numbers, and zero. Use the number line to demonstrate the relationship between numbers and their positions.

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Rules for adding integers:
- Adding two positive integers: add the values (keeps positive sign)
- Adding two negative integers: add absolute values (keeps negative sign)
- Adding integers with different signs: subtract the smaller absolute value from the larger, then use the sign of the number with the larger absolute value

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Let's have some practice adding and subtracting negative numbers. So the first example I want to look at is 2 minus 3. So right now I'm just subtracting a positive number from another positive number, but you might already see that I'm subtracting a larger number from a smaller number. So I'm probably, or I will, definitely end up with a negative number. But let's just think about this a little bit. And I'm going to do it with a number line. So there's my number line right over there. Now this is 0, this is 1, this is 2, this is negative 1, this is negative 2. We could view this as starting at 2. So this is 2 right over here, and then we're going to subtract 3 from that 2. So we're going to move 3 to the left on the number line. So we're going to move 3 to the left, 1, 2, 3. And that gets us to negative 1. This is equal to negative 1. Now let's mix it up a little bit more. Let's imagine what would happen if we had negative 2 minus 3. So this was positive 2 minus 3. Now let's think about negative 2 minus 3. So once again, let's draw our number line. And I'll put 0 over here. So this is 0, this is 1, this is negative 1, negative 2, negative 3, negative 4, negative 5, negative 6, and I could keep going. But we're starting at negative 2, and then we're subtracting 3 again. So once again, we're going to move three to the left of negative 2. So we go 1, 2, 3. We end up at negative 5. So this is negative 5. So notice in both situations we subtracted 3, we moved 3 to the left on the number line. It's just here we started 2 to the right of 0. Here we started 2 to the left of 0. This is negative 2. Let's do another example with these same numbers. Let's imagine negative 2 plus 3. I encourage you to pause this video, and try to think about this on your own. So we could draw the number line-- I could draw a straighter number line than that-- so draw the number line again. And let's say that this is negative 2, negative 1, 0, 1, and 2 again. We're starting at negative 2, we're starting 2 to the left of zero. So we're starting at negative 2, and we're going to add 3. So we're going to go 3 to the right now, 1, 2, 3, and we end up at positive 1. Now let's think about 2, so positive 2, and we're going to subtract a negative 3. And other videos we've already talked about this. In fact, there's a video explaining why this actually makes sense. But when you subtract a negative, this is the same thing as adding the positive. So 2 minus negative 3 is the exact same thing as 2 plus 2 plus positive 3. These two statements are equivalent, and this just boils down to, this right over here, is just going to be 5. Now, let's mix it up a little bit more. Let's imagine negative 2 minus negative 3. Now, this might seem really intimidating to have all of these negatives in place here, but you just have to remember subtracting a negative, like this, is going to get you a positive. So this is the exact same thing as negative 2 plus 3, and negative 2 plus 3, we've already seen it right over here. You start at negative 2, you start 2 to the left of 0, and then we're going to go 3 to the right, we're adding 3, 1, 2, 3.

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Adding & subtracting negative numbers (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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When subtracting integers, convert the subtraction problem to an addition problem by changing the sign of the second number and then using the rules for addition.

Example: 5 - (-3) = 5 + 3 = 8

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Subtracting Integers | How to Subtract Positive and Negative Integers

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In small groups, students will solve the following problems and explain their reasoning to each other:
1. -7 + 12
2. 8 + (-15)
3. -9 - 4
4. 6 - (-8)

Use Padlet to have each group post their solutions with explanations.

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Rules for multiplying integers:
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
- Negative × Positive = Negative

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Multiplying Integers: Multiplying a Positive by a Negative | Positive x Negative | Math with Mr. J

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Rules for dividing integers:
- Positive ÷ Positive = Positive
- Negative ÷ Negative = Positive
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative

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RULE 1: The product of a positive integer and a negative integer is negative.

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Complete the following problems independently:
1. -8 × 4
2. 15 ÷ (-3)
3. -12 ÷ (-4)
4. -5 × (-7)
5. 6 × (-2) + 9
6. -18 ÷ 3 - 5

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Solve integer addition and subtraction problems while uncovering a hidden picture in this fun game for middle school math!

You can choose the range of numbers to be used in the addition and subtraction problems, which means you can make the practice easy or difficult according to your need and grade level.

For example, choose a range from −10 to 10 for students that have just recently learned about integer addition and subtraction (6th and 7th grades). For a little more advanced practice, use −20 to 20, and for advanced level, −50 to 50.

Range for numbers to be subtracted: Go!

Screenshot:

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Integer addition & subtraction mystery picture game

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Solve integer addition and subtraction problems while uncovering a hidden picture in this fun game for middle school math! You can choose the range of numbers to be used in the addition and subtraction problems, which means you can make the practice easy or difficult according to your need and grade level.

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For students who need additional support:
- Use number line manipulatives
- Practice with simpler problems first
- Provide a reference sheet with the rules for integer operations
- Work in smaller guided groups

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For students ready for a challenge:
- Create real-world problems involving integers
- Solve multi-step equations with integers
- Work with rational numbers (fractions and decimals) as well as integers
- Investigate patterns in integer operations

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During the lesson, monitor student understanding through:
- Observation during group work
- Questioning strategies
- Review of students' work on whiteboards
- Student explanations of their thinking

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Students will answer these questions on a mini-whiteboard:
1. What is -7 + 4?
2. What is 8 - (-3)?
3. What is -6 × 5?

Hold up your board when finished for a quick check.

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In pairs, have students create a Padlet post explaining one of the integer operation rules (addition, subtraction, multiplication, or division) with examples. Students should include a real-world application of their assigned operation.

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Integer Operations Real World Applications | 6th Grade Math

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At the end of the unit, students will complete a quiz with the following sections:
- Identifying integers on a number line
- Computing integer operations
- Solving word problems involving integers
- Explaining the rules for integer operations

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As a class, create a summary of what we learned about integers today. What are the key rules for each operation? What patterns did you notice?

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Before leaving class, answer these questions on your exit ticket:
1. What was the most important thing you learned today?
2. What rule helps you remember how to multiply integers with different signs?
3. What questions do you still have about integer operations?

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Create a reference sheet for yourself with the rules for adding, subtracting, multiplying, and dividing integers. Include at least one example for each operation.

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Complete the following integer operation problems:
1. -15 + 8
2. 12 - (-7)
3. -4 × 9
4. -36 ÷ (-4)
5. 5 + (-12) + 3
6. -8 × 4 ÷ (-2)

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Welcome to the integers worksheets page at Math-Drills.com where you may have a negative experience, but in the world of integers, that's a good thing! This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers.

If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand. Banks like you to keep negative balances in your accounts, so they can charge you loads of interest. Deep sea divers spend all sorts of time in negative integer territory. There are many reasons why a knowledge of integers is helpful even if you are not going to pursue an accounting or deep sea diving career. One hugely important reason is that there are many high school mathematics topics that will rely on a strong knowledge of integers and the rules associated with them.

We've included a few hundred integers worksheets on this page to help support your students in their pursuit of knowledge. You may also want to get one of those giant integer number lines to post if you are a teacher, or print off a few of our integer number lines. You can also project them on your whiteboard or make an overhead transparency. For homeschoolers or those with only one or a few students, the paper versions should do. The other thing that we highly recommend are integer chips a.k.a. two-color counters. Read more about them below.

Most Popular Integers Worksheets this Week

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Integers worksheets including comparing and ordering, adding, subtracting, multiplying and dividing integers.

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Find and describe 3 real-world situations where you might use negative numbers. Examples could include temperature, elevation, or finance. For each situation, write and solve a math problem involving integers.

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Complete the online practice activities for integer operations. These interactive exercises will help reinforce today's learning and provide immediate feedback.

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10 Integer Games for 7th Graders - The Sassy Math Teacher

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Are your 7th graders struggling with integers? This blog post is your secret weapon! We’ll show you 10 creative and engaging integer games…

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In your math journal, answer the following questions:
1. How does understanding integers help us in everyday life?
2. What strategies do you use to remember the rules for integer operations?
3. Create your own word problem involving negative integers and solve it.