# Ch 2: Common Core Math Grade 7 - The Number System: Integer Operations

### About This Chapter

**Standard** : 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. (CCSS.Math.Content.7.NS.A.1)

**Standard**: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (CCSS.Math.Content.7.NS.A.2)

**Standard**: Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. (CCSS.Math.Content.7.NS.A.2.B)

**Standard**: Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. (CCSS.Math.Content.7.NS.A.2.D)

**Standard**: Solve real-world and mathematical problems involving the four operations with rational numbers. (CCSS.Math.Content.7.NS.A.3)

## About This Chapter

Students who have mastered this standard will have the ability to add, subtract, multiply and divide integers and understand terms such as absolute value and additive inverse property. These lessons can help students with the following:

- Using the additive inverse property
- Apply arithmetic operations to integers
- Find the opposite of an integer
- Understand the concept of absolute value
- Learn how to distribute positive and negative signs
- Follow the long division process
- Perform calculations with signed numbers

The lessons could prove useful to students who might be struggling to grasp certain concepts relating to mathematical operations involving integers. Students who master this standard could be ready to move on to more complex mathematical systems and principles.

### How to Use These Lessons in Your Classroom

You might apply these suggestions to your regular curriculum in order to meet the standards for the Common Core.

#### Apply Concepts from the Lessons to Regular Classroom Assignments

Write several addition, subtraction, multiplication and division problems involving integers on the board. Have students solve the problems. Then have chosen students go the board and explain how they arrived at their answers.

#### Create a Fun Class Activity

Have students create a large number line on paper. Instruct two students to hold up the number line at either side and another student to stand at 0. Place another student at -2 and another at 3. Ask the class to solve an integer problem, such as 'What is -2 + 3?' Move the student at -2 three steps to the right. The student will now stand at 1 on the number line. Continue to use problems with both positive and negative integers, having the students move appropriately.

#### Assign an Integer Homework Project

Instruct the students to create a project that will be unique to each individual. Have each student create three tables with the headings 'Year of Event', 'Event' and 'Corresponding Integer'. Have students list five events in the first table that happened before they were born, add a picture of the event and determine the negative integer under the corresponding integer heading (subtract year of the event from the year they were born).

Inform the students to do the same for the year the student was born (corresponding integer will be 0 for each event) and for events after they were born (corresponding integers will be positive). Let students know that pictures of the events can be printed from the Internet, cut from magazines or taken from personal photo collections.

### 1. Absolute Value & Opposite Integers

After watching this video lesson, you'll understand what an absolute value is, and you'll also learn how to find the opposite of an integer. In addition, you'll learn how every pair of opposite integers will always add up to zero.

### 2. Additive Inverse Property: Definition & Examples

In this lesson, we will examine the additive inverse of a given number. We will also learn about the additive inverse of a variable and how it can be represented graphically. Finally, we will explore the most widely employed application of the additive inverse.

### 3. Adding Integers: Rules & Examples

In this lesson, we will learn about adding integers or signed numbers. Using the number line and idea of absolute value, we will see that the rules used to add them are simply an extension of the rules of basic arithmetic.

### 4. Subtracting Integers: Rules & Examples

In this lesson, we will cover definitions, rules, and examples for subtracting integers. We'll also provide some helpful tips for dealing with tricky math problems.

### 5. Distributing Positive and Negative Signs

It's not just numbers and variables that get distributed. Positive and negative signs can, too. In this lesson, we'll learn how to distribute positive and negative signs correctly.

### 6. Multiplying Integers: Rules & Examples

In this lesson, we will discuss what numbers are included in the integers and how to multiply them. We will deal with 1-, 2-, and 3-digit numbers as well as negatives and positives. There are some definitions included as well as a quiz at the end.

### 7. Dividing Integers: Rules & Terminology

In this lesson, we will learn how to divide integers or signed numbers. Determining the correct sign of the answer is a very simple but important step in these calculations. We will also learn the role of zero in division of integers.

### 8. Performing Long Division with Large Numbers: Steps and Examples

After watching this video lesson, you will be able to divide larger numbers. You'll learn an easy to follow procedure that you can use to divide any two numbers.

### 9. Arithmetic Calculations with Signed Numbers

Signed numbers are often referred to as integers. Integers include both positive and negative numbers. In this lesson, you will learn how to add, subtract, multiply, and divide integers.

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### Other Chapters

Other chapters within the Common Core Math Grade 7 - The Number System: Standards course