# Ch 2: Common Core Math Grade 6 - Expressions & Equations: Algebraic Equations

### About This Chapter

**Standard** : Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. (CCSS.Math.Content.6.EE.B.5)

**Standard** : Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. (CCSS.Math.Content.6.EE.B.6)

**Standard** : Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. (CCSS.Math.Content.6.EE.B.7)

**Standard** : Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. (CCSS.Math.Content.6.EE.B.8)

## About This Chapter

The lessons in this chapter are designed to help students learn how to apply arithmetic operations to algebraic expressions. They will understand how to solve addition, subtraction, multiplication and division problems with variables. Use these lessons to help your students:

- Define and apply the distributive property
- Explain the mathematical properties addressing inverses
- Solve various types of equations with one variable
- Answer linear inequality problems
- Understand how to graph a function and plot points on a graph

These concepts are discussed in simple and easy-to-follow terms that are beneficial to middle grade students who might be struggling with these topics. Once they have mastered this standard, students could be prepared to move on to more complex algebraic problems.

### How to Use These Lessons in Your Classroom

Below you will find some tips as to how these lessons can be adopted into your regular curriculum to meet the Common Core Standards.

#### Use Fun Activities in the Classroom

Tell your students to use their artistic abilities to create a flipbook focusing on such topics as inequalities, graphing functions or linear equations. Have them use index cards for sturdiness. Make sure each page solves another part of the problem until the problem is solved on the final page.

#### Create a Group Activity

Separate the class into groups of four. Have the students create their own algebraic equations based on real-life situations. Instruct each group to create four equations. Tell the groups to exchange equations with each other and each group solve the others' equations. Facilitate a group discussion afterward to see what the students have learned.

#### Have the Students Stage an In-Class Algebraic Equations Competition

Divide the class into two groups. Write ten each of one-variable addition, subtraction, multiplication and division equations on a blackboard. Have one student from each group go up and solve one equation each. Keep rotating students for each problem. The first group that successfully answers all of the questions wins.

### 1. Distributive Property: Definition, Use & Examples

After completing this lesson, you will be able to state the distributive property and apply it to various types of problems. You will also be able to accurately perform the mathematical operations that are involved with the distributive property.

### 2. Inverse Operations in Math: Definition & Examples

In mathematics, inverse operations are operations that 'undo' each other. Most operations have an inverse. This lesson describes the most common operations and their inverses, and it provides some examples and a quiz to cement your knowledge.

### 3. Writing & Solving Addition Equations with One Variable

After watching this video lesson, you will know how to properly write an addition equation and how to solve any addition equation that you come across. Learn what the steps are to solve these equations that have one variable in them.

### 4. Writing & Solving Subtraction Equations with One Variable

After watching this video lesson, you will know what is needed in order to write a subtraction equation. You will also know how to solve any subtraction equation that you are given or that you write.

### 5. Writing & Solving Multiplication Equations with One Variable

After watching this video lesson, you will know the components that go into a complete multiplication equation. You will also learn the steps that are needed to solve a multiplication equation.

### 6. Writing & Solving Division Equations with One Variable

In this video lesson, you will learn the proper format of a division equation. Learn what components are needed for a complete division equation. Also learn what steps you need to take to solve these division equations.

### 7. Solving One-Step Linear Inequalities

In this video lesson, you will learn how you can solve any kind of linear inequality that only requires one step. Learn when you need to subtract, when you need to add, when you need to multiply, and when you need to divide.

### 8. Graph Functions by Plotting Points

Let's say you have a function. What does it look like? How do you graph it? In this lesson, we'll learn how to graph functions by determining and plotting points.

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### Other Chapters

Other chapters within the Common Core Math Grade 6 - Expressions & Equations: Standards course