# Ch 1: Common Core Math Grade 6 - Expressions & Equations: Algebraic Expressions

### About This Chapter

**Standard:** Write and evaluate numerical expressions involving whole-number exponents. (CCSS.MATH.CONTENT.6.EE.A.1)

**Standard:**Write, read, and evaluate expressions in which letters stand for numbers. (CCSS.MATH.CONTENT.6.EE.A.2)

**Standard:** Write expressions that record operations with numbers and with letters standing for numbers. *For example, express the calculation 'Subtract y from 5' as 5 - y.* (CCSS.MATH.CONTENT.6.EE.A.2.A)

**Standard:** Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. *For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.* (CCSS.MATH.CONTENT.6.EE.A.2.B)

**Standard:** Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). *For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.* (CCSS.MATH.CONTENT.6.EE.A.2.C)

**Standard:** Apply the properties of operations to generate equivalent expressions. *For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.* (CCSS.MATH.CONTENT.6.EE.A.3)

**Standard:** Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). *For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.* (CCSS.MATH.CONTENT.6.EE.A.4)

## About This Chapter

You'll be able to tell that your students have mastered this standard when they are able to apply previous arithmetic skills to algebraic expressions. The lessons in this collection can help you teach students about the following:

- Exponential notation
- Simplifying and solving expressions with exponents
- Translating addition, subtraction, multiplication and division statements into algebraic expressions
- Algebraic variables
- Showing relationships as algebraic expressions
- Evaluating simple expressions
- Writing equivalent algebraic expressions

Students who have mastered this standard are able to write, read and evaluate expressions involving variables and whole-number exponents. They'll also be able to recognize when two expressions are equivalent and apply the properties of operations to produce equivalent expressions.

### How to Use These Lessons in Your Classroom

Below are some tips to help you incorporate these collection materials into your lesson plans.

#### Write Equivalent Expressions

Watch the lesson 'Writing Equivalent Expressions.' Divide students into groups of three. Have each student write a simple algebraic expression on a piece of paper. Pass the papers, then have each student try to write an equivalent expression for the previous student's work. Pass again, and have students check the two expressions for equivalency by plugging in sample values. Repeat the exercise several times until students have mastered the concept.

#### Translate Math Statements Into Equations

As a class, view the lessons on translating statements into algebraic expressions. Give students a worksheet with word problems that require addition, subtraction, multiplication and division. Have students translate the statements into algebraic expressions, then solve the expressions.

#### Assess Knowledge With a Trivia Game

Use the practice quizzes to create a trivia game to assess how well students are grasping the concepts. Have the students buzz in with correct answers to win a small prize or extra credit points.

### 1. How to Use Exponential Notation

Exponential notation is a mathematical method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with exponential notation and give some examples of how it is used.

### 2. Simplifying and Solving Exponential Expressions

What do we do with an exponent? In this lesson, we'll learn how to simplify and solve expressions containing exponents. We'll solve a variety of types of exponential expressions.

### 3. Translating an Addition Statement into an Algebraic Expression

Watch this video lesson to learn how you can turn an addition statement from words into an algebraic expression. Learn how the key terms translate into mathematical symbols.

### 4. Translating a Subtraction Statement into an Algebraic Expression

After watching this video lesson, you will be able to take a statement that you hear or read in words and translate it into an algebraic expression that you can solve. Learn what key words to look for when writing your expressions.

### 5. Translating a Multiplication Statement into an Algebraic Expression

After watching this video lesson, you will be able to translate a multiplication problem that you hear or read from words into an algebraic expression that you can solve. Learn what key words to look for.

### 6. Translating a Division Statement into an Algebraic Expression

In this video lesson, you will see that when it comes to math and the real world, there will be situations when you have to translate a statement that you hear or read in words into a math problem that you can solve.

### 7. What is a Variable in Algebra?

Did you ever encounter something like a + b = c and wonder how all these letters snuck into a math problem? In this lesson, we'll learn about variables, as well as other parts of equations, constants and coefficients.

### 8. Expressing Relationships as Algebraic Expressions

What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions.

### 9. Evaluating Simple Algebraic Expressions

In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.

### 10. Writing Equivalent Expressions: Definition & Examples

In this lesson, you'll learn what an algebraic expression is and what makes two algebraic expressions equivalent. You'll also see some examples of equivalent expressions.

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### Other Chapters

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