GRADE 6
Teacher Guidelines ▶ pages 1 – 2
Instructional Pages ▶ pages 3 – 4
Activity Page ▶ page 5
Practice Page ▶ page 6
Homework Page ▶ page 7
Answer Key ▶ pages 8 – 10
EQUIVALENT
EXPRESSIONS
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how to find equiava=olent expressions
Typology: Cheat Sheet
2022/2023
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EQUIVALENT
- GRADE - Teacher Guidelines ▶ pages 1 –
- Instructional Pages ▶ pages 3 – - Activity Page ▶ page - Practice Page ▶ page - Homework Page ▶ page - Answer Key ▶ pages 8 –
*Lessons are aligned to meet the education objectives and goals of most states. For more information on your state objectives, contact your local Board of Education or Department of Education in your state.
Classroom Procedure: Approximate Grade Level : 6
Objectives : Students will be able to identify two equivalent expressions. State Educational Standards* LB.Math.Content.6.EE.A. Class Sessions ( 45 minutes ): 1 Teaching Materials Worksheets : Equivalent Expressions content pages Activity pages Practice page Homework page Student Supplies : Scissors Glue Extra paper Prepare Ahead of Time : Copy Materials Options for Lesson : Have each student share an expression and then have all the other students create an equivalent expression, allow for students to rotate as the leader, and use white boards to make the process faster; incorporate mathematical properties into the lesson to see if students can link the concepts together for a thorough application
- Begin by discussing the concept of equal in various settings. Quickly review the difference between 2x and x^2.
- While reading the content pages, reinforce vocabulary and give students additional examples of Equivalent Expressions problems in order to help them practice. Use the additional resources to enhance understanding.
- Introduce notes on Equivalent Expressions. Have students practice problems with different operations and variables.
- Follow Activity page with students. Have students work individually on the activity.
- Distribute Practice page. Check and review the students’ responses as a class.
- Distribute the Homework page. Have students work a few problems at the beginning of the next class to reinforce their understanding.
- In closing, ask students to explain why there could be an infinite number of equivalent expressions. Allow for responses and discussion.
Equivalent Expressions
An algebraic expression is a mathematical phrase that contains rational numbers, operators, and/or variables. Equivalent means the same or equal. Equivalent expressions are two expressions that look different but are the same value. Here are some examples of equivalent expressions:
3 + 4 and 6 + 1
5 * 4 and 2 * 10
10 – 4 and 18 – 12
Notice that the value of the expression is equal.
3 + 4 = 7 and 6 + 1 = 7 Both equal 7.
5 * 4 = 20 and 2 * 10 = 20 Both equal 20.
10 – 4 = 6 and 18 – 12 = 6 Both equal 6.
There are many other ways that we could write expressions to equal 7.
There is an infinite number of possibilities!
Equivalent expressions can also have variables. Consider these two expressions:
5x and 2x + 3x
They are equivalent because 2x + 3x is equal to 5x. Consider these two expressions:
9x – 3x and 2(3x)
They are equivalent because both expressions equal 6x. Consider these two expressions:
2x and x
These expressions are NOT equivalent because 2x is not the same as x^2. This is because 2x is x + x while x^2 is x * x. Equivalent expressions are important to understand in math because often times you may find it easier to work with or simplify a problem using an equivalent expression.
Practice Name __________________________ Date _________
Instructions Decide if each set of expressions are equivalent. If they are not equivalent, rewrite one of the expressions to make them equivalent. 1.) 4x = x + x + x + x True False 2.) 3y^2 = 3 • 3 • y True False
- ) 2x + 4y = x + x + y + y + y
- y True False 4.) 3x – y = y – x + x + x True False 5.) 2y^2 + 4 = 4 + 2 • y • y True False 6.) 6xyz = 3 • 2 + x + y + z True False 7.) 10(x + 2) = 20 + 10x True False 8.) 63x/7 = 9x True False 9.) 2(x + 7) = x^2 + 7x True False Write three expressions that are equivalent to 24x^3
Homework Name __________________________ Date _________
Instructions Circle all the expressions that are equal to 5(2 + x)
7x 10 + 5x 15x 2x + 5
x + x + x + x + x + 3 + 3 + 3 + 1 5x + 2(5)
5 + 5 + 5x x • x • x • x • x + 1 + 7 + 2
Write three expressions that are equivalent to 12x + 4x^2 Write three expressions that are equivalent to 12x + 4x^2 Write three expressions that are equivalent to 12x + 4x^2 Why are 2x and x^2 not equivalent? _________________________________________________________
Practice Name __________________________ Date _________
Answer Key
Instructions Decide if each set of expressions are equivalent. If they are not equivalent, rewrite one of the expressions to make them equivalent. 1.) 4x = x + x + x + x True False 2.) 3y^2 = 3 • 3 • y True False 3 • y • y 3.) 2x + 4y = x + x + y + y + y + y True False 4.) 3x – y = y – x + x + x True False -3x + y 5.) 2y^2 + 4 = 4 + 2 • y • y True False 6.) 6xyz = 3 • 2 + x + y + z True False 3 • 2 • x • y • z 7.) 10(x + 2) = 20 + 10x True False 8.) 63x/7 = 9x True False 9.) 2(x + 7) = x^2 + 7x True False x(x + 7) Write three expressions that are equivalent to 24x^3 Answers will vary. Possible answers are: 8(3x^3 ); 12x^2 • 2x; (3x)(2x)(4x)
Homework Name __________________________ Date _________
Answer Key
Instructions Circle all the expressions that are equal to 5(2 + x)
7x 10 + 5x 15x 2x + 5
x + x + x + x + x + 3 + 3 + 3 + 1 5x + 2(5)
5 + 5 + 5x x • x • x • x • x + 1 + 7 + 2
Write three expressions that are equivalent to 30 Answers will vary. 25 + 5 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3
- 3
Write three expressions that are equivalent to 18x^2 Answers will vary. 9x * 2x 3 * 6 * x^2 18 * x * x Write three expressions that are equivalent to 12x + 4x^2 Answers will vary. 2x * 6 + 2x * 2x 3 * 4 * x + 4x * x 4 * x * x + 2 * 2 * 3 * x Why are 2x and x^2 not equivalent? 2x is equal to x plus x while x^2 is equal to x times x – they are two different operations