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Examples
Example: The expression 5(3x+1) can be rewritten equivalently as 15x+5.Example: If the expression 2x+3x represents the profit the cheerleading team can make when selling the same number of cupcakes, sold for $2 each, and brownies, sold for $3 each. The expression 5x can express the total profit.
Clarifications
Clarification 1: Properties include associative, commutative and distributive.Clarification 2: Refer to Properties of Operations, Equality and Inequality (Appendix D).
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Coefficient
- Distributive Property
- Expression
- Integer
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 5, students evaluated multi-step numerical expressions using order of operations including parentheses, whole numbers, decimals and fractions. In grade 6, variable terms are introduced to create algebraic expressions with whole number coefficients. In grade 7, rational number coefficients will be used in variable expressions.- Instruction focuses on students using the properties of operations to generate equivalent algebraic expressions.
- Within this benchmark, all variables will have an exponent value of 1. Laws of exponents are introduced in grade 7.
- Students should understand if values are equivalent, they are worth the same amount.
- For example, a 1 dollar bill, 4 quarters, 10 dimes, 20 nickels, 2 half-dollars or 100 pennies have equal values and can be represented as 1 = 4, 1 = 10, 1 = 20, 1 = 2 or 1 = 100, respectively.
- Instruction includes generating equivalent expressions and comparing with other students’ solutions. Discussion focuses around looking for similarities and relationships between students’ approaches (MTR.4.1).
- Instruction includes the use algebra tiles or other concrete representations to provide visual representation of the properties of operations.
- Students should be encouraged to generate equivalent expressions in ways that are mathematically accurate and make sense to the individual. Students should be able to justify their process using properties of operations.
- Instruction includes having expressions with more than one variable as well as nested grouping symbols.
- Expression with more than one variable
−4 + 3 − 2
- Nested grouping symbols−2[3( − 3)]
- Expression with more than one variable
Common Misconceptions or Errors
- Students may incorrectly think there is only one right answer or equivalent value to be found. Although the most simplified version of an expression is an equivalent expression, it may not be the only equivalent expression.
- Students may incorrectly perform operations involving nested grouping symbols. Students can be taught or reminded that each grouping symbol is treated similarly to parentheses.
Strategies to Support Tiered Instruction
- Instruction includes providing students with algebra tiles and two different expressions. Students should represent the provided expressions with the algebra tiles and determine if the two expressions are equivalent or not by comparing the number of each tile.
- Teacher provides opportunities for students to use algebra tiles to represent various given expressions, manipulate the tiles to show the expression a different way and then write the corresponding expression.
- Instruction includes building a foundation for the properties of operations by modeling the associative, commutative, and distributives properties with algebra tiles for numeric and algebraic expressions and allowing the students to manipulate the algebra tiles as well.
- Instruction includes providing students with two different expressions already represented with algebra tiles and then allowing the students to manipulate the algebra tiles to determine if they are equivalent. Students should be allowed to justify their reasoning for why the expressions are equivalent, or not.
- Teacher reminds students that each grouping symbol is treated similarly to parentheses.
Instructional Tasks
Instructional Task 1 (MTR.2.1, MTR.5.1)
Look at the following expressions.
- Part A. Simplify the expressions shown above.
- Part B. Can any grouping symbols be removed from the expressions without changing the value of the expression?
Instructional Task 2 (MTR.2.1)
How can you show the two expressions, 2(x + 5) and 2(x) + 2(5), are equivalent? Explain.
Instructional Items
Instructional Item 1
Tamika is selling chocolate candy bars for $1 and bags of popcorn for $3 at the school fair. She sells y candy bars and (y − 7) bags of popcorn. The expression 1 y + 3(y−7) represents Tamika’s total sales. Rewrite the expression in a different but equivalent form.*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Problem-Solving Tasks
Tutorials
Video/Audio/Animation
MFAS Formative Assessments
Students are asked to write expressions equivalent to a given one by using the Associative and Commutative Properties.
Students are asked to generate and justify an expression equivalent to a given one using the properties of operations.
Students are asked to identify expressions equivalent to a given exponential expression and justify their responses.
Students are asked to determine if pairs of expressions are equivalent and to justify their responses.
Students are asked to write equivalent expressions using the Distributive Property.
Students are asked to identify expressions equivalent to a given expression and justify their responses.
Students are asked to identify expressions equivalent to a given expression and justify their responses.
Computer Science Original Student Tutorials
Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.
Click below to check out the other tutorials in the series.
Student Resources
Original Student Tutorial
Explore computer coding on the farm by using IF statements and repeat loops to evaluate mathematical expressions. In this interactive tutorial, you'll also solve problems involving inequalities.
Click below to check out the other tutorials in the series.
- MacCoder’s Farm Part 1: Declare Variables
- MacCoder’s Farm Part 2: Condition Statements
- MacCoder's Farm Part 3: IF Statements
Type: Original Student Tutorial
Problem-Solving Tasks
Students are asked to determine if given expressions are equivalent.
Type: Problem-Solving Task
The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.
Type: Problem-Solving Task
This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.
Type: Problem-Solving Task
Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.
Type: Problem-Solving Task
Tutorials
In this video, you will practice using arithmetic properties with integers to determine if expressions are equivalent.
Type: Tutorial
Learn how to apply the distributive law of multiplication over addition and why it works. This is sometimes just called the distributive law or the distributive property.
Type: Tutorial
Learn how to apply the distributive property of multiplication over subtraction. This is sometimes just called the distributive property or distributive law.
Type: Tutorial
Learn how to apply the distributive property to algebraic expressions.
Type: Tutorial
Students will simplify an expression by combining like terms.
Type: Tutorial
This tutorial is an explanation on how to combine like terms in algebra.
Type: Tutorial
This is an introduction to combining like terms in this tutorial.
Type: Tutorial
Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.
Type: Tutorial
Parent Resources
Problem-Solving Tasks
Students are asked to determine if given expressions are equivalent.
Type: Problem-Solving Task
The purpose of this task is to ask students to write expressions and to consider what it means for two expressions to be equivalent.
Type: Problem-Solving Task
This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.
Type: Problem-Solving Task
Students are asked to use properties of operations to match expressions that are equivalent and to write equivalent expressions for any expressions that do not have a match.
Type: Problem-Solving Task
