Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 65260
Equivalent Expressions
Students are asked to determine if pairs of expressions are equivalent and to justify their responses.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, like terms, distributive, equivalent, expression, equation
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_EquivalentExpressions_Worksheet.docx
MFAS_EquivalentExpressions_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Equivalent Expressions worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand what it means for expressions to be equivalent.
Examples of Student Work at this Level
The student does not demonstrate an understanding of the meaning of equivalent. The student:
Identifies expressions that are not equivalent. For example, the student identifies as equivalent:
5n and 6n – 1 because “6n – 1 = 5n.”
2d – d and 2 because “2d – d = 2.”
5x + 3y and 8xy because “they each involve an x and a y and 5 + 3 = 8.”
Does not recognize 10t – 7t and 3t as equivalent.
Tries to “solve” expressions as if they are equations.
page 1 of 3 States that it is not possible to determine whether or not the expressions are equivalent because the value of the variable is not known.
Questions Eliciting Thinking
What does it mean for two expressions to be equivalent?
What does 5n mean? What does 6n – 1 mean?
What do you know about the properties of operations (e.g., the Commutative Property, the Associative Property, and the Distributive Property)?
What is the difference between an expression and an equation? Can an expression be solved?
Do you have to know what the variable represents in order to determine if the expressions are equivalent?
Instructional Implications
Explain what it means for two expressions to be equivalent (e.g., two expressions are equivalent if they always result in the same number when evaluated for the same
values of the variables). Demonstrate the equivalence of two expressions (e.g., 10t – 7t and 3t) by evaluating each for the same value of t. Explain to the student that it is
not possible to evaluate each expression for every possible value of t to check for equivalence, but properties of operations can be used to verify equivalence. For example,
explain that 10t – 7t = 3t by the Distributive Property [e.g., 10t – 7t = (10 – 7)t = 3t].
Review the properties of operations and the associated vocabulary as needed (e.g., equivalent, expression, factor, term, coefficient, variable, constant, distribute).
Emphasize the Distributive Property and how it can be used to both expand and factor expressions to generate equivalent expressions. Model using the Distributive Property
to generate equivalent expressions. Emphasize that the properties of operations ensure that expressions are equivalent for every value of the variable(s). Provide
opportunities for the student to use properties of operations to generate equivalent expressions.
Make explicit the difference between an expression and an equation. Explain that expressions can be evaluated for particular values of the variable but cannot be “solved.”
Demonstrate evaluating an expression and solving an equation and make clear the distinction.
Consider administering other MFAS tasks aligned to standard 6.EE.1.4.
Making Progress
Misconception/Error
The student is unable to identify equivalent expressions using properties of operations.
Examples of Student Work at this Level
The student “tests” the expressions by evaluating them for a particular value of the variable and concludes that only 10t – 7t and 3t are equivalent.
Questions Eliciting Thinking
Can you determine if the expressions are equivalent without replacing the variable with a number and evaluating each expression? Explain.
Can you think of any properties you could use to justify your choices? Explain.
Instructional Implications
Confirm that the student’s approach is consistent with the definition of equivalent expressions; however, he or she only tested the expressions for one possible value of the
variable. Clarify that expressions can be shown to not be equivalent by evaluating each for particular values of the variable and showing that they result in different numbers.
Yet, showing that expressions are equivalent requires using definitions and properties. Show the student a pair of expressions such as 2x and 3x or 2x and
. Evaluate the
pairs of expressions for a particular value for which they are equal (e.g., x = 0 and x = 2, respectively). Then evaluate the pairs of expressions for another value to show
that they are not always equal and are not, therefore, equivalent.
Review the properties of operations and the associated vocabulary as needed (e.g., term, coefficient, variable, constant, distribute). Emphasize the Distributive Property and
how it can be used to both expand and factor expressions to generate equivalent expressions. Model using the Distributive Property to generate equivalent expressions.
Emphasize that the properties of operations ensure that expressions are equivalent for every value of the variable(s). Provide opportunities for the student to use properties
of operations to generate equivalent expressions.
Consider administering other MFAS tasks aligned to standard 6.EE.1.4.
page 2 of 3 Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student explains that only 10t – 7t and 3t are equivalent. The student explains the equivalence by stating that 10t and 7t are like terms and, when subtracted, equal
3t. The student also uses the concept of “like terms” to explain why the other pairs of expressions are not equivalent. The student may also evaluate each pair of
expressions for a particular value of the variable to show that they are not equivalent.
Questions Eliciting Thinking
Why can’t you subtract one from 6n to get 5n? What would you have to subtract from 6n to make it equivalent to 5n?
Given 2d – d, why don’t you just remove the d from 2d when you subtract?
Instructional Implications
Review the properties of operations and challenge the student to explain why 10t – 7t = 3t using the Distributive Property.
Consider administering MFAS task Property Combinations (6.EE.1.4).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Equivalent Expressions worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.6.EE.1.4:
Description
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.
page 3 of 3