Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 65767
Equivalent Rational Expressions
Students are given a polynomial with rational coefficients and asked to identify equivalent expressions from a given list.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, polynomial, like terms, rational coefficients, combine like terms, equivalent expressions,
properties
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_EquivalentRationalExpressions_Worksheet.docx
MFAS_EquivalentRationalExpressions_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 Rational Expressions worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not have a correct strategy to find equivalent expressions.
Examples of Student Work at this Level
The student does not simplify expressions correctly. The student:
Combines unlike terms.
page 1 of 5 Drops the variables and then attempts to evaluate the expression.
Makes equivalency decisions based on how the expression “looks.” For example, the student says, this expression is not equivalent because it:
Has “extra numbers” that aren’t in the original expression.
Has “addition and subtraction in the wrong place.”
Should not have things multiplied or “does not look like” the original expression.
Has an “extra z term” or “too many variables.”
Has “the negative outside parentheses” or “should not have parentheses.”
Questions Eliciting Thinking
How do you simplify an expression? When can you combine terms?
What does like term mean? In the given expression, which terms are like terms?
What does a variable represent? Can you simply remove the variables to write an equivalent expression?
What does equivalent mean? Is it possible to have two expressions that look different from each other still be equivalent?
Instructional Implications
Explain what it means for expressions to be equivalent and provide instruction on using the Commutative and Associative Properties to rewrite the terms of an expression to
demonstrate equivalence. Review the Distributive Property and explain how it can be used to combine variable terms such as -5x and 2x (e.g., -5x + 2x = (-5 + 2)x = -3x).
Eventually introduce the concept of “like terms” and transition the student to simplifying expressions by distributing (when necessary) and combining like terms. Next use
the Distributive Property to introduce the concept of factoring. Emphasize that the Distributive Property can be used to both expand (e.g., multiply) and factor expressions.
Provide additional opportunities for the student to rewrite linear expressions with rational coefficients in factored form using the fewest number of terms. Guide the student
to check factorizations by expanding and comparing to the original expression.
Review other properties of operations, such as the Additive and Multiplicative Inverse Properties and the Identity Properties of Addition and Multiplication. Demonstrate how
these properties can be applied to determine and justify that two expressions are equivalent.
Consider using a variety of 6.EE.1.3 and 6.EE.1.4 MFAS tasks to review expression equivalency concepts.
Moving Forward
Misconception/Error
The student does not consistently apply properties of operations or uses properties incorrectly.
Examples of Student Work at this Level
The student:
Uses the Distributive Property incorrectly:
Does not distribute the factor to every term.
Does not distribute the negative to every term.
Distributes the incorrect factor (e.g., multiplies the expression,
·(­1.8x – 11.76y + 10.8) · 2, by 2
).
page 2 of 5 Gives incorrect property names with no work or explanation.
Note: The student does not have to name the properties, but should show through work or explanation how the properties were applied.
Questions Eliciting Thinking
Can you explain how this expression is different from the original expression?
What is the Distributive Property? In general, how do you multiply something like a(b + c)?
Does adding zero change the value of the expression? Which property assures you that adding zero to a quantity does not change the quantity’s value?
Does multiplying by one change the value of the expression? Which property assures you that multiplying a quantity by one does not change the quantity’s value?
Does the Commutative Property apply to multiplication? To which example could you apply the Commutative Property? How is that helpful?
Instructional Implications
Review properties such as the Commutative Properties, the Associative Properties, Additive and Multiplicative Inverse Properties, and the Identity Properties of Addition and
Multiplication. Guide the student to look for opportunities to use these properties as strategies for simplifying rational expressions. Provide examples in which these properties
have been applied and ask the student to explain how the properties were used to write equivalent expressions.
Review how the Distributive Property can be used to expand expressions of the form a(b + c) where a, b, and c contain rational coefficients, both positive and negative.
Next use the Distributive Property to introduce the concept of factoring. Emphasize that the Distributive Property can be used to both expand (e.g., multiply) and factor
expressions.
Consider using the MFAS task Factored Forms (7.EE.1.1) for additional practice using the Distributive Property for factoring.
Almost There
Misconception/Error
The student gives an incomplete or mathematically incorrect explanation to justify the answer(s).
Examples of Student Work at this Level
The student:
Gives one or more unclear explanations.
Gives an explanation for only their “yes” answers.
Makes a mathematically incorrect statement in their explanation.
page 3 of 5 Questions Eliciting Thinking
How did you determine your answers? Can you explain in more detail? Do you know which properties you can use to justify your answers?
Instructional Implications
Provide direct feedback to the student regarding his or her error and allow the student to correct it. Provide additional opportunities for the student to rewrite expressions
with rational coefficients by applying the Distributive Property to expand expressions and combine like terms.
Assist the student in developing a more formal understanding of the properties of operations and model using the properties to justify the steps in rewriting expressions in
equivalent forms. Allow Got It students to present their explanations and justifications to the class to serve as a model for the student who is having difficulty explaining and
justifying.
Consider using the MFAS task Identify Equivalent Multistep Expressions (7.EE.1.1) for additional practice explaining reasons for equivalency.
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 correctly determines which expressions are equivalent to the given one and justifies each response. For example, the student writes:
A. Yes, because adding zero does not change the value of the expression. (Associative and Inverse Properties of Addition)
B. No, because -1.8 was only factored out of the first term. (Distributive Property)
C. Yes, because multiplying the original expression by one does not change the value. (Commutative, Inverse and Identity Properties of Multiplication)
D. Yes, because adding zero does not change the original expression. (Zero Property of Multiplication)
E. No, because -1 was only factored out of the first term. (Distributive Property)
Questions Eliciting Thinking
How can you change the expressions that are not equivalent so that they become equivalent? Which property could then be used to show the equivalency?
Can you rewrite the given expression in an equivalent form? If the given expression had been written this way, would it change any of your answers for the other
expressions?
Instructional Implications
Assist the student in developing a more formal understanding of the properties of operations and model using the properties to justify the steps in rewriting expressions in
equivalent forms. Provide the student with an expression involving fractional coefficients and constants, both positive and negative, and challenge the student to rewrite
the expression in an equivalent form. Ask the student to justify each step of the work.
Consider using the MFAS task Equivalent Perimeters (7.EE.1.1) for practice using fractions in expressions.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Equivalent Rational Expressions worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
page 4 of 5 Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.EE.1.1:
Description
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational
coefficients.
page 5 of 5