Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 58276
Factored Forms
Students are given two expressions and asked to rewrite each in factored form using the fewest number of terms.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, factors, distributive property, expression, coefficient, term, constant
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_FactoredForms_Worksheet.docx
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 Factored Forms worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand what it means to write an equivalent expression.
Examples of Student Work at this Level
The student:
Substitutes a value for x and attempts to evaluate the expression.
Imposes an equal sign somewhere in the expression and attempts to “solve” it.
page 1 of 4 Multiplies terms together and attempts to evaluate the expression.
Questions Eliciting Thinking
What is the difference between an expression and an equation? What is the difference between rewriting and solving?
Do you know what “like terms” are? Are the terms 4x and 8 like terms?
What does it mean to factor an expression?
Instructional Implications
Explain the distinction between an expression and an equation. Provide examples of each in both real-world and mathematical contexts. (E.g., Pose scenarios that provide
the opportunity to write expressions and equations such as, “Gena is twice as old as Mattie. Adam is three years older than Mattie. If the sum of their ages is 51, how old is
each?”). Review the terms variable, constant, and coefficient. Then guide the student to write expressions that represent each person’s age in the problem. Ask the
student to identify examples of variables, constants, and coefficients in the expressions. Then guide the student to use the information that the ages sum to 51 to write an
equation. Ask the student to identify expressions within the equation making clear the distinction between an expression and an equation. Provide additional opportunities
for the student to write expressions and equations.
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 in
a more “convenient” order. 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.
Moving Forward
Misconception/Error
The student does not correctly apply the Distributive Property either to expand, factor, or combine like terms.
Examples of Student Work at this Level
The student combines like terms (either correctly or incorrectly) but does not factor the expression:
Questions Eliciting Thinking
How did you know which terms to combine?
What does it mean to factor?
What is the Distributive Property? How is it related to factoring?
Instructional Implications
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.
Almost There
Misconception/Error
page 2 of 4 The student makes computational errors when calculating with coefficients and constants.
Examples of Student Work at this Level
The student:
Makes a sign error, rewriting 3x – 12 + 6x + 9 as 3x – 6x + 12 + 9.
Says the sum of -12 and 9 is positive three.
Factors 9x – 3 as 3(x – 1).
Questions Eliciting Thinking
Which terms in the original expression are negative or contain a negative coefficient?
I think you made a mistake combining like terms. Can you check your work?
How can you check your final answer to determine if it is equivalent to the original expression?
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 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.
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 uses the fewest number of terms and correctly factors each expression. The student writes:
4x + 8 + 2 = 4x + 10 = 2(2x + 5)
3x – 12 + 6x + 9 = 9x – 3 = 3(3x – 1)
Questions Eliciting Thinking
In the second problem, how did you know that you could combine -12 and 9? They are not next to each other in the expression.
In the second problem, how did you know that you could combine 3x and 6x? What property justifies this?
How is factoring related to the Distributive Property?
Are there any other ways to rewrite either expression in an equivalent factored form?
Instructional Implications
Challenge the student to factor each expression in a variety of other ways. (E.g., Ask the student to rewrite 4x + 10 as the product of
and a linear expression so that
their product is equivalent to 4x + 10.).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Factored Forms 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
page 3 of 4 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 4 of 4