Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 65222
Generating Equivalent Expressions
Students are asked to write equivalent expressions using the Distributive Property.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, expressions, Distributive Property, equivalent
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_GeneratingEquivalentExpressions_Worksheet.docx
MFAS_GeneratingEquivalentExpressions_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 Generating Equivalent Expressions worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to apply the Distributive Property to generate equivalent expressions.
Examples of Student Work at this Level
The student:
Distributes to only one term of the expression.
page 1 of 4 Attempts to rewrite the expression as an equation and solve for x.
Questions Eliciting Thinking
What does it mean for expressions to be equivalent?
Is x + 2 equivalent to 2x? If you evaluated each expression for x = 5, would you get the same result?
Can you explain the Distributive Property? What does the word distribute mean?
What do you think the parentheses mean?
Instructional Implications
Explain what it means for expressions to be equivalent (i.e., the value of each expression is the same when evaluated for the same values of the variables). Demonstrate
that two expressions [e.g., 2(a + 3) and 2a + 6] are equivalent by asking the student to evaluate each expression for various values of a. Also, provide an example of two
expressions such as 2(a + 3) and 2a + 3 and demonstrate that they are not equivalent by evaluating each expression for a particular value of a. Be sure the student
understands that a demonstration that two expressions are equivalent for a variety of values does not constitute a proof that they are equivalent. To prove two expressions
are equivalent, properties and theorems must be used.
Provide instruction on the Distributive Property and be very clear in describing what the property means. Explain that the Distributive Property of Multiplication over Addition
states that a(b + c) = ab + ac for all values of a, b, and c. Initially demonstrate the property with a numerical example, such as 4(8 + 3), by rewriting it as (4
8) + (4
3).
Then evaluate each expression using the order of operations rules to show that the expressions are equivalent. Next, demonstrate the property with algebraic expressions
such as 5(2x + 9). Initially, rewrite 5(2x + 9) as (5
2x) + (5
9) and then as 10x + 45. Describe this use of the Distributive Property as “expanding” the expression. Be
sure the student understands that the Distributive Property applies to subtractions as well since any subtraction can be rewritten as an addition. For example, an expression
such as 6(4y – 5) = 6[4y + (-5)] = (6
4y) + [6
(-5)] = 24y + (-30) or 24y – 30.
Make clear that since the Distributive Property says that a(b + c) = ab + ac for all values of a, b, and c then it is also the case that ab + ac = a(b + c) for all values of a, b,
and c. Guide the student to use the Distributive Property to rewrite expressions such as 7m + (7
3) as 7(m + 3). Describe this process as factoring since the expression is
being rewritten as a product of the factors 7 and (m + 3). Explain the usefulness of factoring by guiding the student through problem #2. Show the student that by
rewriting the expression for the area of the rectangle, 8x + 16, as 4(2x + 4), the length of the rectangle, (2x + 4), is revealed. Challenge the student to factor expressions
such as 5n + 25 and 12d – 18 in as many ways as possible using the Distributive Property.
Provide additional opportunities to both expand and factor expressions using the Distributive Property.
Making Progress
Misconception/Error
The student is able to apply the Distributive Property to expand the expression but not to factor it.
Examples of Student Work at this Level
The student rewrites 3(35 + x) as 105 + 3x but is unable to rewrite 8x + 16 as 4(2x + 4). Instead the student:
Divides one of the terms, 16, by 4.
Rewrites the expression as if it were 8(x + 16).
Indicates he or she does not know.
page 2 of 4 Substitutes four for x and evaluates the expression.
Questions Eliciting Thinking
Can you explain the Distributive Property? How is this property used?
Is there more than one way to apply the Distributive Property?
Instructional Implications
Make clear that since the Distributive Property says that a(b + c) = ab + ac for all values of a, b, and c, then it is also the case that ab + ac = a(b + c) for all values of a, b,
and c. Guide the student to use the Distributive Property to rewrite expressions such as 7m + (7 x 3) as 7(m + 3). Describe this process as factoring since the expression is
being rewritten as a product of the factors 7 and (m + 3). Explain the usefulness of factoring by guiding the student through problem #2. Show the student that by
rewriting the expression for the area of the rectangle, 8x + 16, as 4(2x + 4), the length of the rectangle, (2x + 4), is revealed.
Provide additional opportunities to both expand and factor expressions using the Distributive Property.
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 rewrites:
3(35 + x) as 105 + 3x (or 3x + 105).
8x + 16 as 4(2x + 4).
Questions Eliciting Thinking
Can you apply another property to 105 + 3x to write it in another equivalent form?
What does rewriting 8x + 16 as 4(2x + 4) reveal about the rectangle?
Instructional Implications
Provide more complex expressions for the student to rewrite using the Distributive Property such as 3x(2x + 5) and 12x + 8y – 24.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Generating 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.1.3:
Description
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to
the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression
24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce
the equivalent expression 3y.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
page 3 of 4 By applying properties of operations to generate equivalent expressions, students use properties of operations that
they are familiar with from previous grades’ work with numbers — generalizing arithmetic in the process.
page 4 of 4