Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 57164
Applying Rational Number Properties
Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, fractions, rational numbers, properties, distributive, commutative, associative
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ApplyingRationalNumberProperties_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 Applying Rational Number Properties worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student uses incorrect strategies to multiply rational numbers.
Examples of Student Work at this Level
The student multiplies mixed numbers by multiplying all the whole numbers then multiplying all the fraction parts.
page 1 of 4 The student completes calculations by working from left to right rather than using the correct order of operations.
The student rewrites fractions with common denominators instead of multiplying them.
Questions Eliciting Thinking
How do you multiply fractions?
How do you multiply mixed numbers?
What steps did you use to multiply the mixed numbers? Are there any other steps you should take when multiplying mixed numbers?
In what order did you do your operations for #2? How should you decide which order to do operations in when there are several in a problem? What is the correct order of
operations?
Instructional Implications
Review multiplication of fractions and mixed numbers. Guide the student to interpret mixed numbers such as
Property and apply it to multiplying mixed numbers by whole numbers (e.g.,
numbers by mixed numbers (e.g., rewrite
as
as sums, e.g.,
. Then review the Distributive
). Next use the Distributive Property to multiply mixed
). Then rewrite the expression by applying the Distributive Property (e.g.,
).
Continue using the Distributive Property to complete the calculation.
Review other properties such as the Commutative Properties, the Associative Properties, the Additive and Multiplicative Inverse Properties and guide the student to look for
opportunities to use these properties as strategies for adding, subtracting, multiplying, and dividing rational numbers. Provide examples in which these properties have been
employed and ask the student to identify the use of the properties.
Moving Forward
Misconception/Error
The student evaluates the expressions using order of operations rather than properties.
Examples of Student Work at this Level
The student evaluates the expressions using order of operations rather than properties. The student may make a minor error.
Questions Eliciting Thinking
You did a good job using order of operations, but can you think of any properties of operations that you could have used to make your work easier?
What properties do you remember? How does each one work?
Can you read through your problem to look for any math errors?
Instructional Implications
Show the student how properties of operations could have been used to complete the two problems on the worksheet. Review other properties of operations and guide
the student to look for opportunities to use these properties as strategies for adding, subtracting, multiplying, and dividing rational numbers. Provide examples in which
these properties have been employed and ask the student to identify the use of the properties.
Almost There
page 2 of 4 Misconception/Error
The student uses properties of operations as the strategy to multiply rational numbers but is unable to identify the use of properties in his or her work.
Examples of Student Work at this Level
The student demonstrates the use of the properties but is unable to identify the properties used. The student:
Rearranges the factors in #1 to multiply
before multiplying by the factor
.
Factors out a seven from each term in #2 before adding the mixed numbers.
Questions Eliciting Thinking
How did you rearrange the expression you wrote in your work? How do you know you can change it like that?
What is it called to rearrange/regroup the factors?
Why did you factor out the seven? What property ensures that the answer will be the same as that of the original expression when you use this strategy?
Instructional Implications
Identify the properties of operations used by the student in his or her work. Provide examples in which these properties have been employed and ask the student to
identify the use of the properties. Pair the student with a Got It student to compare answers and reconcile differences.
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 rewrites
as
and finds the product of
and 3 mentally. The student correctly finds the product of 4 and
and
indicates a use of the Commutative and Associative Properties to reorder and regroup the factors to get an answer of 10.
The student rewrites
as
and correctly completes the calculation by mentally adding
and
and then multiplying the sum by 7 getting a
final answer of 42. The student indicates having used the Distributive Property.
Questions Eliciting Thinking
Can these properties be used with all kinds of numbers (e.g., whole numbers, integers, rational numbers, and irrational numbers)?
Is there a Commutative Property of Subtraction? Why or why not?
Is there a Commutative Property of Division? Why or why not?
Instructional Implications
Ask the student to make a comprehensive list of properties of operations that includes explanations and examples. Provide an opportunity for the student to copy and share
the list with classmates. Consider using other MFAS tasks related to multiplication and division of rational numbers from 7.NS.1.2 as well as tasks with rational number addition
and subtraction in 7.NS.1.1.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Applying Rational Number Properties 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
Description
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational
numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue
to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) =
1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world
contexts.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with
page 3 of 4 MAFS.7.NS.1.2:
non­zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients
of rational numbers by describing real-world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number
terminates in 0s or eventually repeats.
Remarks/Examples:
Fluency Expectations or Examples of Culminating Standards
Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four
basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers
by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex
numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number
arithmetic in later grades and because so much other work in grade 7 depends on rational number arithmetic,
fluency with rational number arithmetic should be the goal in grade 7.
page 4 of 4