Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 114866
Positive and Negative Fractions
Students are asked to add, subtract, multiply, and divide positive and negative fractions.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Keywords: MFAS, fractions, rational numbers, positive, negative
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_PositiveAndNegativeFractions _Worksheet.docx
MFAS_PositiveAndNegativeFractions _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 Positive and Negative Fractions worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to correctly compute with fractions.
Examples of Student Work at this Level
The student uses an incorrect strategy for either adding, subtracting, multiplying, or dividing fractions. The student may also have difficulties computing with positive and
negative numbers.
page 1 of 4 Questions Eliciting Thinking
Can you explain your strategy for adding (subtracting, multiplying, or dividing) these fractions?
Can you explain why you need a common denominator to add and subtract fractions?
Does the fact that some of the fractions are negative alter your strategy? How would you have added (subtracted, multiplied, or divided) these fractions if both were
positive?
Instructional Implications
If needed, review the concept of a fraction, specifically the meaning of both the numerator and the denominator. Provide models to illustrate equivalent fractions and
review computational methods for creating sets of equivalent fractions. Review strategies for adding, subtracting, multiplying, and dividing fractions. Assist the student in
understanding the need for a common denominator when adding and subtracting fractions. Once the student is proficient computing with fractions, review computing with
integers. Then introduce computing with rational numbers. Provide opportunities for the student to work with rational numbers in a variety of contexts. Include rational
numbers in both real-world and mathematical situations.
Moving Forward
Misconception/Error
The student is unable to correctly compute with integers.
Examples of Student Work at this Level
The student can correctly add, subtract, multiply, and divide fractions but makes errors related to the signs of the fractions.
Questions Eliciting Thinking
Can you explain your strategy for adding (subtracting, multiplying, or dividing) integers?
Does the fact that these numbers are fractions alter your strategy for computing with positive and negative numbers? How would you have added (subtracted, multiplied,
or divided) these numbers if they were whole numbers with the same signs instead of fractions?
Instructional Implications
Review how to add, subtract, multiply, and divide integers. Then assist the student in applying strategies for working with integers to rational numbers. Provide additional
opportunities to add, subtract, multiply, and divide rational numbers in both real-world and mathematical situations.
Almost There
Misconception/Error
The student makes a computational or other minor error.
Examples of Student Work at this Level
The student appears to understand how to compute with rational numbers. However, the student:
Makes an error when rewriting an improper fraction as a mixed number.
Makes an error when reducing fractions while multiplying.
page 2 of 4 Drops a negative symbol from the final answer.
Questions Eliciting Thinking
I think you made an error in this problem. Can you find and correct it?
Should this product be positive or negative? Why?
Instructional Implications
If needed, assist the student in locating his or her error and ask the student to make corrections. Provide additional opportunities to add, subtract, multiply, and divide
rational numbers in both real-world and mathematical situations.
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 completes each problem with work coherently shown getting answers equivalent to:
1.
2. 3
3. -2
4.
Questions Eliciting Thinking
Are there other equivalent forms in which these answers could be written?
How is computing with positive and negative fractions the same as or different from computing with positive and negative whole numbers?
Do you know any other strategies for adding, subtracting, multiplying, or dividing fractions?
Instructional Implications
If the student did not write answers as fractions in lowest terms, ask the student to do so. Challenge the student to find, explain, and justify another correct strategy for
dividing fractions.
Provide additional opportunities to add, subtract, multiply, and divide rational numbers in real-world situations.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Positive and Negative Fractions worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Solve real-world and mathematical problems involving the four operations with rational numbers.
page 3 of 4 MAFS.7.NS.1.3:
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
When students work toward meeting this standard (which is closely connected to 7.NS.1.1 and 7.NS.1.2), they
consolidate their skill and understanding of addition, subtraction, multiplication and division of rational numbers.
page 4 of 4