Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 114108
Complex Fractions
Students are asked to rewrite complex fractions as simple fractions in lowest terms.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Keywords: MFAS, complex fractions, simple fractions, lowest terms
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ComplexFractions _Worksheet.docx
MFAS_ComplexFractions _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 Complex Fractions worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not have an effective strategy for rewriting complex fractions as equivalent simple fractions.
Examples of Student Work at this Level
The student:
Rewrites the complex fraction as a multiplication replacing the main fraction bar with a multiplication symbol.
page 1 of 5 Rewrites the complex fraction as a division and then divides the larger numerator by the smaller numerator and the larger denominator by the smaller denominator.
Rewrites the complex fraction as a multiplication of the reciprocals of both the numerator and denominator.
Rewrites the fractions within the complex fraction in decimal form (either correctly or incorrectly) and then attempts to use long division to divide.
Questions Eliciting Thinking
Can you explain your strategy for rewriting these complex fractions?
Should 18 divided by
Should
be greater than or less than 18?
divided by 15 be greater than or less than
?
Instructional Implications
Review the concept of division of fractions using visual models. For example, guide the student to interpret a problem such as
are in
÷ as determining how many halves
. Illustrate the problem with a visual diagram such as an area or number line model. Then review strategies for dividing fractions (6.NS.1.1). Be sure the student
understands that a fraction bar can be interpreted as division so that
can be rewritten as
÷ . Guide the student to then use his or her understanding of fraction
division to rewrite complex fractions as simple fractions.
Moving Forward
Misconception/Error
The student makes an error working with fractions that is unrelated to rewriting complex fractions as simple fractions.
Examples of Student Work at this Level
The student demonstrates that he or she can correctly rewrite complex fractions as equivalent multiplications. However, the student makes another type of error when
working with fractions. For example, the student:
Rewrites 18 as a fraction in a nonequivalent form such as
Rewrites the reciprocal of 15 as
.
.
page 2 of 5 Reduces both numerators by a common factor.
Attempts to divide both the numerator and denominator by a common factor when the complex fraction is written as a division.
Questions Eliciting Thinking
Can you explain your strategy for rewriting these complex fractions?
Is 18 really equivalent to
? How can you rewrite 18 as a fraction in an equivalent form?
How can you rewrite 15 as a fraction in an equivalent form? What is the reciprocal of this fraction?
Can you explain your strategy for writing fractions in lowest terms?
Instructional Implications
Review writing whole numbers as fractions in equivalent forms and finding reciprocals. Make clear that a number such as 15 is equivalent to
. Then guide the student to
use this representation to determine the reciprocal of 15.
Review the process of reducing products of fractions before multiplying (e.g., rewriting
a numerator and a denominator by a common factor. Show the student that, for example,
as
). Be sure the student understands the rationale for dividing both
is not equivalent to
(which was obtained by dividing both
numerators in the original expression by three) by finding each product and showing that they are not equal. Also, address attempting to divide both the numerator and
denominator by a common factor in a division problem.
Provide more experience with multiplying and dividing fractions and whole numbers in the context of simplifying complex fractions.
Almost There
Misconception/Error
The student makes a computational or other minor error.
Examples of Student Work at this Level
The student correctly rewrites each complex fraction as an equivalent multiplication but:
Makes a multiplication error.
Makes an error when reducing fractions before multiplying.
Rewrites
as a mixed number as if it were
.
page 3 of 5 Writes a final answer as its reciprocal.
Does not write final answers in lowest terms.
Questions Eliciting Thinking
I think you made an error in this problem. Can you find and correct it?
Is
equivalent to 6
? What is 6
as an improper fraction?
Can you check to see if you wrote your answers in lowest terms?
Instructional Implications
If needed, assist the student in locating his or her error and ask the student to make corrections. Provide additional opportunities to rewrite complex fractions as equivalent
simple fractions in lowest terms.
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 each complex fraction as an equivalent multiplication, completes each multiplication, and writes each final answer in lowest terms.
1. 27
2.
3.
Questions Eliciting Thinking
Are there other equivalent forms in which these answers could be written?
Do you know any other strategies for writing complex fractions as simple fractions?
Instructional Implications
Introduce the student to another approach to rewriting fractions as equivalent simple fractions. For example, choose one of the complex fractions on the Complex Fractions
worksheet and ask the student to rewrite the fractions in the numerator and denominator with a common denominator (e.g., rewrite
student to find a strategy for rewriting the fraction as a simple fraction (e.g.,
=
÷ =
=
as
). Then guide the
=27). Ask the student to consider why it might be
advantageous to first rewrite the fractions in the numerator and denominator with a common denominator and when this step might be omitted.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Complex Fractions worksheet
page 4 of 5 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
MAFS.7.NS.1.3:
Description
Solve real-world and mathematical problems involving the four operations with rational numbers.
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 5 of 5