Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 64673
Fractions Divided by Whole Numbers
Students are given a division expression and asked to write a story context to match the expression and use a visual fraction model to solve the
problem.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, division, fraction, visual fraction model, story context
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_FractionsDividedByWholeNumbers_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
The teacher provides the student with the Fractions Divided by Whole Numbers worksheet and asks the student to create a word problem to match the expression and
use a visual fraction model to determine the quotient.
Note: The student may choose to complete this task by writing the story context first and then solve using a visual fraction model or solve using a visual fraction model
before writing the story context.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to both write a story context and use a visual fraction model to find the quotient.
Examples of Student Work at this Level
The student attempts to divide
by 4 but is unable to do so even with prompting. Additionally, the student’s story context does not accurately match the division
problem.
The student writes a word problem written as an addition, subtraction, or multiplication and is unable to determine the correct quotient.
page 1 of 4 The student is able to use a visual fraction model to model the action in the story context, but makes an error in the drawing or model. Also, the student’s story context
does not show division of a fraction by a whole number.
The story context shows division, but does not make sense within the context. For example, the student writes, “There were one out of three students eating a candy
and the student wanted to split the candy bar into four pieces.”
The story context is incomplete and the student is unable to draw a visual fraction model.
Questions Eliciting Thinking
What does division mean?
What does the problem 12 ÷ 4 mean? Can you write a word problem and draw a picture to solve that problem?
Can you think of a situation in which you have five of something that will be shared? How could you write a story to match that?
How is dividing
by 4 like dividing 12 by 4?
Can you write a story context for 12 ÷ 4? Can you use that same context for ÷ 4?
Instructional Implications
Encourage the student to apply what he or she knows about division of whole numbers to division of fractions. Have the student brainstorm a list of vocabulary terms that
suggest division (e.g., each, per, share equally). Encourage the student to compose a word problem using division of whole numbers. Then ask the student if that same
context will work if the dividend is a fraction. If not, assist the student in revising the context. Provide the student with another expression of a fraction divided by a whole
number and ask the student to create a story context to match the expression.
Provide clear instruction on how to use a visual fraction model to solve division problems involving a fraction divided by a whole number. Ensure the student understands, in
this case, the fraction is partitioned into the number of equal-sized portions given by the denominator.
Consider reading problems such as
÷ 4 as, “How can you divide into four equal sized parts?” This can help the student understand what is meant by a fraction divided
by a whole number.
Continue to provide opportunities for the student to work on writing story contexts that show division of a fraction by a whole number. Additionally, allow the student
practice solving division of fraction problems using a visual fraction model. Consider using a model like the one shown in the image below. Each color shows one of the four
equal groups created.
Making Progress
Misconception/Error
The student makes an error either in writing a story context or determining the quotient.
Examples of Student Work at this Level
The student is able to use a visual fraction model to determine the quotient but is unable to write a story context to accurately match the expression.
The student is able to write an accurate story context but:
Struggles to use a visual fraction model to determine the quotient.
Poses a question that does not correspond to the model and context.
page 2 of 4 Questions Eliciting Thinking
Read your story context again. Where do you see division in that problem?
Does your story problem show
÷ 4 or 4 ÷ ? How can we rewrite it to show
÷ 4?
Instructional Implications
Provide many examples of division story contexts in which fractions are divided by whole numbers. Initially, keep the context simple. For example, “Roberto had a bag of
candy that he wanted to share equally with each of four friends. What fraction of the bag of candy will each friend get?” Have the student write a division equation to
match the action in each problem. Then have the student use a visual model to determine the quotient.
Provide additional opportunities to write and solve word problems involving a fraction divided by a whole number and have the student explain his or her answer using a
visual model.
Consider using the MFAS task Relay Race (5.NF.2.7), which provides a story context in which a fraction is divided by a whole number.
Show the student how to use fraction tiles to find equivalent fractions for
that are divisible by four.
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’s story context matches the given division, and he or she uses a visual fraction model to determine the correct quotient as .
Questions Eliciting Thinking
What other situations can you think of in which a fraction is divided by a whole number?
Can you think of a different way to solve your problem?
How is dividing by a whole number the same as multiplying by a unit fraction (e.g., 3 ÷ 4 and 3 × )? Can this idea be applied to dividing a fraction by a whole number?
Instructional Implications
Encourage the student to explore different ways to divide a fraction by a whole number including the relationship between dividing by a whole number and multiplying by a
unit fraction.
Encourage the student to think of a variety of contexts in which a fraction is divided by a whole number.
Pair the student with a classmate at the Making Progress level. Have him or her help the Making Progress student identify situations in which fractions are divided by whole
numbers.
Provide opportunities for the student to divide a fraction by a whole number. Consider using the MFAS task Whole Numbers Divided By Fractions (5.NF.2.7).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Fractions Divided by Whole Numbers 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
page 3 of 4 MAFS.5.NF.2.7:
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by
unit fractions.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create
a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between
multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story
context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between
multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole
numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For
example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3cup servings are in 2 cups of raisins?
page 4 of 4