Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 62844
Multiplying Fractions by Whole Numbers
Students are asked to consider an equation involving multiplication of a fraction by a whole number and create a visual fraction model. Additionally,
the student is asked to interpret multiplying the number of parts by the whole number.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, equation, fraction, multiplication, word problem
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_MultiplyingFractionsByWholeNumbers_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.
1. The teacher provides the student with the Multiplying Fractions By Whole Numbers worksheet and reads aloud the following equation to the student:
x4=
2. The teacher then asks the student to create a visual fraction model for this equation.
3. Finally, the teacher asks the student to explain using the model how multiplying 2 × 4 can help determine the product of and 4.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to create a visual fraction model for the given equation.
Examples of Student Work at this Level
The student attempts to create a visual fraction model to show that
x4=
. However, even with prompting the student is unable to do so. Additionally, the student
page 1 of 4 is unable to determine how multiplying two by four can help determine the product of
and four.
Questions Eliciting Thinking
How could we show
x 2 using a visual model? What would we draw? What do you think
x 2 is equal to? Is it greater than or less than two wholes?
If I have two halves of cakes, how much cake do I have? Could you draw a picture to represent that?
Instructional Implications
Show the student that an area model can be used to multiply fractions as well as whole numbers. Begin with multiplying whole numbers by fractions as seen in the image
below. Notice that the number of columns is four; however
of each one is shaded in. Guide the student to see that the shaded area of the whole is the product of
x
4.
Consider using the MFAS task How Much Sugar? (4.NF.2.4) to assess the student’s understanding of determining the product of a fraction by a whole number such as x
4.
Making Progress
Misconception/Error
The student is unable to determine how multiplying two by four can help determine the product of
and four.
Examples of Student Work at this Level
The student says that the product of two and four is eight which is the numerator. However, the student is unable to explain that because each smaller rectangle in the
visual fraction model represents one fifth, one could multiply two by four to determine the number of fifths contained in the model of
x 4.
Questions Eliciting Thinking
What is the area of each of the smaller rectangles in your model?
What are the dimensions of each of the smaller rectangles?
What would two times four tell us in this model?
How many one fifth rectangles did you highlight? How is this related to the product of two and four?
Instructional Implications
Work with the model that the student developed and help the student determine the area of each of the smaller rectangles. Next help the student understand the
relationship between the model and multiplying two by four.
Show the student the image below and explain that the number of parts shaded in the model is the same as the product of 2 and 4. Allow the student to consider why
this is and encourage him or her to devise an explanation. Show how to use the area of the shaded section (8 rectangular units) to determine how many rectangular units
of the area
comprise the area of the
by 4 rectangle.
Got It
Misconception/Error
page 2 of 4 The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly draws a visual fraction model and states that each smaller rectangle of the visual fraction model has an area of
. So, if we can multiply two by four
to determine that there would be eight fifths.
Note: It is important that the student uses an area model since this standard requires students to interpret multiplication of a fraction by a whole number in terms of area.
Questions Eliciting Thinking
Can you describe what a visual fraction model would look like for a fraction less than one multiplied by a fraction less than one?
How is your model like the procedure for multiplying fractions?
Instructional Implications
Consider using the MFAS task Multiplying Fractions by Fractions (5.NF.2.4).
Challenge the student to use an area model to multiply fractions by fractions as seen in the image below. In this example, the product corresponds to the area of the
rectangle which has been partitioned into
by
squares, each with an area of
by
since the whole rectangle has been partitioned into 20 equal size units.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Multiplying Fractions 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
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a
sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create
a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
page 3 of 4 MAFS.5.NF.2.4:
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction
side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply
fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
When students meet this standard, they fully extend multiplication to fractions, making division of fractions in grade
6 (6.NS.1) a near target.
page 4 of 4