2014-2015 Curriculum Blueprint
Grade: 5
Course: Math
Approximate Time:
12 days
Unit 7: Understanding the Concept of Multiplying Fractions by Fractions and Interpreting a
Fraction as Division
Learning Goal
Students will solve real-world problems involving multiplication of fractions and mixed
numbers.
Unit Overview
Students extend their understanding of multiplying fractions by a whole number to multiplying fractions by
fractions. In previous grades students have developed understanding of fractions as numbers. Students
develop an understanding between fractions and division.
Link to Multiplying and Dividing Fractions Learning Scale (use only the indicators from this unit)
Essential Question(s)
How can I interpret a fraction as division?
How can I find and represent the area of a rectangle if one of the lengths is a fraction?
How can I interpret and model the product of a fraction problem?
Focus Standards
Some standards may be revisited several times during the course; others may be
only partially addressed in different units, depending on the focus. The text of the
standards written in black font denote this focus. Text which is deemphasized with
gray font will not be addressed in this unit, but will be addressed in subsequent
units. (adapted from the Charles A. Dana Center)
Bullets are the deconstructed standards These should be used to develop concise learning
statements/daily objectives/scales. Grade 5 Test Item Specifications
MAFS.5.NF.2.3 (DOK 2) Interpret a fraction as division of the numerator by the denominator
(a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in
the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to
represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that
3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each
person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by
weight, how many pounds of rice should each person get? Between what two whole numbers
does your answer lie?
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Interpret a fraction as division of the numerator by the denominator.

Interpret the remainder as a fractional part of the problem.

Solve word problems involving division of whole numbers leading to answers in the
form of fractions or mixed numbers.
MAFS.5.NF.2.4 (DOK 2) 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.)
b) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the
Vertical Progression
http://www.turnonccmath.net/ K-8 Learning Trajectories (This could be used to determine remediation needs
or enrichment opportunities)
4th Grade
Students solve word problems involving multiplication of a fraction by a whole number
6th Grade
Students solve word problems involving division of fractions by fractions.
Resources
*Be selective in choosing problems aligned to the
standards within each lesson. The unit sequence
should be determined through collaborative unit
planning.
Textbook Correlation
End of Year Resources
Lessons 3 Repeated addition with fractions
Lesson 4 Repeated subtraction with fractions
Please refer to the Supplemental Resources for

support in teaching to the full intent of the standards.
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Supplemental Resources
These resources may provide students with

experiences aligned to the full intent of the standards.

It is important to access many of these resources

during the planning process.

th
5 Grade Common Core Flip Book Provides additional 
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Essential Vocabulary
Denominator

Division

Greater than

Interpret
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Less than
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Mixed number

Multiplication

Number
Numerator
Product
Scaling
Unit fraction
Whole number
Area
Higher Order Questions/Stems
How can decomposing fractions help us multiply
fractions?
Why should we use models to solve problems with
fractions?
How can we model an area with fractional pieces?
How else can you model this problem?
How would you model this equation?
Interpret the product of a fraction.
Can you explain the relationship between the
Revised 10/27/2014 pg. 1
2014-2015 Curriculum Blueprint
Grade: 5
Course: Math
Approximate Time:
12 days
Unit 7: Understanding the Concept of Multiplying Fractions by Fractions and Interpreting a
Fraction as Division
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.

Multiply fractions by whole numbers.

Multiply fractions by fractions.

Interpret the product of fractions times a whole number as total number of parts of
the whole.

Determine the sequence of operations that results in the total number of parts of
the whole.

Interpret the product of a fractions times a fractions as the total number of parts of
the whole.

Represent fraction products as rectangular areas.

Justify multiplying fractional side lengths to find the area is the same as tiling a
rectangle with unit squares of the appropriate unit fraction side lengths.

Find area of a rectangle with fractional side lengths using different strategies.

Model the area of rectangles with fractional side lengths with unit squares to show
the area of rectangles.
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.4.1 Model with mathematics.
MAFS.K12.MP.5.1 Use appropriate tools strategically.
information and sample problems for every standard
numerator and denominator?
Georgia Unit 4 Multiplying fraction tasks

Engage NY Module 4 (Topic C, E) Multiplication of
fractions
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Lesson: Stuffed with Pizza

Lesson: Time for Recess
Fraction Times Fraction or Whole Number
Performance Task - Cindy's Cats
Problem of Month - Party
Teaching Channel: Multiplying Fractions
Writing Connections
Student will write a context (story problem) for a
given equation.
Write to explain why multiplying a given number by
a fraction less than one results in a product smaller
than the given number.
Represent the problem you are solving and explain
your model.
Writing Template Tasks These template tasks are
designed from the Mathematical Practice Standards.
When filled in, these templates become teaching tasks
that create opportunities for teaching literacy skills in
mathematics.
Link to Problem Solving Rubric
Link to Webb’s DOK Guide
Illustrative Mathematics Tasks Search for tasks by
standard
Florida Interim Assessment Item Bank and Test
Platform
Revised 10/27/2014 pg. 2