2014-2015 Curriculum Blueprint
Grade: 5
Course: Math
Approximate Time:
6 days
Unit 8: Interpreting Multiplying Fractions as Scaling
Learning Goal
Students will solve real-world problems involving resizing by multiplying fractions and mixed
numbers.
Link to Multiplying and Dividing Fractions Learning Scale
Unit Overview
Students build on their work with “compare” problems to develop an understanding of multiplication as
scaling. They interpret, represent, and explain situations of multiplying a fraction by a fraction. Students
apply their whole number work with multiplication to develop conceptual understanding of multiplying a
fraction by a fraction. Scaling is foundational for developing an understanding of ratios and proportions in
future grades.
Essential Question(s)
What are the results when multiplying a given number by a fraction greater than 1? Less than 1?
How can I use visual models or equations to solve real world problems involving multiplication
of fractions and mixed numbers?
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.2.5 (DOK 3) Interpret multiplication as scaling (resizing), by:
a) Comparing the size of a product to the size of one factor on the basis of the size of the
other factor, without performing the indicated multiplication.
b) Explaining why multiplying a given number by a fraction greater than 1 results in a product
greater than the given number (recognizing multiplication by whole numbers greater than
1 as a familiar case); explaining why multiplying a given number by a fraction less than 1
results in a product smaller than the given number; and relating the principle of fraction
equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
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Know that scaling (resizing) involves multiplication.
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Know that multiplying whole numbers and fractions results in products greater than
or less than one depending upon the factors.
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Compare the size of a product to the size of one factor on the basis of the size of the
other factor, without performing the indicated multiplication.
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Draw a conclusion multiplying that a fraction greater than one will result in a product
greater than the given number.
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Draw a conclusion that when you multiply a fraction by one, the resulting fraction is
equivalent.
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Draw a conclusion that when you multiply a fraction by a fraction, the product will be
smaller than the given number.
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.
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Textbook Correlation
There are no correlations in the Go Math! textbook
that align to the standards in this unit. Refer to the
supplemental materials below.
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.
5th Grade Common Core Flip Book Provides additional
information and sample problems for every standard
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Essential Vocabulary
Denominator
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Fraction
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Interpret
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Mixed number
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Multiplication
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Multiply
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Number
Numerator
Product
Scaling
Resizing
Unit fraction
Whole number
Higher Order Questions/Stems
Compare the size of a product to the size of a
factor. Examine how numbers change when we
multiply by fractions.
What are some various strategies to solve word
problems involving the multiplication of a fraction
by a mixed number?
How can comparing factor size to one help us
predict what will happen to the product?
Writing Connections
Revised 8/19/2014 pg. 1
2014-2015 Curriculum Blueprint
Grade: 5
Course: Math
Approximate Time:
6 days
Unit 8: Interpreting Multiplying Fractions as Scaling
MAFS.5.NF.2.6 (DOK 2) Solve real world problems involving multiplication of fractions and
mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
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Represent word problems involving multiplication of fractions and mixed numbers.
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Solve real world problems involving multiplication of fractions and mixed numbers.
Engage NY Module 4 (Topic F) Multiplication with
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fractions as scaling
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Georgia Unit 4 P. 90-117 Reasoning with fractions to
include scaling
Utah CCMA - Scaling
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.6.1 Attend to precision.
Problem of Month - Scaling
Performance Task - Cindy's Cats
Video - Clash of the Iguanas (teacher’s guide &
activities located on same page)
Students create a situation involving scaling.
Write to explain how the size of a factor in relation
to one will determine if the product of two factors
will increase, decrease, or remain the same.
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 8/19/2014 pg. 2