MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
Unit
Description
Unit 6
Operations with Fractions
Suggested Length: 6 weeks
Big Idea(s)
Enduring Understanding(s)
 Develop fluency with fraction operations of addition & subtraction
 Develop understanding of fraction multiplication & division
What
enduring
understandin
gs are
essential for
application
to new
situations
within or
beyond this
content?
Enduring Skills Rubric measures competency of the following skills:
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Essential
Question(s)
What


Solves word problems involving addition and subtraction of
fractions, using equivalent fractions in cases of unlike denominators
by using visual fractions or equations
Recognizes reasonableness of answer using benchmark fractions
Uses equivalent fractions to add/subtract fractions and/or mixed
numbers with unlike denominators
Constructs and communicates a well-organized and complete
written response using a logical progression of steps.
Makes a line plot to display a data set of measurements in fractions
of a unit with denominators limited to 2, 4, and 8, and uses
operations on fractions to solve problems involving information on
line plots
Solves word problems involving division of whole numbers leading
to answers in the form of fractions or mixed numbers AND interprets
the fraction as division of the numerator by the denominator AND
identifies a simple model representing the situation.
Solves real world problems by multiplying a mixed number by a
fraction, a fraction by a fraction, and a whole number by a
fraction and interprets the product by using given context
Solves real world problems by dividing a fraction by a whole
number and a whole number by a fraction using visual fraction
models and interpreting the quotient by using given context
Multiplies a mixed number by a fraction, a fraction by a fraction,
and a whole number by a fraction and interprets the product
Divides a fraction by a whole number and a whole number by a
fraction using visual fraction models and interpreting the quotient
Assesses reasonableness of a product of two fraction factors
without performing the multiplication with either factor being
greater or less than one
How can I solve real-world problems that involve addition and
subtraction of fractions?
How does multiplying fractions relate to real world problems?
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
questions will
provoke and
sustain
student
engagement
while
focusing
learning?
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

How do I show multiplication of fractions using a visual model?
How does dividing fractions relate to real world problems?
How do I show division of fractions using a visual model?
Standards
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students
2.
3.
4.
5.
6.
7.
8.
make sense of the meaning of addition, subtraction, multiplication
and division of fractions with whole- number multiplication and
division.
Reason abstractly and quantitatively. Students demonstrate
abstract reasoning to create and display area models of
multiplication and both sharing and measuring models for division.
They extend this understanding from whole numbers to their work
with fractions.
Construct viable arguments and critique the reasoning of others.
Students construct and critique arguments regarding their
understanding of fractions greater than, equal to, and less than
one whole and one half. Students recognize reasonable answers
when performing operations with fractions.
Model with mathematics. Students draw representations of their
mathematical thinking as well as use words and numbers to explain
their thinking
Use appropriate tools strategically. Students select and use tools
such as visual models, measuring sticks/line plots, and
manipulatives of different fraction sizes to represent situations
involving the relationship between fractions.
Attend to precision. Students attend to the precision when
performing operations with fractions. Students use appropriate
terminology when referring to fractions.
Look for and make use of structure. Students develop the concept
of all operations with fractions with fractions including drawing
visual representations and working with like and unlike
denominators through the use of various manipulatives
Look for and express regularity in repeated reasoning. Students
relate new experiences to experiences with similar contexts when
allowing students to develop relationships for fluency and
understanding of fractional computation. Students explore
operations with fractions with visual models and begin to formulate
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
generalizations.
Standards for Mathematical Content
5.NF.1 Add and subtract fractions with unlike denominators (including
mixed numbers) by replacing given fractions with equivalent
fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators. For example, 2/3 +
5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.2 Solve word problems involving addition and subtraction of fractions
referring to the same whole, including cases of unlike
denominators, e.g., by using visual fraction models or equations to
represent the problem. Use benchmark fractions and number sense
of fractions to estimate mentally and assess the reasonableness of
answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7,
by observing that 3/7 < 1/2.
5.NF.3
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?
5.NF.4
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 appropriate unit fraction side
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
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.
5.NF.5
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.
5.NF.6 Solve real world problems involving multiplication of fractions and
mixed numbers, e.g., by using visual fraction models or equations to
represent the problem.
5.NF.7 Apply and extend previous understandings of division to divide unit
fractions by whole numbers and whole numbers by unit fractions.
(Note: Students able to multiply fractions in general can develop
strategies to divide fractions in general, by reasoning about the
relationship between multiplication and division. But division of a
fraction by a fraction is not a requirement at this grade.)
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
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
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 1/3-cup servings are in 2 cups of raisins?
Supporting 5.MD.1
Convert among different sized standard measurement units
Standard(s)
within a given measurement system (e.g., convert 5 cm to 0.05 m),
Which related
and use the conversion to solve multi-step real world problems.
standards will
be
incorporated
to support
and enhance
the enduring
standards?
Instruction
al
Outcomes
What must
students learn
and be able
to by the end
of the unit to
demonstrate
mastery?
Vocabular
y
What
vocabulary
must students
know to
understand
5.MD.2 Make a line plot to display a data set of measurements in
fractions of a unit (1/2, ¼, 1/8). Use operations on fractions for this
grade to solve problems involving information presented in line
plots.
I am learning to…
 Calculate equivalent fractions in order to add or subtract fractions
and mixed numbers
 Interpret the product of a multiplication problem based on the size
of the factors
 Explain the inverse relationship between multiplication and division
 I can explain how fractions are related to division by using models
and/or equations
 I can solve word problems that include division of whole numbers
and explain the quotient as it relates to whole numbers, mixed
numbers, or fractions
 Model the multiplication of fractions
b ab

when multiplying fractions
c
c
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Explain why a 
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Model the division of whole numbers and fractions
Solve real world problems that require operations of fractions
Use benchmark fractions to determine reasonability of an answer
Essential Vocabulary
Area model
Array
Denominator
Dividend
Divisor
Equal parts
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
and
communicat
e effectively
about this
content?
Resources
& Activities
What
resources
could we use
to best teach
this unit?
Equivalent fraction
Factor
Fraction
Improper fraction
Like/common denominator
Mixed number
Numerator
Of
Product
Quotient
Skip count
Unit fraction
Supporting Vocabulary
Associative property
Distributive property
half
Inverse relationship
Remainder
Whole
Stepping Stones
(www.origoeducation.com)
5.NF.1
o Module 2: Lessons 1-5
o Module 4: Lessons 1-7
o Module 6: Lessons 2-7
5.NF.2
o Module 4: Lesson 8
o Module 6: Lesson 8
o Module 9: Lesson 9
5.NF.3
o
Module 11: Lessons 1-2
o
Module 9: Lessons 1-8
5.NF.4
5.NF.5
o
Module 9: Lesson 4,6,7
o
Module 9: Lessons 8-9
o
Module 11: Lessons 3-8
5.NF.6
5.NF.7
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
Engage NY
(https://www.engageny.org/resource/grade-5-mathematics)
5.NF.1
o Module 3: Topics A, B, C, D
5.NF.2
o Module 3: Topics B, C, D
5.NF.3
o Module 4: Topic B
5.NF.4
o Module 4:Topics C, D, E
o Module 5: Topic C
5.NF.5
o Module 4: Topic F
5.NF.6
o Module 4: Topics D, E, F
o Module 5: Topic C
5.NF.7
o
Module 4: Topic G
Howard County Website
(https://grade5commoncoremath.wikispaces.hcpss.org/home)
K-5 Math Teaching Resources
5.NF.1
o http://www.k-5mathteachingresources.com/support-files/creatingequivalent-fractions-to-add-unlike-fractions1.pdf
o http://www.k-5mathteachingresources.com/support-files/creatingequivalent-fractions-to-subtract-unlike-fractions.pdf
o http://www.k-5mathteachingresources.com/support-files/fractionword-problems-unlike-denominator.pdf
o http://www.k-5mathteachingresources.com/support-files/addingmixed-numbers-with-unlike-denominators.pdf
o http://www.k-5mathteachingresources.com/supportfiles/subtracting-mixed-numbers-with-unlike-denominators.pdf
o http://www.k-5mathteachingresources.com/supportfiles/magicsquaresadditionfractions.pdf
o http://www.k-5mathteachingresources.com/support-files/closestto-25.pdf
o http://www.k-5mathteachingresources.com/support-files/the-sumof-two-mixed-numbers.pdf
o http://www.k-5mathteachingresources.com/support-files/thedifference-between-2-mixed-numbers.pdf
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6
o
o
http://www.k-5mathteachingresources.com/support-files/thewishing-club-1.pdf
http://www.k-5mathteachingresources.com/support-files/thewishing-club-2.pdf
5.NF.2
o http://www.k-5mathteachingresources.com/supportfiles/fractionwordproblem1.pdf
o http://www.k-5mathteachingresources.com/supportfiles/fractionwordproblem2.pdf
5.NF.3
o http://www.k-5mathteachingresources.com/support-files/relatingfractions-to-division.pdf
5.NF.4
o http://www.k-5mathteachingresources.com/supportfiles/multiplying-fractions-by-dividing-rectangles.pdf
o http://www.k-5mathteachingresources.com/support-files/fractionx-fraction-word-problems.pdf
o http://www.k-5mathteachingresources.com/support-files/areaword-problems-fractional-side-lengths-5nf4b.pdf
5.NF.5
o http://www.k-5mathteachingresources.com/supportfiles/multiplication-and-scale-problems.pdf
5.NF.6
o http://www.k-5mathteachingresources.com/support-files/fractionx-mixed-no.-word-problems-5nf6.pdf
o http://www.k-5mathteachingresources.com/support-files/wholenumber-x-mixed-number-models.pdf
o http://www.k-5mathteachingresources.com/support-files/mixednumber-x-fraction-models.pdf
5.NF.7
o http://www.k-5mathteachingresources.com/support-files/divide-aunit-fraction-by-a-whole-number.pdf
o http://www.k-5mathteachingresources.com/support-files/dividinga-whole-number-by-a-unit-fraction-ver.2.pdf
o http://www.k-5mathteachingresources.com/support-files/divide-awhole-number-by-a-unit-fraction.pdf
o http://www.k-5mathteachingresources.com/supportfiles/divisionoffractionwordproblems.pdf
Created by Beth Richardson (Elizabeth.richardson@madison.kyschools.us):
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 5
Unit 6

Fraction of the Day
http://www.commoncoresheets.com/Fractions.php
Making Math Magic
http://www.makingmathmagic.net/kcm.html
Teachers Pay Teachers
Dividing Fractions Task Cards (TPT $2.75):
https://www.teacherspayteachers.com/Product/Dividing-Fractions-TaskCards-Divide-with-Visual-Models-660430
Multiplying Fractions Task Cards (TPT $2.50):
https://www.teacherspayteachers.com/Product/Multiplying-FractionsTask-Cards-Multiply-with-Visual-Models--623369
Adding and Subtracting Fractions Task Cards (TPT $2.50):
https://www.teacherspayteachers.com/Product/Adding-SubtractingFractions-Task-Cards-Add-Subtract-UNLIKE-denominators--594267
Common Core Assessment Pack-Common Core Grade 5 (TPT $12.50):
https://www.teacherspayteachers.com/Product/Common-CoreAssessment-Pack-Math-Grade-5-411127
Illustrative Mathematics
o https://www.illustrativemathematics.org/content-standards/5
Illuminations
o http://illuminations.nctm.org/Search.aspx?view=search&cc=2014_2
024
Remember there are other sources in your school that may not be
listed on this common resources list due to variation in each individual
school. Examples of other great resources your school may have
access to include: Everyday Math Games, Investigations, Everyday
Partner Games, AVMR file folders, Ongoing Assessment Project, etc.
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