MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Unit Description
Big Idea(s)
What enduring
understandings are
essential for application
to new situations within or
beyond this content?
Essential Question(s)
What questions will
provoke and sustain
student engagement
while focusing learning?
Standards
Unit 5
Fraction Equivalence
Suggested Length: 3 weeks
Enduring Understanding
Develop an understanding of fraction equivalence and operations with
fractions
Enduring Skills Rubric measures competency of the following skills:
 Consistently compares two fractions with different numerators and
denominators.
 Consistently adds and subtracts fractions with like denominators.
 Decompose a fraction into a sum of fractions with the same denominator
in more than one way.
 What do the numbers in a fraction represent?
 What is the relationship between the size of the denominator and the size
of each fractional piece (i.e. the numerator)?
 How can equivalent fractions be identified?
 How can I represent fractions in different ways?
 How can I compare fractions?
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them. Students make
sense of problems involving equivalent fractions and comparing fractions.
2. Reason abstractly and quantitatively. Students demonstrate abstract
reasoning about relative size of fractions.
3. Construct viable arguments and critique the reasoning of others. Students
construct and critique arguments regarding the equivalency of fractions.
4. Model with mathematics. Students use fraction strips, fraction squares,
fraction circles, cuisenaire rods, and number lines to demonstrate
understanding of equivalent fractions.
5. Use appropriate tools strategically. Students select and use tools such as
fraction strips, fraction squares, fraction circles, cuisenaire rods, and
number lines to identify equivalent fractions.
6. Attend to precision. Students attend to the language of real-world
situations to determine if one fraction is greater than another.
7. Look for and make use of structure. Students relate the structure of
fractions to the same whole to compare fractions.
8. Look for and express regularity in repeated reasoning. Students relate the
structure of fractions to the same whole to identify multiple equivalent
fractions.
Standards for Mathematical Content
 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b)
by using visual fraction models, with attention to how the number and size
of the parts differ even though the two fractions themselves are the same
size. Use this principle to recognize and generate equivalent fractions.
Curriculum and Instruction
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
4.NF.2 Compare two fractions with different numerators and different
denominators, e.g., by creating common denominators or numerators, or
by comparing to a benchmark fraction such as 1/2. Recognize that
comparisons are valid only when the two fractions refer to the same
whole. Record the results of comparisons with symbols >, =, or <, and justify
the conclusions, e.g., by using a visual fraction model.
 4.OA.3 Solve multistep word problems posed with whole numbers and
having whole-number answers using the four operations, including
problems in which remainders must be interpreted. Represent these
problems using equations with a letter standing for the unknown quantity.
Assess the reasonableness of answers using mental computation and
estimation strategies including rounding.
 4.MD.2 Use the four operations to solve word problems involving
distances, intervals of time, liquid volumes, masses of objects, and money,
including problems involving simple fractions or decimals, and problems
that require expressing measurements given in a larger unit in terms of a
smaller unit. Represent measurement quantities using diagrams such as
number line diagrams that feature a measurement scale.
I am learning to….
4.NF.1
1. create equivalent fractions with concrete models
2. illustrate equivalent fractions with visual models
3. explain why two given fractions are equivalent
4. multiply a given fraction (less than one) by a given fraction (equal
to 1) in order to generate equivalent fractions
5. recognize equivalent fractions with different denominators
4.NF.2
1. explain why comparisons are only valid when fractions refer to the
same whole
2. identify benchmark fractions (½, ¼, and ¾)
3. compare two fractions when one of those fractions is a benchmark
fraction using <, >, and =
4. compare fractions with different numerators, e.g. by comparing to
a benchmark fraction using <, >, and =
5. compare two fractions with different denominators, e.g. by creating
common denominators, or by comparing to a benchmark fraction
6. justify the results of comparing two fractions, e.g. by using a visual
fraction model
Essential Vocabulary
equation
reasonableness
benchmark fraction
common denominator equivalent
simplify (do not use
fraction
common numerator
“reduce”)
line
plot
compare
unit fraction
numerator
visual fraction model
denominator

Supporting
Standard(s)
Which related standards
will be incorporated to
support and enhance
the enduring standards?
Instructional
Outcomes
What must students learn
and be able to do by the
end of the unit to
demonstrate mastery?
Vocabulary
What vocabulary must
students know to
understand and
communicate effectively
about this content?
Curriculum and Instruction
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Supporting Vocabulary
multi-step
Resources/Activities
What resources could we
use to best teach this
unit?
number line diagram
<(less than)
Stepping Stones (www.origoeducation.com)
4.NF.1
o Module 3: Lessons 9,10
o Module 5: Lessons 1-5
o Module 6: Lesson 9
o Module 11: Lesson 1
o Module 12: Lesson 3
4.NF.2
o Module 3: Lessons 11, 12
o Module 5: Lessons 3-5
o Module 6: Lesson 9
>(greater than)
=(equal)
Engage NY (https://www.engageny.org/resource/grade-4-mathematics)
o Module 5, all Topics
Howard County website
o https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.NF.
1
o https://grade4commoncoremath.wikispaces.hcpss.org/Assessing+4.NF.
2
K-5 Math Teaching Resources
4.NF.1
o http://www.k-5mathteachingresources.com/support-files/creatingequivalent-fractions.pdf
o http://www.k-5mathteachingresources.com/support-files/build-afraction-wall.pdf
4.NF.2
o http://www.k-5mathteachingresources.com/support-files/birthdayfractions.pdf
o http://www.k-5mathteachingresources.com/support-files/patternblock-fractions.pdf
o http://www.k-5mathteachingresources.com/support-files/who-atemore-4nf2.pdf
o http://www.k-5mathteachingresources.com/support-files/which-islarger.pdf
o http://www.k-5mathteachingresources.com/support-files/snacktime.pdf
o http://www.k-5mathteachingresources.com/supportfiles/fractioncompare4nf2.pdf
o http://www.k-5mathteachingresources.com/supportfiles/fractioncards.pdf
Curriculum and Instruction
2015-2016
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MADISON COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 4
Illustrative Mathematics
4.NF.1
o https://www.illustrativemathematics.org/contentstandards/4/NF/A/tasks/1064
o https://www.illustrativemathematics.org/contentstandards/4/NF/A/tasks/971
o https://www.illustrativemathematics.org/contentstandards/4/NF/A/1/tasks/743
o https://www.illustrativemathematics.org/contentstandards/4/NF/A/1/tasks/881
4.NF.2
o https://www.illustrativemathematics.org/contentstandards/4/NF/A/2/tasks/183
o https://www.illustrativemathematics.org/contentstandards/4/NF/A/2/tasks/811
o https://www.illustrativemathematics.org/contentstandards/4/NF/A/2/tasks/812
Illuminations
o http://illuminations.nctm.org/Search.aspx?view=search&cc=1973_1
998
o http://illuminations.nctm.org/activitydetail.aspx?id=80
Making Math Magic http://www.makingmathmagic.net/kcm.html
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. The Kentucky
Numeracy Project is also a great resource that can be searched by AVMR
strand, CCSS, and grade level. Find this resource at
http://knp.kentuckymathematics.org/#!/page_knphome. Kentucky teachers
can use it for free. Just put in your school email address and the username
“bluegrass”, and password is “math”.
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2015-2016
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Curriculum and Instruction
2015-2016
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