Unit #: 5
Subject(s): Math Grade(s): 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Erin Yow, Stephanie Conlon, Lori Westerholt
STAGE 1 – DESIRED RESULTS
Unit Title: Representing and Comparing Fractions
Transfer Goals: Students will be able to independently use their learning to
1. explain that unit fractions represent 1 part of a whole
2. fractions can be represented in various ways
Enduring Understandings:
Students will understand that…
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Fractions can be used to solve problems that cannot be
solved with whole numbers.
Understanding unit fractions aides in developing
understanding of other numbers.
Any number can be expressed as a fraction in an infinite
number of ways.
Students will know:
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Shapes can be partitioned into equal areas to show halves,
thirds, fourths, sixths and eighths.
Partitioning shapes into equal parts can help in
understanding fractions.
As the number of equal pieces in the whole increases, the
size of the fractional pieces decreases.
Fractional parts need to be equal sized.
The size of a fractional part is relative to the whole.
Shapes can be partitioned into equal parts to represent a
fraction.
The numerator of a fraction represents the number of equal
parts to be counted.
When a whole is cut into equal parts, the denominator
represents the total number of equal parts.
All fractions can be decomposed into a set of unit
fractions.
Fractions can represent fair share situations.
Essential Questions:
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How do equivalent fractions make problems easier to solve?
Why are unit fractions so important?
When might I use fractions in real life?
Why is the size of the whole in fractions important?
Students will be able to:
3rd Grade Expectation: Denominators of 2, 3, 4, 6, and 8
 Represent fractions using area models.
 Equally partition shapes into halves, fourths, sixths, and eighths.
 Partition shapes into equal parts and label each part as a unit fraction.
 Count a sequence of fractions that increase by 1 unit fraction (1/4, 2/4,3/4…).See
image below from page 23 of the unpacking documents.
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Create and reason about fair share situations using models and fractions.
Build a number line using the interval from 0 to 1 as the whole.
Partition a number line into a number of equal parts.
Locate a unit fraction on a number line from 0 to 1.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revised 7/27/15
1
Unit #: 5
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Subject(s): Math Grade(s): 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Erin Yow, Stephanie Conlon, Lori Westerholt
That representations of the same fraction do not need to be
congruent in shape (see image below from unpacking
document page 23)
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That two fractions are equivalent if they are the same size
or at the same point on a number line.
That when comparing fractions, the wholes must be the
same size.
Key Vocabulary: partition(ed), equal parts, fraction,
equal distance ( intervals), equivalent, equivalence,
reasonable, denominator, numerator, comparison,
compare, ‹, ›, = , justify, inequality, partition, halves,
thirds, fourths, sixths, eighths
Represent fractions (including improper fractions) on a number line. Justify the
location of fractions.
Use reasoning to explain why two fractions are equivalent.
Generate simple equivalent fractions using models.
Use models to justify writing a whole number as a/1.
Represent one as a fraction of a/a.
Compare fractions with either the same numerator or denominator. Justify conclusions
based on reasoning or visual models (area or linear).
Use <, >, = to compare fractions.
Explain reasoning for comparing fractions with the same denominator using
understanding of unit fractions.
Use appropriate mathematical language in discussions: partition(ed), equal parts,
fraction, equal distance ( intervals), equivalent, equivalence, reasonable,
denominator, numerator, comparison, compare, ‹, ›, = , justify, inequality ,
partition, halves, thirds, fourths, sixths, eighths
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revised 7/27/15
2
Unit #: 5
Subject(s): Math Grade(s): 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Erin Yow, Stephanie Conlon, Lori Westerholt
STAGE 1– STANDARDS
Domain
3.G
Standards
Reason with shapes and their attributes.
3.G.2
3.NF.1
3.NF.2
3.NF
Develop understanding of fractions as numbers.
3.NF.3
Partition shapes into parts with equal areas. Express the area of
each part as a unit fraction of the whole. For examples, partition a
shape into 4 parts with equal area, and describe the area of each part
as ¼ of the area of the shape.
Understand a fraction 1/b as the quantity formed by 1 part when a
whole is partitioned into b equal parts; understand a fraction a/b as
the quantity formed by a parts of size 1/b.
Understand a fraction as a number on the number line; represent
fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining
the interval from 0 to 1 as the whole and partitioning it into b equal
parts. Recognize that each part has size 1/b and that the endpoint of
the part based at 0 locates the number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking
off a lengths 1/b from 0. Recognize that the resulting interval has
size a/b and that its endpoint locates the number a/b on the number
line.
Explain equivalence of fractions in special cases, and compare
fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the
same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 =
2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by
using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that
are equivalent to whole numbers. Examples: Express 3 in the form
3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point
of a number line diagram.
d. Compare two fractions with the same numerator or the same
denominator by reasoning about their size. Recognize that
comparisons are valid only when the two fractions refer to the same
whole. Record the results of comparisons with the symbols >, =, or
<, and justify the conclusions, e.g., by using a visual fraction model.
8 Mathematical Practices
MP.1
Make sense of problems and persevere in solving them.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revised 7/27/15
3
Unit #: 5
Subject(s): Math Grade(s): 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Erin Yow, Stephanie Conlon, Lori Westerholt
MP.2
Reason abstractly and quantitatively.
MP.3
Construct viable arguments and critique the reasoning of others.
MP.4
Model with mathematics.
MP.5
Use appropriate tools strategically.
MP.6
Attend to precision.
MP.7
Look for and make use of structure
MP.8
Look for and express regularity in repeated reasoning.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revised 7/27/15
4
Unit #: 5
Subject(s): Math Grade(s): 3
Performance Tasks:
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Designer(s): Lauren Fisher Holland, Anissa Haney, Erin Yow, Stephanie Conlon, Lori Westerholt
STAGE 2 – ASSESSMENT EVIDENCE
Other Evidence:
CMS Performance Task –“No Fair”/Fractions Field Day
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Click here to access the resources listed above.
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NCDPI math tasks:
o 3G2 – Task 1 – Quincy’s Quiche
o 3G2 – Task 2 – Ben’s Backyard
o 3NF1- Task 1 – Building a deck
o 3NF1 – Task 4 – Selling bubble gum
o 3NF2 – Task 1 – Walking along the pond
o 3NF2 – Task 5 – All the jumps
o 3NF3 – Task 1 – Sharing pie
o 3NF3 – Task 3 – Comparing fractions
Representing Numbers on a Fraction Line
Howard County Formative and Summative Assessments
Unit 7 Summative Assessment
Rubric developed by team
Click here to access the resources listed above.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revised 7/27/15
5
Unit #: 5
Subject(s): Math Grade(s): 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Erin Yow, Stephanie Conlon, Lori Westerholt
STAGE 3 – RESOURCES FOR LEARNING PLAN
District Resources: When designing the learning plan, these
Supplemental Resources: These are considered additional resources that are
resources are intended to be a primary resource used by all teachers. recommended by the Curriculum Writing Teams. Those resources with an asterisk* may be
purchased by each individual school.
 Investigations Unit 7 investigations 1 and 2 and supplemental
 Study jams:
lessons 1.4a and 1.4b
o Fractions
o Compare Fractions
 Suggested Investigations Game: Fraction Cookie Game (Unit
o Equivalent Fractions
7, Session 2.2)
 Greg Tang: Satis Fraction game
 Discovery Education videos: Math Mastery Fractions, Make
a model with Miss Bishop
 Engage NY: Fractions as Numbers on the Number Line
 NCDPI Lessons For Learning
 Brainpop: Fractions Games: Battleship Number Line (fractions)
o “Solving Equal Sharing pProblems”(71-75 printed
 Brainpop Jr.:
version)
o “Parts of a whole”
o "Hexagon Sandwiches”(67-70 printed version)
o “Equivalent fractions”
o "Is This Duck One-Half Red?”(96-99 printed
o “More on Fractions”
version)
 Harvey’s Homepage: Domino fractions and fraction wall
o "Finding Fractional Parts of a Rectangle”(100-104
 Learn Zillion Numbers and Operations
printed version)
 LearnZillion
o “Understanding Unit Fractions”(76-95 printed
o Understanding Fractions
version)
o Fractions on a Number Line
 NCDPI Lessons for Learning
o 3.NF.1:
 Georgia Student Frameworks: Grade 3, Unit 5
o “Fraction Roll ‘em" and "Three in a Row
 Number Talks: Adding in Chunks
Gameboard”(56-57 and 59-61 printed version)
 CMS Unit – Fractions on a Number Line
o 3.NF.1 and 2:
 Domino Fraction
o "Fraction Match-up”(53-55printed version)
 Fraction Wall
o 3.NF.1 and 3:
o "Figuring Fourths" and "Figure Eighths”(58 and 62
Click here to access the resources listed above.
printed version)
o 3.NF. 2 and 3:
o "Number Line Madness”(65-66 printed version)
o 3.NF.3:
o "Capturing Hexagons”(67-69printed version)
o "Snail Nim”(70 printed version)
o 3.NF. 2
o “I Have” Fraction Cards(63-64 printed version)
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revised 7/27/15
6
Unit #: 5
Subject(s): Math Grade(s): 3
Designer(s): Lauren Fisher Holland, Anissa Haney, Erin Yow, Stephanie Conlon, Lori Westerholt
Additional resources can be found using these digital tools:
 Defined Stem (main site)
 Discovery Education (main site)
 iCurio (main site)
Click here to access the resources above.
Considerations for Differentiating Instruction (AIG, EL, EC, etc.):
These resources are intended to be used when differentiating instruction to meet the varied needs of students in your classroom.
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AIG Resources from NCDPI
Fraction Creativity
Fraction Flags
What’s the Fractional Part Lesson
ESL Investigations Cookie Game in Spanish
Click here to access the resources listed above.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revised 7/27/15
7