3rd
Unit of Study 6: Understanding Fractions
Global Concept Guides: Area Model, Set Model, Linear Model
Prior Learning: MA.2.A.5.1
Progressions Document Link
Show What You Know Task: Go Math Ch. 7 Show What You Know
Projected Time Allotment: 12 days
Next Generation Sunshine State Standards for Mathematical Content:
Comments:
The Go Math! lessons listed below
do not match the intent of the
NGSSS grade 3 standards. Please
omit them.
 7.7
 7.8
 7.9
 7.10
MA.3.A.2.1 Represent fractions, including fractions greater than one,
using area, set, and linear model.
MA.3.A.2.2 Describe how the size of the fraction part is related to the
number of equal sized pieces in the whole.
Notes on Assessment:
Unit 6 (Modified 7)
See Common Performance Task link
below.
Unpacking the Standards for this Unit: Students express fractions as fair sharing or, parts of a whole. They use
various contexts (candy bars, fruit, and cakes) and a variety of models (circles, squares, rectangles, fraction
bars, and number lines) to develop understanding of fractions and represent fractions. Students need many
opportunities to solve word problems that require them to create and reason about fair share. Initially,
students can use an intuitive notion of “same size and same shape” (congruence) to explain why the parts are
equal, e.g., when they divide a square into four equal squares or four equal rectangles. Students come to
understand a more precise meaning for “equal parts” as “parts with equal measurements.” For example,
when a ruler is partitioned into halves or quarters of an inch, they see that each subdivision has the same
length. In area models they reason about the area of a shaded region to decide what fraction of the whole it
represents. (NCDPI, 2012, p.23)
Common Performance Task with Rubric for this Unit: Mariana’s Fractions - In this performance task, students
explore fair share and the congruence of fractional parts. Click here for the Performance Task and rubric.
Future learning: Later in grade 3, students use their understanding of fractional models to compare and order
fractions and explore equivalency. Grade 4 students learn a fundamental property of equivalent fractions:
multiplying the numerator and denominator of a fraction by the same non-zero whole number results in a
fraction that represents the same number as the original fraction. This property forms the basis for much of
their other work in Grade 4, including the comparison, addition, and subtraction of fractions and the
5
introduction of finite decimals. In grade 5, they connect fractions with division, understanding that 5÷3= 3, or,
𝑎
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1
more generally, 𝑏 = a÷b for whole numbers a and b, with b not equal to zero. They can explain this by working
with their understanding of division as equal sharing. (PCCSSM, 2012, p.11)
3rd
Global Concept 1 of 3 for this Unit of Study: Understanding Fractions Area Model
Projected Time
Allotment: 4 days
Sample Essential Questions:
Day 1: How do you know when you have shared a quantity fairly?
Day 2: How can you show fair shares in different ways?
Day 3: What do the top number and the bottom represent in a fraction?
Day 4: How do you know when a fraction is greater than one? Explain
Related Unit 3 Assessment Questions: Go Math Ch. 7 #1, 3, 9, 13, 15
Instructional Resources
Manipulatives:
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Pattern Blocks/DeciBlocks- use pattern blocks to determine fractional areas of each shape
Fraction Circles- use fraction circles to determine fractional parts
Fraction Tiles- use fraction tiles to determine fractional parts (great connection to linear model and number line)
Cuisenaire Rods- use Cuisenaire rods to determine fractional parts
Geo-boards- students can use rubber bands to split the boards into equal parts
Lesson Ideas:
 Go Math Lesson 7.2-Unlock the Problem p. 295, One Way p. 296, Another Way p. 296, p. 297-298
 Go Math Lesson 7.1-Unlock the Problem p. 291, Problem Solving p. 294
 Go Math Lesson 7.3-Unlock the Problem p. 299, On Your Own p. 301, Problem Solving p. 302
 Go Math Lesson 7.5-Unlock the Problem p. 309, Share and Show p. 310 #1-5, On your Own p. 311 #6-9, Problem
Solving p. 312
 Illuminations- Parts of a Square Utilize Lessons 1 and 2
 Voyages Excursions- Jenna’s Dilemma
Interactive Online Resources:
 Think Central Animated Math Model Part of a Whole
 For more information on teaching fractions, click here
 For more information on teaching fraction models, click here
 For more information on teaching fractions, The Meaning of Fractions
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions : Use these to facilitate student discussion
 How can you prove that there are equal parts?
 How can you represent an amount less than one?
 How do you determine the number of equal parts?
 How can you use numbers to show a part of a whole?
 How does using a model help you identify the fraction represented?
Our students are able to…
Because as teachers we…

For more info on SMP’s click here.
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
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Provide a variety of manipulatives to model fractions
(student choice) (SMP 4)
Incorporate real world sharing tasks to help students
understand fractional relationships (SMP 1, 4)
Communicate precisely using terms such as numerator,
denominator, fraction greater than one, mixed number
etc. (SMP 6)
2

Write a fraction to represent the model (SMP 2)
Create models of a given fraction (SMP 2)
Make sense of unit fractions and understand their
relationship to a whole (SMP 1, 2)
Communicate precisely using terms such as numerator,
denominator, fraction greater than one etc. (SMP 6)
Understand fractional relationships to a whole (SMP 7)
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3rd
Global Concept 2 of 3 for this Unit of Study: Understanding Fractions - Set
Model
Projected Time
Allotment: 3 days
Sample Essential Questions:
Day 1: What is the relationship between the numerator and denominator in the set model?
Day 2: How do you represent fractional amounts using the set model?
Day 3: How do you represent sets that are greater than one whole?
Related Unit 3 Assessment Questions: Go Math Ch. 7 # 12
Instructional Resources
Manipulatives:
 Two color counters- these can be used to create sets
 Centimeter cubes- these can be used to create sets
 Color Tiles- these can be used to create sets
Lesson Ideas:
 Go Math Lesson 7.6-Unlock the Problem p. 313, Fractions Greater than 1 p.314, p.315, Problem Solving 316
 Go Math Lesson - Enrich 7.6 p. E65 (use with whole group)
 Illumination-Eggsactly with fractions (Lessons 1 and 2)
 Voyages Excursions Three Ring Circus Only use student page 271 of this lesson
 Set Models- Group Tasks
Interactive Online Resources:
 For more information on teaching fractions, click here
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions: Use these to facilitate student discussion
 How do you define the whole?
 How does the set model differ from the area model?
 What is another way this set can be represented? Explain.
 How does this fraction match your model? Explain.
Our students are able to…
Because as teachers we…
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Identify sets and subsets and write the fraction that
represents it (SMP 2)
Create models of a given fraction (SMP 2)
Communicate precisely using terms such as
numerator, denominator, fraction greater than one,
mixed number etc. (SMP 6)
Understand fractional relationships to a whole (SMP
7)


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Provide a variety of manipulatives to create sets and
model fractions (SMP 4)
Highlight sets in the real world (SMP 4)
Communicate precisely using terms such as numerator,
denominator, fraction greater than one, mixed
number, etc. (SMP 6)
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3
For more info on SMP’s click here.
3rd
Global Concept 3 of 3 for this Unit of Study: Understanding Fractions Linear Model
Projected Time
Allotment: 4 days
Sample Essential Questions:
Day 1: How can I use fraction strips/tiles to create a number line?
Day 2: How can I plot and identify fractions on a number line?
Day 3: How can I use a number line to represent fractions greater than one and mixed numbers?
Day 4: How does the size of the whole affect the size of the parts?
Related Unit 3 Assessment Questions: Go Math Ch. 7 # 4, 8, 11
Instructional Resources
Manipulatives:
 Number line- create number lines to identify fractions
 Fraction Strips- Connect area model to linear model
Lesson Ideas:
 Go Math Lesson 7.4-Try This! p. 304, Share and Show p. 304 #1, pg. 305 #14-15
 Go Math Lesson 7.5- p. 311 #10-13, p. 312 #18, 20
 Fraction Number Lines
Interactive Online Resources:
 For more information on teaching fractions click here
For more information about integrating the content within this GCG, click here for the PowerPoint
Sample HOT Questions: Use these to facilitate student discussion
 How can I partition a number line to represent a fraction?
 What happens to the size of the pieces when you have a larger digit in the denominator?
 What happens to the size of the pieces when you have a smaller digit in the denominator?
 How does the size of the denominator affect the size of the jump?
Our students are able to…
Because as teachers we…
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

Identify and justify fraction locations on a number
line (SMP 3)
Create linear models of a given fraction (SMP 2)
Communicate precisely using terms such as
numerator, denominator, fraction greater than one,
mixed number (SMP 6)
Understand fractional relationships to a whole (SMP
7)



Provide a variety of manipulatives to model fractions,
including fractions on a number line (SMP 4)
Incorporate real world linear tasks to help students
understand fractional relationships and the connection
to measurement (SMP 1, 4)
Communicate precisely using terms such as numerator,
denominator, fraction greater than one, mixed
number. (SMP 6)
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4
For more info on SMP’s click here.