3.NF.1 - About the Math, Learning Targets, and Rigor

Grade 3 Fractions

3.NF.A.1

About the Math

Full Standard

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. Note: Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8. It includes fractions greater than 1.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

3rd Grade Students Learning 3rd Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 

 

Report Card Measurement Topic: Demonstrates understanding of number and fraction concepts.

 

 

Learning Targets

  • Explain and represent a unit fraction.
  • Explain and represent a non-unit fraction.
  • Describe numerator and denominator.
  • Represent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction circles, and other region or set models.
  • Explain how representations are related.

 

About the Math

One meaning for a fraction is a number that represents a part of the whole. When a fraction is used to describe part of a region, the whole needs to be divided into equal parts. When dividing a region into equal parts, it is not necessary that the parts have the same shape as long as they have the same area.

Third-grade students should work with denominators of 2, 3, 4, 6, and 8. Students should work with fractions greater than 1. Students should not be introduced to the algorithm for converting improper fractions to mixed numbers or vice versa. Instead, students should understand the equal partitions of a whole and that those partitions can continue beyond 1

  • Explain and represent a unit fraction.

A unit fraction is 1 part of a whole divided into equal parts. The size of those parts can vary infinitely. In third grade, students work with equal parts of 2, 3, 4, 6, and 8. A unit fraction can be represented in a variety of ways.

  • Explain and represent a non-unit fraction.

A non-unit fraction is a fraction composed of more than one unit-fractions. For example, 2/3 is a non-unit fraction. It is composed of 2 one-thirds. Like unit fractions, non-unit fractions can be represented in a variety of ways.

  • Describe numerator and denominator.

A denominator identifies the number of equal parts the whole is divided into. A numerator identifies a number of equal parts that are under consideration (what we are discussing, whether it be shaded or unshaded). Students should work with a variety of fraction representations. Be careful not to reinforce that the shaded amount is always the numerator. 

  • Represent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction circles, and other region or set models.

Students should be comfortable representing fractions with all of the tools mentioned in the learning target. 

  • Explain how representations are related.

Students should understand how representations of the same fraction are related. Students should be able to represent any fraction in multiple ways. Essential vocabulary for this standard includes fraction, whole, equal parts, unit fraction, numerator, and denominator.

Fraction Videos


 

 

Progression of Standard within Grade 3

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4

 
  • Explain and represent a unit fraction.
  • Explain and represent a non-unit fraction.
  • Describe numerator and denominator.
  • Represent fractions with color tiles, pattern blocks, Cuisenaire rods, fraction circles, and other region, area, and set models.
  • Explain how representations are related.

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 2 Grade 4
  • Partition circles and rectangles into two, three, or four equal shares (2.G.A.3)
  • Compare measurements of different units (2.MD.A.2)
  • Understand a fraction a/b with a > 1 as a sum of fractions 1/b.  ( 4.NF.3)
  • Multiply a fraction by a whole number (4.NF.4)

 

 

 

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Instructional Tasks

Tasks

 These tasks can be used with small group or whole group instruction.

  • Provide students with Cuisenaire rods (one set per pair of students) and ask students to find a brown rod. Ask "Can you find a different color rod that is one half of the brown? How do you know?" After establishing this first example, then give students time to find all examples of one-half with the rods. Discuss what the numerator and demoninator represents in 1/2 and how that is connected to the rod representations. Repeat with fourths and thirds, continuing to ask students to justify their representations. 
  • Provide students with a color tile and tell them it represents 1/4. What could the whole look like? The discussion should be include the definition of denominator and numerator as well as equal partitions. Repeat where one color tile represents  ⅛ and what could the whole look like?
  • Using fraction manipulatives, ask students to build the unit fractions ⅓, 1/6 and ⅛.  Ask students to notice what they observe as the denominator changes and the numerator stays the same.  Discussion should center around the big idea of how when the same size whole is equally divided into more parts, the parts are smaller; the denominator gets bigger, the parts get smaller.
  • Using geoboards, prompt students to find how many different ways to show one-half of the largest square. Discuss and connect the different representations. Repeat with fourths and then eighths. 
  • Tell about a time when you would use ½.
  • Show three different representations of ¾.
  • Using a fractions manipulative set, show students ⅝ and ask students what fractions are needed to make 8/8. (This is not about subtraction of fractions, it is about counting on 6/8, ⅞, 8/8 to find the answer.)
  • Think of two real-life situations where you would use fractions.
  • Use pattern blocks and have students identify what each shape represents if the whole is a hexagon. What does each pattern block represent if the trapezoid is the whole? If the rhombus is the whole? If the triangle is the whole?

 

Slide-Based Tasks 

These links are HCPSS created instructional tasks. These tasks are provided in Google slides.  These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 9 • Fractions (Representing)

Represent Unit and Non-unit Fractions with Region/Area Models:

 

 

Additional Tasks

These links provide instructional ideas connected to this standard. 

 

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics  K-3   257 (Correct Shares, Activity 9.1)
257 (Finding Fair Shares, Activity 9.2)
258 (More, Less, or Equal to One Whole, Activity 9.3)
270 (Group the Counters, Find the Names, Activity 9.14)

  Hands-On Standards, Common Core Fractions, Grade 3

 

 3

 
Lessons 1, 2, and 3

 

 
  Hands On Standards (3-4) 3-4 44 (Identify and Write Fractions)
46 (Fractional Pairs)
  Hands On Standards (1-2) 1-2 60-61 (Recognizing Fractions)
62-63 (Identifying Simple Fractions)
  NumberSense 4-6

149-151

154-156
  Problem Driven Math 3 93 - 95 (Robot Round-Up)
  20 Thinking Questions for Rainbow Cubes 3-6 42 and 46
  SuperSource: Snap Cubes
SuperSource: Tangrams
SuperSource: Color Tiles

K-2

K-2
3-4

 62-65
50-53
34-37, 46-49
  Brain-Compatible Activities for Mathematics 2-3

Brain-Compatible Activities for Mathematics 4-5

2-3

4-5

 62-64, 73-76

42-46

Math In Practice

 Teaching Third-Grade Math

3

 Module 8

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

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Assessment

Learning Targets

  • Explain and represent a unit fraction.
  • Explain and represent a non-unit fraction.
  • Describe numerator and denominator.
  • Represent fractions with color tiles, pattern blocks, cuisenaire rods, fraction circles, and other region or set models.
  • Explain how representations are related.

 

 

Learning targets identify what students should be able to do.  This rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

 

Visit the SBIR (Standards Based Instruction and Reporting) tab in Course Essentials for more information and clarification. There you will find the measurement topic crosswalk, report card comments, links to professional learning/resources and guidance.  

 

 

 

 

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 This course content is offered under a CC Attribution Non-Commercial Share Alike Links to an external site. license. Content in this course can be considered under this license unless otherwise noted.