3.NF.2 - About the Math, Learning Targets, and Rigor

Grade 3 Fractions

3.NF.A.2

About the Math

Full Standard

Understand a fraction as a number on the number line; represent fractions on a number line diagram. 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.

  1. 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.
  2. 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.

 

Measurement Topic

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

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

 

 

Report Card Measurement Topic: Demonstrates understanding of number concepts and relationships (including fractions).

 

About the Math

Skills and concepts below are learning goals for this standard.

Fractions can be represented as part of a whole. Fractions can also be represented as points on a number line. Representing fractions on a number line illustrates the value of fractions. It helps students see which fractions are close to 0, 1/2, and 1.

  • Represent any fraction (a/b) less than 1 on a number line.
  • Determine where a fraction is located on a number line by partitioning.

It is important that students work with number lines in which one is recorded in various positions. This helps students develop a deep understanding of what and how a fraction relates to a whole number. When students are continuously presented with stagnant endpoints they may show understanding that is not truly held.

  • Connect region representations of fractions with number line representations of fractions.

Students first develop an understanding of fractions as partitions of circles, rectangles, and other shapes. It is important for students to related those representations to fractions on number lines to reinforce that fractions represent quantity.

  • Represent a fraction less than 5 on a number line.

Fractions can have a value greater than one. These values can be represented on a number line as well. Third-grade students should be able to show fractions less than one and fractions greater than one on a number line using similar strategies. As students see fractions greater than one such as 7/4, they may see the connection to 1 3/4.  Conversions should not be explicitly taught.

Essential vocabulary for this standard includes: fraction, unit fraction, and number line.

 

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
 

 
  • Represent any fraction (a/b) less than 1 on a number line.
  • Determine where a fraction is located on a number line by partitioning.
  • Connect region representations of fractions with number line representations of fractions.
  • Represent a fraction less than 5 on a number line.
    

 

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
This concept is not taught prior to Grade 3.

Understand addition and subtraction of fractions (4.NF.3)

 

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Instructional Tasks

TASKS

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

  • Prepare strips of paper with a straight line drawn from one end of the strip to the other. Distribute one these strips of paper to each student. Ask students to fold their strip in half and then open it back up. Model this as students do the work as well. Ask: How much does the space from the one side to the middle represent? and from the middle to the other end? What should this point (middle) be labeled? "Yes, 1/2 because that is where we end once we have completed the journey from 0 to 1/2." Ask students to label their number line and teacher models at the same time. Now fold the strip back and then again to repeat with labeling fourths: 1/4, 2/4 (under 1/2), 3/4. You can also label 2/2 and 4/4 under one whole if space provides. Repeat with eighths if space allows.
  • Have students use fraction tiles, fraction towers and/or Cuisenaire Rods to plot equally spaced points on a blank number line.
  • Make an important connection between fractions on a number line and rulers. Customary rulers are a measuring tool that is literally fractions on a number line. Distribute a paper with multiple blank number lines drawn with exactly 12 inches between zero and one. The zero and one should be labeled before photocopying and distribution to students. 12 inches is desirable because you can divide into halves, thirds, fourths, and sixths using whole inches. Eighths can be achieved with 1 1/2 increments. You can also create 10 inch lines to work more easily with tenths and fifths.  Students should use a ruler to subdivide and label the number lines into equal parts. 
  • Provide an empty ("unticked") number line with the point ⅙ plotted on the line. Ask students to place 0 and 1 on the line. (Students can use a ruler for precision.) Provide a number line where 3/2 is plotted on the line. Ask students to place 0, 1, and 2 on the line.
  • Show 0-1 number line with ⅓ marked with a dot (unlabeled), what value do you think the dot represents?
  • Ask students to draw a number line and place the following values on the line: 0, ¼, ½, ¾, 1. Encourage students to use precision with this activity and then explain their reasoning.
  • Give students two number lines, one with endpoints of 0 and 1 and the other with endpoints marked 0 and ½ . Ask students to place ¼ on both lines. Explain why ¼ is placed differently on each number line.
  • Provide a 12 inch number line 0 and 1 as the endpoints. Have students locate and label ⅙, ¾, 2/3, and ⅚ on the line. Students should explain their reasoning.

 

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 10 • Fractions (Number Line) and Basic Facts (9s)

Represent Unit and Non-Unit Fractions on a Number Line:

 

 

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 

263 (Zero , One-Half, or One, Activity 9.5)
263 (Close Fractions, Activity 9.6,)
263 (About How Much?, Activity 9.7)
  Hands-On Standards, Common Core Fractions, Grade 3

 

 3

 
24 - 36 (Lessons 4-6)

 

 
Nimble with Numbers 4-5  4-5 108
  20 Thinking Questions for Fraction Circles, 3-6
20 Thinking Questions for Geoboards, 3-6
20 Thinking Questions for Rainbow Cubes , 3-6		 3-6
  Brain-Compatible Activities for Mathematics 2-3 2-3 70-72
Number Sense 4-6 

3

59-61

99-101
  Ten Minute Math   33

The Super Source Color Tiles 3-4 26-29

Math In Practice

Teaching Third-Grade Math

 3 Module 8

 

More Ideas

 

 

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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

Full Standard

Understand a fraction as a number on the number line; represent fractions on a number line diagram. 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.

  1. 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.
  2. 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.

 

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

 

2nd Grade Students Learning 3rd Grade Standards by Measurement Topic

Demonstrates understanding of number concepts and relationships (including fractions)

 Quarter 3

  • Represent fractions (denominators 2,3,4,6 and 8, including fractions >1) on a number line.

 

3NF2 Anecdotal Data Collection Tool Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification. 

 

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Screenshot 2023-06-12 104305.png

Rubric for Tasks (pdf) Links to an external site.

 

Exemplars for this standard (if available)

These samples are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.

 

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