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

Grade 5 Fractions

5.NF.3

About the Math

Full Standard

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers (e.g., by using visual fraction models or equations to represent the problem). For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

 

Measurement Topic

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

5th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

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

 

  
4th Grade Students Learning 5th Grade Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of division.

 

 

 

Learning Targets (I can)

  • Explain that fractions represent division with representations (i.e. 3 hoagies shared by 4 people is 3/4 of a hoagie per person)
  • Represent word problems that involve division of whole numbers.
  • Write an equation for a word problem (i.e. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? 50 ÷ 9 = ? or 50/9 = ?)
  • Represent and explain a remainder as a fraction. 

 

About the Math

When fractions represent division, the denominator acts as the divisor and the numerator is the multiplier. This means that 3/4 is three times what you get when you divide a whole into four parts. So if you were to divide 3 pancakes among 4 people ( 3 ÷ 4), each person would get 3 pieces or 3/4 of a pancake. Students need to understand that numerator is the same as the dividend and denominator is the same as the divisor. Essential vocabulary for this standard includes: mixed number, improper fraction, dividend, divisor, quotient, numerator, and denominator. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

 

Progression of Standard within Grade 5

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 that fractions represent division with representations (i.e. 3 hoagies shared by 4 people is 3/4 of a hoagie per person)
  • Represent word problems that involve division of whole numbers.
  • Write an equation for a word problem (i.e. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? 50 ÷ 9 = ? or 50/9 = ?)
  • Represent and explain a remainder as a fraction. 

 

    

 

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 4 Grade 6
  • Multiplicative comparison (4.OA.1)
  • Use the four operations to solve word problems (4.MD.2)
  • Multiply or divide to solve word problems involving multiplicative comparison (4.OA.2)
  • Understand the concept of a unit rate (6.RP.2)

 

 

 

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Instructional Tasks

TASKS

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

  • Launch the lesson by posing each problem and allowing students to work with partners to solve each prompt. Consider providing circle cut-outs for students to break into parts to represent the cookies. Before each question is solved, ask students if students will have more or less than one whole cookie?
    • Prompt: Your family’s Girl Scout Cookie order has arrived! You and your sibling are sharing the Thin Mints equally! Use your manipulatives and an equation to represent your thinking!
    • 8 cookies split between 2 people.
    • 4 cookies split between 2 people.
    • 2 cookies split between 2 people.
    • Oh No! The sleeve of cookies is almost gone and there is only 1 cookie left! Can it be split between two people? If so, how much does each person get?
    • 3 cookies split between 2 people.
    • 5 cookies split between 3 people.
    • What pattern did you notice?
  • Students will need access to post-it notes and scissors for this activity. For each scenario posed, allow students to fold or cut the post-it notes so that they can accurately represent the problem and identify a solution. Students should be able to identify a fraction that answers the question "How much of the whole?" Examples of scenarios include:
    • Five friends are sharing one sandwich equally. How much of the sub does each friend get to eat?
    • Five friends are sharing 3 cookies equally. How much cookie does each friend get to eat?
    • The four-person USA Olympic team is running a relay. If race is 6 miles long, how far will each athlete run?
  • What is the relationship between 7 divided by 8 and ⅞?
  • How do the numerator and denominator of a fraction compare with the dividend and divisor of a division expression?
  • Every kid in the car on its way to swim practice got ¾ of a sub. There were four kids. How many subs did the mom get?
  • Why do some people write ⅘ when they mean 4÷5 ?
  • Draw pictures or build models to show why ⅛ = 1 ÷ 8, why 8/3 = 8 ÷ 3 =, and why ⅜ = 3 ÷ 8
  • 15 friends want to share 3 watermelons equally. What fraction of a watermelon will each friend get?

 

 

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 4 • Fractions as Division

Fractions as Division:

 

 

 

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

 

6-8

How much for One?, Activity 8.22, Page 137
Expanded Lesson: Division-of-Fractions Stories, Pages 141-142
Hands-On Standards, Common Core Fractions

5 32-38 Lesson 1 and 2
  Hands-On Standards 5-6 48 "Lesson 15: Meaning of Division"

Math In Practice

Teaching Fifth-Grade Math

 5 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

rubric

  • Explain that fractions represent division with representations (i.e. 3 hoagies shared by 4 people is 3/4 of a hoagie per person)
  • Represent word problems that involve division of whole numbers.
  • Write an equation for a word problem (i.e. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? 50 ÷ 9 = ? or 50/9 = ?)
  • Represent and explain a remainder as a fraction. 

 

 

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.