MAFS.5.NF.2.3Archived Standard

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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?
General Information
Subject Area: Mathematics
Grade: 5
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    Quotients in division items may not be equivalent to a whole number. Items may contain fractions greater than 1. Items may not use the terms “simplify” or “lowest terms.” Only use whole numbers for the divisor and dividend of a fraction. For given fractions in items, denominators are limited to 1-20.
  • Calculator :

    No

  • Context :

    Allowable

Sample Test Items (3)
  • Test Item #: Sample Item 2
  • Question:

    Joe has a board that is 6 feet long. He needs to cut the board into 15 equal-length pieces.

    How many feet long should each piece of the board be?

  • Difficulty: N/A
  • Type: EE: Equation Editor
  • Test Item #: Sample Item 3
  • Question:

    An art teacher gives a total of 35 pounds of clay to her students. She gives each of her 16 students the same amount of clay.

    How many pounds of clay does each student get?

  • Difficulty: N/A
  • Type: EE: Equation Editor

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5020120: STEM Lab Grade 5 (Specifically in versions: 2016 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Formative Assessments

Two Thirds:

Students are asked to interpret a fraction and write a word problem to match the context of the fraction.

Type: Formative Assessment

Five Thirds:

Students are asked to interpret an improper fraction and then write a word problem to match the context of the fraction.

Type: Formative Assessment

Sharing Brownies:

Students are asked to draw a visual fraction model to solve a division word problem.

Type: Formative Assessment

Sharing Pizzas:

Students are asked to draw a visual fraction model to solve a division word problem.

Type: Formative Assessment

Lesson Plans

Fraction Frenzy! (Division/Fractional Word Problems):

Students will draw models to solve real-life word problems and show the relationship between division and fractions. This is not an introductory lesson to this standard.  By the end of this lesson, they should be able to create their own word problems and explain if the answer will be a mixed number or a fraction less than one.

Type: Lesson Plan

Sharing Fairly:

The students will connect fractions with division. They will solve word problems involving the division of whole numbers by using the strategy of drawing a model and/or equations with a fraction or mixed number for the answer. Next they will write word problems with a story context that represent problems involving division of whole numbers that lead to a fraction or mixed number answer.

Type: Lesson Plan

Wildlife Refuge MEA- Feeding the Animals:

Students use mathematical practices to recommend food packages for the Wildlife Refuge of North America to order.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Birds Now:

The Birds Now Pet Store is increasing the size of its bird department. By increasing the number and types of birds, they need to purchase more bird food and the type of food needs to be one that different types of birds can eat. The students need to rank the companies that sell bird food base on the basic requirements out lined in the client's letter.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Picture This! Fractions as Division:

In this lesson the student will apply and extend previous understandings of division to represent division as a fraction. This includes representations and word problems where the answer is a fraction.

Type: Lesson Plan

Those Pesky Remainders:

This is a lesson to help students understand how to interpret the remainder in a division problem. Real world problems are presented in a PowerPoint so students may visualize situations and discover the four treatments of a remainder. 

Type: Lesson Plan

Original Student Tutorials

Buffy's Bakery Part 4- Multiplying a Fraction by a Whole: Standard Algorithm:

Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.

This is part 4 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Bee A Coder Part 1: Declare Variables:

Learn how to define, declare and initialize variables as you start the journey to "bee" a coder in this interactive tutorial. Variables are structures used by computer programs to store information.  You'll use your math skills to represent a fraction as a decimal to be stored in a variable.

This is part 1 of a 4-part series on coding. Click below to open the other tutorials in the series.

 

Type: Original Student Tutorial

#InterpretAFractionAsDivision:

Learn to identify a fraction as division of the numerator by the denominator using fraction models in this interactive tutorial.  

Type: Original Student Tutorial

Problem-Solving Tasks

How Much Pie?:

The purpose of this task is to help students see the connection between a÷b and a/b in a particular concrete example.  This task is probably best suited for instruction or formative assessment.

Type: Problem-Solving Task

Converting Fractions of a Unit into a Smaller Unit:

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

Type: Problem-Solving Task

Teaching Idea

Divide Fractions:

This interactive resource provides three activities which model the concept of dividing fractions, as well as mixed numbers, by using number lines or circle graphs.  It includes the equation showing the standard algorithm.

Type: Teaching Idea

STEM Lessons - Model Eliciting Activity

Birds Now:

The Birds Now Pet Store is increasing the size of its bird department. By increasing the number and types of birds, they need to purchase more bird food and the type of food needs to be one that different types of birds can eat. The students need to rank the companies that sell bird food base on the basic requirements out lined in the client's letter.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Wildlife Refuge MEA- Feeding the Animals:

Students use mathematical practices to recommend food packages for the Wildlife Refuge of North America to order.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

MFAS Formative Assessments

Five Thirds:

Students are asked to interpret an improper fraction and then write a word problem to match the context of the fraction.

Sharing Brownies:

Students are asked to draw a visual fraction model to solve a division word problem.

Sharing Pizzas:

Students are asked to draw a visual fraction model to solve a division word problem.

Two Thirds:

Students are asked to interpret a fraction and write a word problem to match the context of the fraction.

Original Student Tutorials Mathematics - Grades K-5

#InterpretAFractionAsDivision:

Learn to identify a fraction as division of the numerator by the denominator using fraction models in this interactive tutorial.  

Buffy's Bakery Part 4- Multiplying a Fraction by a Whole: Standard Algorithm:

Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.

This is part 4 of a 4-part series. Click below to open other tutorials in the series.

Computer Science Original Student Tutorials

Bee A Coder Part 1: Declare Variables:

Learn how to define, declare and initialize variables as you start the journey to "bee" a coder in this interactive tutorial. Variables are structures used by computer programs to store information.  You'll use your math skills to represent a fraction as a decimal to be stored in a variable.

This is part 1 of a 4-part series on coding. Click below to open the other tutorials in the series.

 

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Buffy's Bakery Part 4- Multiplying a Fraction by a Whole: Standard Algorithm:

Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.

This is part 4 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Bee A Coder Part 1: Declare Variables:

Learn how to define, declare and initialize variables as you start the journey to "bee" a coder in this interactive tutorial. Variables are structures used by computer programs to store information.  You'll use your math skills to represent a fraction as a decimal to be stored in a variable.

This is part 1 of a 4-part series on coding. Click below to open the other tutorials in the series.

 

Type: Original Student Tutorial

#InterpretAFractionAsDivision:

Learn to identify a fraction as division of the numerator by the denominator using fraction models in this interactive tutorial.  

Type: Original Student Tutorial

Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Problem-Solving Tasks

How Much Pie?:

The purpose of this task is to help students see the connection between a÷b and a/b in a particular concrete example.  This task is probably best suited for instruction or formative assessment.

Type: Problem-Solving Task

Converting Fractions of a Unit into a Smaller Unit:

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

How Much Pie?:

The purpose of this task is to help students see the connection between a÷b and a/b in a particular concrete example.  This task is probably best suited for instruction or formative assessment.

Type: Problem-Solving Task

Converting Fractions of a Unit into a Smaller Unit:

The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.

Type: Problem-Solving Task