Standard #: MAFS.5.NF.2.3 (Archived 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
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    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 # Question Difficulty Type
Sample Item 1

Which expression is equivalent to begin mathsize 12px style 8 over 15 end style?

 

N/A MC: Multiple Choice
Sample Item 2

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?

N/A EE: Equation Editor
Sample Item 3

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?

N/A EE: Equation Editor


Related Courses

Course Number1111 Course Title222
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 Resources

Educational Game

Name Description
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.

Formative Assessments

Name Description
Two Thirds

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

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.

Lesson Plans

Name Description
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.

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.

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.

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

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.

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. 

Original Student Tutorials

Name Description
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.

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.

 

#InterpretAFractionAsDivision

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

Problem-Solving Tasks

Name Description
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.

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.

Teaching Idea

Name Description
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.

Student Resources

Original Student Tutorials

Name Description
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.

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.

 

#InterpretAFractionAsDivision:

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

Educational Game

Name Description
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.

Problem-Solving Tasks

Name Description
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.

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.



Parent Resources

Problem-Solving Tasks

Name Description
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.

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.



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