Standard #: MA.5.FR.1.1


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Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction.


Examples


At Shawn’s birthday party, a two-gallon container of lemonade is shared equally among 20 friends. Each friend will have begin mathsize 12px style 2 over 20 end style of a gallon of lemonade which is equivalent to one-tenth of a gallon which is a little more than 12 ounces.

Clarifications


Clarification 1: Instruction includes making a connection between fractions and division by understanding that fractions can also represent division of a numerator by a denominator.

Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms. 

Clarification 3: Fractions can include fractions greater than one.



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 5
Strand: Fractions
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • NA

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is for students to understand that a division expression can be written as a fraction by explaining their thinking when working with fractions in various contexts. This builds on the understanding developed in grade 4 that remainders are fractions (MA.4.NSO.2.4), and prepares students for the division of fractions in grade 6 (MA.6.NSO.2.2). 
  • When students read 58 as "five-eights," they should be taught that 58 can also be interpreted as “5 divided by 8,” where 5 represents the numerator and 8 represents the denominator of the fraction (5 = 5 ÷ 8) and refers to 5 wholes divided into 8 equal parts.
  • Teachers can activate students' prior knowledge of fractions as division by using fractions that represent whole numbers (e.g., 246). Familiar division expressions help build students’ understanding of the relationship between fractions and division (MTR.5.1). 
  • During instruction, provide examples accompanied by area and number line models. 
  • When solving mathematical or real-world problems involving division of whole numbers and interpreting the quotient in the context of the problem, students will be able to represent the division of two whole numbers as a mixed number, where the remainder is the fractional part’s numerator and the size of a group is its denominator (for example, 17 ÷ 3 equals 5 23 which is the number of size 3 groups you can make from 17 objects 3 including the fractional group). Students should demonstrate their understanding by explaining or illustrating solutions using visual fraction models or equations.

 

Common Misconceptions or Errors

  • Students can believe that the fraction bar represents subtraction in lieu of understanding that the fraction bar represents division. 
  • Students can have the misconception that division always results in a smaller number. 
  • Students can presume that dividends must always be greater than divisors and, thus, reorder when representing a division expression as a fraction. Show students examples of fractions with greater numerators and greater denominators to create a division equation.

 

Strategies to Support Tiered Instruction

  • Instruction includes making the connection to models and tools previously used to understand division as equal groups or sharing, but now as a fraction in a real-world context. 
    • For example, “Eight friends share four brownies” can be represented as 48. This 8 means that 4 ÷ 8 can be represented using the model below. Four is divided into 8 equal parts, each part is 12 of the brownie. 
models
      • Connecting the real-world application to the fraction will help students understand that the fraction really means division. 
  • Instruction includes making the connection to models and tools previously used to understand division as equal groups or sharing, but now as a fraction in a real-world context. 
    • For example, “Marcos has 8 toy cars that he wants to put into 4 boxes equally. How many cars can go in each box?” 8 ÷ 4 can be shown using a model of 8 wholes divided into 4 groups. The quotient would be the total number of pieces in each group. The model below would show that 8 ÷ 4 = 2. This can also be expressed as 84 = 2. 
   
  • Instruction includes examples of fractions with greater numerators and greater denominators to create a division equation.

 

Instructional Tasks

Instructional Task 1 (MTR.7.1

Create a real-world division problem that results in an answer equivalent to 310.

 

Instructional Task 2 (MTR.3.1)

Write a mixed number that is equivalent to 10 ÷ 3. 

 

Instructional Task 3 (MTR.7.1

Monica has a ribbon that is 8 feet long. She wants to make 12 bows for her friends. How long will each piece of the ribbon be? Express your answer in both feet and inches. 

 

Instructional Task 4 (MTR.7.1

Albert baked 18 fudge brownies for his video game club members. He wants to share the brownies with the 5 club members. How many brownies will each club member get?

 

Instructional Items

Instructional Item 1 

Which expression is equivalent to 712
  • a. 7−12 
  • b. 7÷12  
  • c. 12−7 
  • d. 12÷7 

 

Instructional Item 2 

Amanda has 12 pepperoni slices that need to be distributed equally among 5 mini pizzas. How many pepperoni slices will go on each mini pizza? 
  • a. 512 
  • b. 2 25 
  • c. 7 
  • d. 60 

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



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))
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

Access Point Number Access Point Title
MA.5.FR.1.AP.1 Explore the connection between fractions and division in a real-world problem.


Related Resources

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.

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.

Original Student Tutorials

Name Description
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.

Student Resources

Original Student Tutorials

Name Description
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.



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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