MAFS.5.NF.1.2

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Clarifications

Examples of Opportunities for In-Depth Focus

When students meet this standard, they bring together the threads of fraction equivalence (grades 3–5) and addition and subtraction (grades K–4) to fully extend addition and subtraction to fractions.
General Information
Subject Area: Mathematics
Grade: 5
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use equivalent fractions as a strategy to add and subtract 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
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    Fractions greater than 1 and mixed numbers may be included. Expressions may have up to three terms. Least common denominator is not necessary to calculate sums or differences of fractions. Items may not use the terms “simplify” or “lowest terms.” For given fractions in items, denominators are limited to 1-20. Items may require the use of equivalent fractions to find a missing term or part of a term.
  • Calculator :

    No

  • Context :

    Required

Sample Test Items (4)
  • Test Item #: Sample Item 1
  • Question:

    John and Sue are baking cookies. The recipe lists begin mathsize 12px style 3 over 4 end style cup of flour. They only have begin mathsize 12px style 3 over 8 end style cup of flour left. 

    How many more cups of flour do they need to bake the cookies?

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

  • Test Item #: Sample Item 2
  • Question:

    Javon, Sam, and Antoine are baking cookies. Javon has begin mathsize 12px style 1 half end style cup of flour, Sam has begin mathsize 12px style 1 1 over 6 end style cups of flour, and Antoine has begin mathsize 12px style 1 3 over 4 end style cups of flour.

    How many cups of flour do they have altogether?

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

  • Test Item #: Sample Item 3
  • Question:

    Richard and Gianni each bought a pizza. The pizzas are the same size.

    • Richard cut his pizza into 12 slices.
    • Gianni cut his pizza into 6 slices, and ate 2 slices.
    • Together, Richard and Gianni ate begin mathsize 12px style 9 over 12 end style

    How many slices of his pizza did Richard eat?

     

  • Difficulty: N/A
  • Type: MC: Multiple Choice

  • Test Item #: Sample Item 4
  • Question:

    Jasmine has begin mathsize 12px style 3 over 4 end style cup of flour in a mixing bowl. After adding more flour to the mixing bowl, Jasmine says that she now has begin mathsize 12px style 5 over 8 end style cup of flour.

    Which of the following explains why Jasmine's statement is incorrect?

     

  • Difficulty: N/A
  • Type: MC: Multiple Choice

Related Courses

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

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.5.NF.1.AP.2a: Solve word problems involving the addition and subtraction of fractions using visual fraction models.

Related Resources

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

Assessments

Sample 4 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

Sample 3 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

Formative Assessments

Maris Has a Party:

Students are given a word problem involving fractions with unlike denominators and are asked to estimate the sum, explain their reasoning, and then determine the sum.

Type: Formative Assessment

Sarah’s Hike:

Students are asked to estimate the difference between two fractional lengths and then calculate the difference.

Type: Formative Assessment

Just Run:

Students are given a word problem involving subtraction of fractions with unlike denominators. Students are asked to determine if a given answer is reasonable, explain their reasoning, and calculate the answer.

Type: Formative Assessment

Baking Cakes:

Students are asked to estimate the sum of two mixed numbers and then calculate the sum.

Type: Formative Assessment

Lesson Plans

Let's Have a Fraction Party!:

In this lesson, students will use addition and subtraction of fractions with unlike denominators to solve word problems involving situations that arise with the children who were invited to a party. They will use fraction strips as number models and connect the algorithm with these real-life word problems.

Type: Lesson Plan

Fractions make the real WORLD problems go round:

In this lesson students will use a graphic organizer to to solve addition and subtraction word problems. Students will create their own word problems in PowerPoint, by using pen and paper, or dry erase boards to help them to connect to and understand the structure of word problems.  

Type: Lesson Plan

Aaron and Anya's Discovery: Adding Fractions with Unlike Denominators:

In this situational story, Aaron and Anya find several pieces of ribbon/cord of varying fractional lengths. They decide to choose 3 pieces and make a belt. All of the fractions have different denominators; students have to determine common denominators in order to add the fractional pieces. After students successfully add three fractional pieces, they make a belt and label it with their fractional pieces.

Type: Lesson Plan

Estimating Fractions Using Benchmark Fractions 0, 1/2, or 1:

In this lesson, students use models (fractions tiles or number lines) to round fractions using benchmark fractions of 0, 1/2, or 1.

Type: Lesson Plan

Using Models to Subtract Fractions with Unlike Denominators:

This lesson is specific to subtracting fractions with unlike denominators. It requires students to already have a working knowledge of subtracting fractions with common denominators and equivalent fractions. 

Type: Lesson Plan

Discovering Common Denominators:

Students use pattern blocks to represent fractions with unlike denominators. Students discover that they need to convert the pattern blocks to the same size in order to add them. Therefore, they find and use common denominators for the addition of fractions.

Type: Lesson Plan

Looking for Patterns in a Sequence of Fractions:

A sequence of fractions is generated by means of a simple formula, namely x' = 2x when x < 1/2 and x' = 2(1-x) otherwise, where x is a fraction in the sequence and x' is the next fraction. Students will generate the sequence for a variety of starting fractions and observe the characteristics of the sequence generated.

Type: Lesson Plan

Problem-Solving Tasks

Salad Dressing:

The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.

Type: Problem-Solving Task

Do These Add Up?:

This task addresses common errors that students make when adding fractions. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.

Type: Problem-Solving Task

Teaching Idea

Adding and Subtracting Fractions:

Kahn Academy video - How to add and subtract fractions with like and unlike denominators.

Type: Teaching Idea

MFAS Formative Assessments

Baking Cakes:

Students are asked to estimate the sum of two mixed numbers and then calculate the sum.

Just Run:

Students are given a word problem involving subtraction of fractions with unlike denominators. Students are asked to determine if a given answer is reasonable, explain their reasoning, and calculate the answer.

Maris Has a Party:

Students are given a word problem involving fractions with unlike denominators and are asked to estimate the sum, explain their reasoning, and then determine the sum.

Sarah’s Hike:

Students are asked to estimate the difference between two fractional lengths and then calculate the difference.

Student Resources

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

Problem-Solving Tasks

Salad Dressing:

The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.

Type: Problem-Solving Task

Do These Add Up?:

This task addresses common errors that students make when adding fractions. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.

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

Salad Dressing:

The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.

Type: Problem-Solving Task

Do These Add Up?:

This task addresses common errors that students make when adding fractions. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.

Type: Problem-Solving Task