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Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Standard #: MAFS.6.NS.1.1Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 6
Domain-Subdomain: The Number System
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of multiplication and division to divide fractions by 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
Related Courses
Related Resources
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.
Formative Assessments
  • Models of Fraction Division # Students are asked to explain the relationship between a fraction division word problem and either a visual model or an equation.
  • Fraction Division # Students are asked to complete two fraction division problems – one with fractions and one with mixed numbers.
  • Contextualizing Fraction Division # Students are asked to write a story context for a given fraction division problem.
  • Juicing Fractions # Students are asked to write and evaluate a numerical expression involving division of fractions and mixed numbers to model and solve a word problem.
Lesson Plans
  • Gr. 6 Lesson 2-A Drop in the Bucket # Students will recognize the concern for water quantity and water flow to the Everglades through a demonstration and activity.
  • Dividing Fractions: Increasing Procedural Skill # This lesson helps students develop procedural skills in dividing fractions. During this lesson students will discuss prior knowledge of the concept of dividing fractions and will solve problems independently and in pairs using the standard algorithm. The lesson also incorporates music and poster-making to reinforce the learning objective. This lesson was originally designed for a 6th-grade Intensive Math class and should only be used following lessons where students have developed a solid conceptual understanding of dividing fractions. This lesson may take up to 3 days depending on how much practice and extra activities your students require.
  • The Price is Right # In this activity the students will apply their knowledge of mathematical calculations to solve a real-world problem. They will analyze a collection of shipping boxes to determine which box will ship the most for the $100 allowed.
  • Fancy Fractions Catering Company Project # Fancy Fractions Catering Company will be hosting a party and need your help to make it happen! Your help is needed to determine which recipe would be best for them to use in their pasta dish taking into account ingredient cost and customer preference. 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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
  • Dividing Fractions # In this lesson students will explore the different methods available for dividing fractions through a student-based investigation. The teacher will facilitate the discussion, but the students will discover the different methods on their own or with a partner as they work through the different steps.
  • Dividing Fractions (Part 1) - Tackling Word Problems # This lesson allows the students to explore the foundation for dividing fractions as well as correctly solving word problems involving division of fractions. It includes the use of the Philosophical Chairs activity and numerical solutions. Group activities are included to foster cooperative learning.
  • Dividing by Fractions Discovery # This lesson allows students to derive an algorithm for dividing fractions using visual fraction models and equations to represent the problem.
Problem-Solving Tasks
  • Running to School, Variation 2 # Students are asked to solve a distance problem involving fractions.
  • Making Hot Cocoa, Variation 1 # Students are asked to solve a fraction division problem using both a visual model and the standard algorithm within a real-world context.
  • Making Hot Cocoa, Variation 2 # Students are asked a series of questions involving a fraction and a whole number within the context of a recipe. Students are asked to solve a problem using both a visual model and the standard algorithm.
  • Running to School, Variation 3 # Students are asked to solve a distance problem involving fractions. The purpose of this task is to help students extend their understanding of division of whole numbers to division of fractions, and given the simple numbers used, it is most appropriate for students just learning about fraction division because it lends itself easily to a pictorial solution.
  • Traffic Jam # Students are asked to use fractions to determine how many hours it will take a car to travel a given distance.
  • Video Game Credits # Students are asked to use fractions to determine how long a video game can be played.
  • Baking Cookies # The purpose of this task is to help students get a better understanding of multiplying and dividing using fractions.
  • Cup of Rice # The purpose of this task is to help give students a better understanding of multiplying and dividing fractions.
  • Dan’s Division Strategy # The purpose of this task is to help students explore the meaning of fraction division and to connect it to what they know about whole-number division. Students are asked to explain why the quotient of two fractions with common denominators is equal to the quotient of the numerators of those fractions.
  • Drinking Juice, Variation 2 # This task builds on a fifth grade fraction multiplication task, "Drinking Juice." This task uses the identical context, but asks the corresponding "Number of Groups Unknown" division problem. See "Drinking Juice, Variation 3" for the "Group Size Unknown" version.
  • Drinking Juice, Variation 3 # Students are asked to solve a fraction division problem using a visual model and the standard algorithm.
  • How Many _______ Are In. . . ? # This instructional task requires that the students model each problem with some type of fractions manipulatives or drawings. This could be pattern blocks, student or teacher-made fraction strips, or commercially produced fraction pieces. At a minimum, students should draw pictures of each. The above problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.
  • How Many Containers in One Cup / Cups in One Container? # The purpose of this problem is to help students deepen their understanding of the meaning of fractions and fraction division and to see that they get the same answer using standard algorithm as they do just reasoning through the problem. These two fraction division tasks use the same context and ask "How much in one group?" but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.
Professional Development
Student Center Activity
  • Edcite: Mathematics Grade 6 # Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.
Tutorial
Video/Audio/Animation
STEM Lessons - Model Eliciting Activity
  • Fancy Fractions Catering Company Project # Fancy Fractions Catering Company will be hosting a party and need your help to make it happen! Your help is needed to determine which recipe would be best for them to use in their pasta dish taking into account ingredient cost and customer preference. 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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
MFAS Formative Assessments
  • Contextualizing Fraction Division # Students are asked to write a story context for a given fraction division problem.
  • Fraction Division # Students are asked to complete two fraction division problems – one with fractions and one with mixed numbers.
  • Juicing Fractions # Students are asked to write and evaluate a numerical expression involving division of fractions and mixed numbers to model and solve a word problem.
  • Models of Fraction Division # Students are asked to explain the relationship between a fraction division word problem and either a visual model or an equation.
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