 # Standard #: MAFS.6.NS.1.1

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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?

### Clarifications

Examples of Opportunities for In-Depth Focus

This is a culminating standard for extending multiplication and division to fractions.

Fluency Expectations or Examples of Culminating Standards

Students interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions. This completes the extension of operations to fractions.

### General Information

Subject Area: Mathematics
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 of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes

### Test Item Specifications

N/A

Assessment Limits :
At least the divisor or dividend needs to be a non-unit fraction. Dividing a unit fraction by a whole number or vice versa (e.g., ÷ ?? or ?? ÷ , where a is a whole number) is below grade level.
Calculator :

No

Context :

Allowable

### Sample Test Items (4)

 Test Item # Question Difficulty Type Sample Item 1 An expression is shown. What is the value of the expression? N/A EE: Equation Editor Sample Item 2 An expression is shown. What is the value of the expression? N/A EE: Equation Editor Sample Item 3 A rectangular plot of land has an area of square kilometers and a length of kilometer.What is the width of the plot of land? N/A EE: Equation Editor Sample Item 4 Which question can be answered using the expression ? N/A MC: Multiple Choice

#### Related Courses

 Course Number1111 Course Title222 1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020 (current), 2020 and beyond) 1204000: M/J Intensive Mathematics (MC) (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond (current)) 7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

#### Related Access Points

 Access Point Number Access Point Title MAFS.6.NS.1.AP.1a Divide fractions using visual fraction models.

#### Assessments

 Name Description Sample 4 - Sixth Grade Math State Interim Assessment This is a State Interim Assessment for sixth grade. Sample 2 - Sixth Grade Math State Interim Assessment This is a State Interim Assessment for sixth grade.

#### Educational Games

 Name Description Ice Ice Maybe: An Operations Estimation Game This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents. Various levels of difficulty make this game appropriate for multiple age and ability levels. Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals. Multiplication/Division: The multiplication and addition of fractions and decimals. Percentages: Identify the percentage of a whole number. Fractions: Multiply and divde a whole number by a fraction, as well as apply properties of operations. 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 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

 Name Description 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 is a lesson designed to help students develop procedural skill 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 find out how much of each ingredient is needed to feed 200 people and the most economical way of doing this (Brand name brands or store brand). You also have the option of omitting up to three ingredients from the recipe. 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 the algorithm for dividing fractions using visual fraction models and equations to represent the problem. Predicting the decimal equivalent for a fraction - terminating or repeating? This lesson encourages students to make an important discovery. Will a given fraction yield a terminating or repeating decimal? Discussion includes why knowing this is important. The lesson is structured to allow exploration, discovery, and summarization. Wheeling Around Students are taught the vocabulary used for circles and apply a formula to find the circumference of a bicycle wheel.

#### Professional Development

 Name Description Fractions, Percents, and Ratios, Part A: Models for Multiplication and Division of Fractions This professional development module shows teachers how to use area models to understand multiplication and division of fractions.

#### Student Center Activity

 Name Description 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.

#### 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.

#### Tutorial

 Name Description Dividing Mixed Numbers In this tutorial, you will see how mixed numbers can be divided.

#### Video/Audio/Animation

 Name Description Reciprocals and Divisions of Fractions When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.

#### Educational Games

 Name Description Ice Ice Maybe: An Operations Estimation Game: This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents. Various levels of difficulty make this game appropriate for multiple age and ability levels. Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals. Multiplication/Division: The multiplication and addition of fractions and decimals. Percentages: Identify the percentage of a whole number. Fractions: Multiply and divde a whole number by a fraction, as well as apply properties of operations. 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.

#### Student Center Activity

 Name Description 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

 Name Description Dividing Mixed Numbers: In this tutorial, you will see how mixed numbers can be divided.

#### Video/Audio/Animation

 Name Description Reciprocals and Divisions of Fractions: When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.