MA.6.NSO.2.2

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Extend previous understanding of multiplication and division to compute products and quotients of positive fractions by positive fractions, including mixed numbers, with procedural fluency.

Clarifications

Clarification 1: Instruction focuses on making connections between visual models, the relationship between multiplication and division, reciprocals and algorithms.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Number Sense and Operations
Standard: Add, subtract, multiply and divide positive rational numbers.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.NSO.2.AP.2: Use tools to calculate the product and quotient of positive fractions by positive fractions, including mixed numbers, using the standard algorithms.

Related Resources

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

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.

Type: Educational Game

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.

Type: Formative Assessment

Fraction Division:

Students are asked to complete two fraction division problems – one with fractions and one with mixed numbers.

Type: Formative Assessment

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.

Type: Formative Assessment

Lesson Plans

Using Nets to Find the Surface Area of Pyramids:

In this lesson, students will explore and apply the use of nets to find the surface area of pyramids.

Type: Lesson Plan

Multiplying a Fraction by a Fraction:

Students will multiply a fraction times a fraction. The students will section off a square through rows and columns that will represent the strategy of multiplying numerators and then denominators.

Type: Lesson Plan

Modeling Fraction Multiplication:

This lesson involves students modeling fraction multiplication with rectangular arrays in order to discover the rule for multiplication of fractions.

Type: Lesson Plan

Professional Development

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.

Type: Professional Development

Teaching Ideas

Space Math - Big Moons and Small Planets:

Students use a scale representation of the top 26 small planets and large moons in the solar system to compare their relative sizes to Earth. Students will use simple fractions to solve real world problems.

Type: Teaching Idea

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.

Type: Teaching Idea

Tutorials

Dividing Mixed Numbers:

In this tutorial, you will see how mixed numbers can be divided.

Type: Tutorial

How Do You Divide Fractions?:

This five-minute video answers the question "Must one always invert and multiply?" when dividing fractions. An alternative algorithm is presented which works well in certain cases. The video focuses on sense-making in using either method, and on judging the reasonableness of answers.

Type: Tutorial

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Video/Audio/Animation

Reciprocals and Divisions of Fractions:

When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.

Type: Video/Audio/Animation

MFAS Formative Assessments

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.

Student Resources

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

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.

Type: Educational Game

Tutorials

Dividing Mixed Numbers:

In this tutorial, you will see how mixed numbers can be divided.

Type: Tutorial

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial

Video/Audio/Animation

Reciprocals and Divisions of Fractions:

When working with fractions, divisions can be converted to multiplication by the divisor's reciprocal. This chapter explains why.

Type: Video/Audio/Animation

Parent Resources

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

Tutorials

How Do You Divide Fractions?:

This five-minute video answers the question "Must one always invert and multiply?" when dividing fractions. An alternative algorithm is presented which works well in certain cases. The video focuses on sense-making in using either method, and on judging the reasonableness of answers.

Type: Tutorial

Multiplying Fractions:

The video describes how to multiply fractions and state the answer in lowest terms.

Type: Tutorial