# Standard 2: Add, subtract, multiply and divide positive rational numbers. Export Print
General Information
Number: MA.6.NSO.2
Title: Add, subtract, multiply and divide positive rational numbers.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.6.NSO.2.AP.1
Solve one-step multiplication and division problems involving positive decimals whose place value ranges from the tens to the hundredths places.
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.
MA.6.NSO.2.AP.3a
Solve one-step real-world problems involving any of the four operations with positive decimals ranging from the hundreds to hundredth place value.
MA.6.NSO.2.AP.3b
Solve one-step real-world problems involving any of the four operations with positive fractions and mixed numbers with like denominators.

## Related Resources

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

## 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

Multiplying Multidigit Decimals:

Students are asked to multiply multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Subtracting Multidigit Decimals:

Students are asked to subtract multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Students are asked to add multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Dividing Multidigit Decimals:

Students are asked to divide multidigit decimal numbers and are assessed for both accuracy and fluency.

Type: Formative Assessment

Multiplying By Ten Three Times:

Students consider why a number multiplied by 10 to the third power will have three zeros in the product.

Type: Formative Assessment

Running:

Students are asked to solve a word problem involving division of a whole number by a decimal using a model or drawing, a strategy based on place value, the relationship between multiplication and division, or properties of operations.

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

Contextualizing Fraction Division:

Students are asked to write a story context for a given fraction division problem.

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

Florida Food Round Up!:

Most families must buy food and household items that they will need every few weeks. Instead of randomly throwing things into a shopping cart and paying whatever the total is, many families must stick carefully to a predetermined budget to buy all of the items they need. A helpful way to make sure that you are able to buy everything needed is to use a list that is written before going shopping. Families must also determine, if they will purchase "name brand" or "store brand" products. Today, students will practice using a grocery list with a predetermined budget as they add and subtract decimals.

Type: Lesson Plan

Sound Is Not The Only Place You Hear About Volume!:

This lesson introduces the idea of finding volume. Volume in sixth grade math is very "rectangular" (cubes, rectangular prisms) and this lesson brings to light that volume is simply a measure of available space, but can take on many shapes or forms (cylinders for example - graduated cylinders and beakers) in science. Students will be left to design their own data collection and organizing the data that they collect. They will apply the skill of finding volume to using fractional parts of a number (decimals) and finding the product using the volume formula.

Type: Lesson Plan

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

Wrapping Up Geometry (Lesson 1 of 2):

This lesson is the first of two in a unit on surface area. This lesson provides a foundation for understanding the concept of surface area by introducing nets of right rectangular prisms.

Type: Lesson Plan

Area of a Triangle:

This lesson is primarily formative in nature and is designed to introduce students to the area of a triangle by having them derive the formula themselves using the relationship between rectangles and triangles. During the lesson the teacher will be facilitating their students as they work with their teams and shoulder partners to solve problems.

Type: Lesson Plan

Vacation:

In this Model Eliciting Activity, MEA, the purpose of this lesson is to provide students with the opportunity to solve real-world problems using addition, subtraction, multiplication, and division of multi-digit decimals. They will write arguments to support claims with clear reasons and relevant evidence. Engage effectively in a range of collaborative discussions.

Type: Lesson Plan

How Many Rubik's Cubes Can You Pack?:

This two-day lesson uses a hands-on problem-solving approach to find the volume of a right rectangular prism with positive rational number edge lengths. Students first design boxes and fill with Rubik's Cubes. They create a formula from the patterns they find. Using cubes with fractional edges requires students to apply fractional units to their formulas.

Type: Lesson Plan

A Healthy Outlook:

In this Model Eliciting Activity, MEA, students will learn about nutrition and the importance of keeping things balanced on their plate using the FDA recommendations. Students will need to rank meal plans and shake plans in order to help a restaurant catering company keep a successful business going. After students have evaluated and created rankings for their meal choice, they will write a letter explaining their rationale and thinking and find the bundle price. They will then receive a second letter asking for their help in ranking vegetarian shakes from highest to lowest to support an expanded customer base and find the bundle price. Students will now have the chance to learn a little more about vegetarians and their food choices.

Type: Lesson Plan

The Classroom Money Vault:

This activity has students predict the number of one hundred dollar bills that can fit inside the classroom. The students use volume measurements to explain their estimation.

Type: Lesson Plan

This MEA asks the students to decide which company would be the “best and the worst” to use to purchase scuba diving masks for Tino’s Scuba Diving School to provide to their diving certification students. Furthermore, the students are asked to suggest which type of scuba diving masks should be purchased in term of multiple panes – single pane mask, double pane mask, full face mask, skirt color, fit, durability, and price. Students must provide a "top choice" scuba diving mask to the company owner and explain how they arrived at their solution.

Type: Lesson Plan

Teen Cell Phone Plans:

In this Model Eliciting Activity, MEA, the purpose of this lesson is to solve real-world and mathematical problems. Students will also use operations with multi-digit decimals to solve problems. They will write arguments to support claims with clear reasons and relevant evidence. Students will engage effectively in a range of collaborative discussions.

Type: Lesson Plan

Area of a Right Triangle:

Area of a Right Triangle

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

Dividing Decimals Investigations:

In this introductory lesson, students test how the basic operations performed on the dividend and divisor affect the quotient of a pair of numbers. Students then conclude whether the results of their trials can be applied to solve problems with a decimal divisor.

Type: Lesson Plan

Enrique's Ruined Carpet:

In this activity, students use a house blueprint to find the area of carpeted floor by decomposing composite shapes into rectangles and triangles. As students critique each other's reasoning, they refine their thinking of surface area.

Type: Lesson Plan

Uncle Henry's Dilemma:

Uncle Henry's Dilemma is a problem solving lesson to determine the global location for the reading of Uncle Henry's will. The students will interpret data sets which include temperature, rainfall, air pollution, travel cost, flight times and health issues to rank five global locations for Uncle Henry's relatives to travel to for the reading of his will. This is an engaging, fun-filled MEA lesson with twists and turns throughout. Students will learn how this procedure of selecting locations can be applied to everyday decisions by the government, a business, a family, or individuals.

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

“Dinner with Friends”:

The students will determine what to order at a dinner with friends yet stay within a budget. The students will try to maximize their budgets and order as much food as they possibly can with their given amount of money.

Type: Lesson Plan

## Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Overview:

Why did the math teacher KROS the ocean? Because it made for a wonderful way to engage students and do something unique.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Type: Perspectives Video: Teaching Idea

## 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

Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals.

Type: Teaching Idea

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

Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

Type: Tutorial

Multiply and Divide Powers of 10: Zero Patterns:

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.

Type: Tutorial

Dividing Mixed Numbers:

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

Type: Tutorial

Dividing by a Multi-Digit Decimal:

This video demonstrates dividing two numbers that are decimals.

Type: Tutorial

Multiplying Decimals:

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

Subtracting Decimals 2:

Let's show subtracting with digits up to the thousandths place in this tutorial.

Type: Tutorial

Subtracting Decimals 1:

Watch as we align decimals before subtracting in this tutorial.

Type: Tutorial

Learn how to add decimals and use place value in this tutorial.

Type: Tutorial

Creating Common Denominators:

This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).  The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion.

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

## Student Resources

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

## 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

Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

Type: Tutorial

Multiply and Divide Powers of 10: Zero Patterns:

This Khan Academy tutorial video presents the methodology of understanding and using patterns in the number of zeros of products that have a factor that is a power of 10. While the standard does not mention exponents, the place value understanding of multiplying or dividing by powers of ten will help students understand multiplying and dividing by decimals.

Type: Tutorial

Dividing Mixed Numbers:

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

Type: Tutorial

Dividing by a Multi-Digit Decimal:

This video demonstrates dividing two numbers that are decimals.

Type: Tutorial

Multiplying Decimals:

This video demonstrates how to multiply two decimal numbers.

Type: Tutorial

Subtracting Decimals 2:

Let's show subtracting with digits up to the thousandths place in this tutorial.

Type: Tutorial

Subtracting Decimals 1:

Watch as we align decimals before subtracting in this tutorial.

Type: Tutorial

Learn how to add decimals and use place value in this tutorial.

Type: Tutorial

Creating Common Denominators:

This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).  The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion.

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 topic.

## Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Overview:

Why did the math teacher KROS the ocean? Because it made for a wonderful way to engage students and do something unique.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Type: Perspectives Video: Teaching Idea

## 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