# Cluster 1: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (Major Cluster)Archived

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.

General Information
Number: MAFS.7.NS.1
Title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: The Number System

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.7.NS.1.AP.1a
Identify rational numbers that are an equal distance from 0 on a number line as additive inverses.
MAFS.7.NS.1.AP.1b
Find the distance between two rational numbers on a number line.
MAFS.7.NS.1.AP.2a
Solve single-digit rational number multiplication problems using a number line.
MAFS.7.NS.1.AP.2b
Solve division problems with quotients from -100 to 100 using a number line.
MAFS.7.NS.1.AP.2c
Write equations to represent rational number multiplication and division problems solved on a number line and generate rules for the products and quotients of rational numbers.
MAFS.7.NS.1.AP.3a
Solve real-world and mathematical problems involving the four operations with rational numbers from -100 to 100.

## Related Resources

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

## Educational Games

Pinata Fever: A Visual Integer Sums Number Line Game:

Practice adding and subtracting positive and negative numbers to intercept the descending piñatas and then whack them for candy. Come on, keep the party going!

Type: Educational Game

Integers Jeopardy Game:

This interactive game has 4 categories: adding integers, subtracting integers, multiplying integers, and dividing integers. Students can play individually or in teams.

Type: Educational Game

## Formative Assessments

Complex Fractions:

Students are asked to rewrite complex fractions as simple fractions in lowest terms.

Type: Formative Assessment

Positive and Negative Fractions:

Students are asked to add, subtract, multiply, and divide positive and negative fractions.

Type: Formative Assessment

Find Decimal Using Long Division:

Students are asked to use long division to convert four different fractions to equivalent decimals and to identify those that are rational.

Type: Formative Assessment

Trail Mix Munchies:

Students are asked to solve a word problem involving division of fractions.

Type: Formative Assessment

A Rational Number Expression:

Students are given a numerical expression to evaluate.

Type: Formative Assessment

Monitoring Water Temperatures:

Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.

Type: Formative Assessment

Using Positive and Negative Numbers in Context:

This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures:

• starting temperature + change in temperature = final temperature
• final temperature – change in temperature = starting temperature
• final temperature – starting temperature = change in temperature

Type: Formative Assessment

Type: Formative Assessment

Rational Water Management:

Students are asked to combine rational numbers, including fractions and decimals, and use the properties of operations to simplify calculations.

Type: Formative Assessment

Understanding Products:

Students are asked to explain why the product of a positive and a negative rational number is negative.

Type: Formative Assessment

Negatives Explained:

Students are asked to describe a real-world context for a given expression involving the product of two rational numbers.

Type: Formative Assessment

Negative Times:

Students are shown a problem that illustrates why the product of two negatives is a positive and are asked to provide a rationale.

Type: Formative Assessment

Applying Rational Number Properties:

Students are asked to evaluate expressions involving multiplication of rational numbers and use the properties of operations to simplify calculations.

Type: Formative Assessment

Integer Division:

Students are asked to describe a real-world context for a given expression involving the quotient of two rational integers.

Type: Formative Assessment

Quotients of Integers:

Students are given an integer division problem and asked to identify fractions which are equivalent to the division problem.

Type: Formative Assessment

Finding the Difference:

Students are asked to find the difference between two integers using a number line.

Type: Formative Assessment

Students are asked to rewrite a subtraction problem as an equivalent addition problem and explain the equivalence using a number line.

Type: Formative Assessment

Students are asked to describe an example of additive inverse and demonstrate the concept on a number line.

Type: Formative Assessment

## Lesson Plans

Budget Committee:

In this MEA, students will take on the role as a member of the Sunshine County Budget Committee. Members will collaborate to determine the optimal sales tax rate, use that rate to calculate how much money can be used for special projects, then decide which special projects to include in the budget proposal. Students will use percentages to problem-solve in context while considering citizen input and constraints on spending.

Type: Lesson Plan

Radioactive Dating Lesson 4 - Recursive Division :

This lesson introduces students to the idea of recursive division and its application to radioactive dating with a worksheet and Scratch programming. This is the final lesson in the Radioactive Dating Unit.

Type: Lesson Plan

Water, Water Everywhere - Natural Disaster Water Filtration:

Students will be tasked with an engineering challenge to design an effective and efficient portable water filtration system. The designs will take dirty water and make it clear so it can be boiled for safe drinking. This lesson aligns to both math and science content standards.

Type: Lesson Plan

Irrigation Station:

This STEM lesson, complete with a design challenge, helps students design, build, and test irrigation methods. Students will incorporate and develop math skills through solving proportions as they work in teams to solve an engineering challenge.

Type: Lesson Plan

Independent Compound Probability:

During this lesson, students will use Punnett Squares to determine the probability of an offspring's characteristics.

Type: Lesson Plan

NASA Salaries:

This is a NASA-themed, MEA (Model Eliciting Activity) lesson that challenges students to solve a real world open ended problem, while promoting collaboration through teamwork. This lesson asks each group of students to choose five positions and assign salaries to the positions with a given budget of \$500,000. The students' original decision (and "twist") will be based on information from the client's letter(s) and data set(s). Groups are to write a detailed letter to the client of the procedure used.

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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Laura’s Babysitting Job:

In this 7th grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.

Type: Lesson Plan

Johansson Family Travel Plans:

In this 7th grade MEA, students will form teams to rank the best vacation package for the Johansson family vacation. They will have to calculate the total cost of the vacation package making sure they don't go over budget. Teams will suggest what the family should do with any excess money. They will also suggest any deletion of activities if the package is over budget. Teams will make a presentation of the first choice recommendation.

Type: Lesson Plan

Which van is the best buy?:

The students will have to decide which van is the "best buy" for a family. They will have to figure monthly payments and will also use critical thinking skills to decide which is the best van to purchase.

Type: Lesson Plan

Increasing and Decreasing Quantities by a Percent:

This lesson unit is intended to help you assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties:

• translating between percents
• decimals and fractions
• representing percent increase and decrease as multiplication
• recognizing the relationship between increases and decreases

Type: Lesson Plan

Best Chicken Franchise for Me:

In this MEA, the students will compare data to decide which franchise would be best for a person who is moving into an area and wants to open up their own fried chicken franchise.

Type: Lesson Plan

Based on a student-focused scenario encouraging healthier lifestyles, students will perform a close and careful reading of an article encouraging active and healthy lifestyles. During the lesson, students will analyze data from Consumer Reports comparing and contrasting treadmills and elliptical exercisers. Using information gathered, students will compile data and persuade administrators to buy equipment that will align with the provided budget and fit in the given space.

Type: Lesson Plan

Using Positive and Negative Numbers in Context:

This lesson unit is intended to help you assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the following structures:

• starting temperature + change in temperature = final temperature
• final temperature – change in temperature = starting temperature
• final temperature – starting temperature = change in temperature

Type: Lesson Plan

Decisions, Decisions!:

In this Model Eliciting Activity, MEA, students will research a list of companies to invest in through purchasing stocks. Students will calculate the amount invested and readjust their investment choices.

Type: Lesson Plan

Pricing The Twelve Days of Christmas:

Students will discover how much the items in the classic song, "The Twelve Days of Christmas," would cost in the current year; and then they will update the list for modern times.

Type: Lesson Plan

We're Going on Vacation!:

Teams of students act as travel agents in order to plan a vacation package for a family of 5. The students must create four vacation packages that include: hotel, car rental, and visits to three theme parks.

Type: Lesson Plan

Let's Understand Multiplication of Positive and Negative Numbers:

This lesson provides teachers with a way to show students why multiplying negative numbers results in a positive answer. The lesson starts with a review of decomposition, the distributive property, and finding missing addends. Then, with teacher guidance, groups of students apply these skills in a systematic way to apply properties of operations to discover the rules governing the signs of products for positive and negative factors and to multiply positive and negative numbers in mathematical and real-world problems. Finally, students independently demonstrate mastery of the lesson objectives by completing an independent practice assessment.

Type: Lesson Plan

Increasing and Decreasing Quantities by a Percent:

This lesson unit is intended to help you assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties:

• Translating between percents, decimals, and fractions.
• Representing percent increase and decrease as multiplication.
• Recognizing the relationship between increases and decreases.

Type: Lesson Plan

Discovering How to Subtract Rational Numbers Using the Additive Inverse:

In this lesson, students will develop an understanding that opposite quantities combine to make zero-sum pairs and will learn how to subtract rational numbers using a horizontal number line and the additive inverse

Type: Lesson Plan

Future Homes for America:

The students will need to look at data and make good decisions on which model home will be constructed for victims hurt by natural disasters.

Type: Lesson Plan

Ranking Banking:

In this activity, the students are given specifics and data tables to figure out which banking institution best fits the needs of the customer. Student have to figure out the company's monthly banking activities and use this information to rank the banks provided in the table(s) to determine which bank will give them the most service for the least cost. The twist adds a new situation to take into consideration that may or may not change their original recommendation.

Type: Lesson Plan

Batteries Included:

In this Model Eliciting Activity, MEA, students will evaluate batteries using empirical data and customer comments to help a Taxi Cab Service decide which battery brand to purchase. In this real-world scenario, students will communicate with the client in letter format stating their suggested ranking. They will also provide calculations and justification for each decision.

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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Zany's Joke Shop Dilemma:

The main problem is that students will help rank products offered at Zany Joke Shop. They will be ranking the products from best overall to least. By helping rank the products, the student will help create a purchase order for the store. They will be expected to create a device to rank the products offered from best to worst. Students will be given tables that show: cost per product, customer rating, profits made and affordability. The second letter offers students a twist since new products are being introduced for the store to sell and a budget constraint will be introduced.

Type: Lesson Plan

Where in the world?:

This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.

Type: Lesson Plan

Forever Green Landscaping:

Students are asked to rank different types of mulch for a Landscaping company.

Type: Lesson Plan

In this lesson, students will use T-charts as a strategy to add and subtract positive and negative numbers.

Type: Lesson Plan

All Around Fences:

Students use problem solving skills to determine how much fencing is needed and the type of fencing in order to secure a pool and recreational area.

Type: Lesson Plan

Whirl Wind:

The Whirl Wind Corporation would like to install Wind Turbines in the Mojave Desert. The company produces various models of these turbines and is looking for help in selecting the best one for the job.

Type: Lesson Plan

Cool Uniforms:

Students are asked to rank fabrics designated for a new women's volleyball team. Students must take into account the uniform color, Ultraviolet Protection Factor, weight of the fabric availability of material and cost. They will compare and contrast fabrics on these factors and calculate yardage needed to manufacture the team's 24 uniforms.

Type: Lesson Plan

Discovering Our Rules for Addition of Integers:

In this lesson, students will develop an understanding of the rules for adding integers by using the absolute value of integers and number lines.

Type: Lesson Plan

Wallpaper Woes Money Math: Lessons for Life:

Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.

Type: Lesson Plan

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.

Type: Lesson Plan

## Original Student Tutorials

Order of Operations with Rational Numbers Part 2: Decimals:

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Rational Numbers Part 1: Fractions:

Evaluate numerical expressions with rational numbers expressed as fractions using the order of operations and properties of operations in this interactive tutorial.

This is part 1 in a two-part series.

Type: Original Student Tutorial

Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial.

Type: Original Student Tutorial

Why Does a Negative Times a Negative Equal a Positive?:

Use mathematical properties to explain why a negative factor times a negative factor equals a positive product instead of just quoting a rule with this interactive tutorial.

Type: Original Student Tutorial

Distances on the Number Line 2:

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Comparing Freezing Points:

In this task, students answer a question about the difference between two temperatures that are negative numbers.

Equivalent fractions approach to non-repeating decimals:

The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.

Operations on the Number Line:

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

Space Math: Lunar Cratering:

Students explore the formation of craters on the lunar surface using real world imaging data and mathematical reasoning. Students make observations and inferences about the time that impact craters were formed using probability and percentages.

## Teaching Ideas

This video offers a quick and easy way for math students to add numbers with positive and negative signs by modelling with colored stickers. The teacher used red stickers for negative numbers, orange as a neutral, and green for positives in order to give the students a visual learning tool to help tackle the world of integer addition.

Type: Teaching Idea

Feeding Time-SeaWorld Classroom Activity:

Students determine the cost to feed a group of ocean animals in captivity, thus solving a real-life problem.

Type: Teaching Idea

## Tutorials

Thinking About the Sign of Expressions:

This video shows some examples that test your understanding of what happens when positive and negative numbers are multiplied and divided.

Type: Tutorial

Converting repeating decimals to fractions :

Students will learn how to convert difficult repeating decimals to fractions.

Type: Tutorial

Converting repeating decimals to fractions :

This tutorial shows students how to convert basic repeating decimals to fractions.

Type: Tutorial

Converting a fraction to a repeating decimal:

Students will learn how to convert a fraction into a repeating decimal. Students should know how to use long division before starting this tutorial.

Type: Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Changing a Fraction to Decimal Form:

In this video, you will practice changing a fraction into decimal form.

Type: Tutorial

Multiplying and Dividing Even and Odd Numbers of Negatives:

You will learn how multiplication and division problems give us a positive or negative answer depending on whether there are an even or odd number of negative integers used in the problem.

Type: Tutorial

Simplifying Expressions with Rational Numbers:

In this tutorial, you will simplify expressions involving positive and negative fractions.

Type: Tutorial

Making Sense of Complex Fractions:

In this tutorial, you will see how to simplify complex fractions.

Type: Tutorial

Multi-Step Word Problem :

Solve a multi-step word problem in the context of a cab fare.

Type: Tutorial

Rational Number Word Problem with Fractions:

In this example, you determine the volume of frozen water and express the answer as a fraction.

Type: Tutorial

Rational Number Word Problem with Decimals:

This video demonstrates adding and subtracting decimals in the context of an overdrawn checking account.

Type: Tutorial

Negative Signs in Numerators and Denominators:

In this tutorial, you will evaluate fractions involving negative numbers and variables to determine if expressions are equivalent.

Type: Tutorial

Dividing Negative Fractions:

In this tutorial, you will see how to divide fractions involving negative integers.

Type: Tutorial

Multiplying Negative and Positive Fractions:

In this tutorial you will practice multiplying and dividing fractions involving negative numbers.

Type: Tutorial

Multiplying Positive and Negative Numbers:

In this tutorial, you will learn rules for multiplying positive and negative integers.

Type: Tutorial

Dividing Positive and Negative Numbers:

In this tutorial you will learn how to divide with negative integers.

Type: Tutorial

Why a Negative Times a Negative Makes a Positive:

In this tutorial you will use the repeated addition model of multiplication to help you understand why multiplying negative numbers results in a positive answer.

Type: Tutorial

Why a Negative Times a Negative is a Positive:

In this tutorial, you will use the distributive property to understand why the product of two negative numbers is positive.

Type: Tutorial

Dividing Fractions Example 2:

This video demonstrates dividing fractions as multiplying by the reciprocal.

Type: Tutorial

Dividing Whole Numbers and Fractions: T-shirts:

This video demonstrates dividing a whole number by a fraction by multiplying by the reciprocal.

Type: Tutorial

Substitution with negative numbers:

Practice substituting positive and negative values for variables.

Type: Tutorial

Interpreting absolute value as distance:

In this video, we work through a bunch of examples that stretch our thinking on interpreting absolute value.

Type: Tutorial

Finding the absolute value as distance between numbers:

In this video, we will find the absolute value as distance between rational numbers.

Type: Tutorial

Creating equivalent expressions with positive and negative numbers:

This video will demonstrate how to create quivalent expressions with positive and negative numbers.

Type: Tutorial

Even More Negative Number Practice:

This video uses the number line to find unknown values in subtraction statements with negative numbers.

Type: Tutorial

Adding Negative Numbers on Number Line Examples:

This video asks you to select the model that matches the given expression.

Type: Tutorial

Negative Number Word Problem:

Use a number line to solve a word problem that includes a negative number.

Type: Tutorial

Finding Initial Temperature from Temperature Changes:

In this video, we figure out the temperature in Fairbanks, Alaska by adding and subtracting integers.

Type: Tutorial

This video demonstrates how to add and subtract negative fractions with unlike denominators.

Type: Tutorial

This video demonstrates use of a number line and absolute value to add negative numbers.

Type: Tutorial

This video demonstrates use of a number line to add numbers with positive and negative signs.

Type: Tutorial

Subtracting a Negative = Adding a Positive:

Find out why subtracting a negative number is the same as adding the absolute value of that number.

Type: Tutorial

Negative Number Practice:

This video demonstrates adding and subtracting integers using a number line.

Type: Tutorial

Examples of Evaluating Variable Expressions:

This video tutorial shows examples of writing expressions in simplified form and evaluating expressions.

Type: Tutorial

Pre-Algebra - Fractions and Rational Numbers:

The first fractions used by ancient civilizations were "unit fractions." Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational numbers."

Type: Tutorial

Pre-Algebra - Multiplying Negative Numbers:

When number systems were expanded to include negative numbers, rules had to be formulated so that multiplication would be consistent regardless of the sign of the operands.

Type: Tutorial

Pre-Algebra - Commutative & Associative Properties of Addition:

A look behind the fundamental properties of the most basic arithmetic operation, addition

Type: Tutorial

Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz.

Type: Tutorial

Multiplying Fractions:

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

Type: Tutorial

## Video/Audio/Animations

Interpreting Integer Expressions on the Number Line:

This video contains three examples of interpreting integer expressions in the context of a number line.

Type: Video/Audio/Animation

Interpreting Negative Number Statements:

Explore negative numbers to represent real world situations in this tutorial.

Type: Video/Audio/Animation

Converting Fractions to Decimal Numbers:

Any fraction can be converted into an equivalent decimal number with a sequence of digits after the decimal point, which either repeats or terminates. The reason can be understood by close examination of the number line.

Type: Video/Audio/Animation

## Virtual Manipulative

Math Match - Concepts Review Game:

This interactive game allows students to review math concepts, including shapes, shape names, addition, multiplication, negative numbers, and equivalent expressions.

Type: Virtual Manipulative

## Student Resources

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

## Original Student Tutorials

Order of Operations with Rational Numbers Part 2: Decimals:

Evaluate numerical expressions with rational numbers expressed as decimals using the order of operations and properties of operations in this interactive tutorial.

Type: Original Student Tutorial

Order of Operations with Rational Numbers Part 1: Fractions:

Evaluate numerical expressions with rational numbers expressed as fractions using the order of operations and properties of operations in this interactive tutorial.

This is part 1 in a two-part series.

Type: Original Student Tutorial

Learn how to explain the meaning of additive inverse, identify the additive inverse of a given rational number, and justify your answer on a number line in this original tutorial.

Type: Original Student Tutorial

Why Does a Negative Times a Negative Equal a Positive?:

Use mathematical properties to explain why a negative factor times a negative factor equals a positive product instead of just quoting a rule with this interactive tutorial.

Type: Original Student Tutorial

## Educational Game

Integers Jeopardy Game:

This interactive game has 4 categories: adding integers, subtracting integers, multiplying integers, and dividing integers. Students can play individually or in teams.

Type: Educational Game

Distances on the Number Line 2:

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Comparing Freezing Points:

In this task, students answer a question about the difference between two temperatures that are negative numbers.

Operations on the Number Line:

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.

## Tutorials

Thinking About the Sign of Expressions:

This video shows some examples that test your understanding of what happens when positive and negative numbers are multiplied and divided.

Type: Tutorial

Converting repeating decimals to fractions :

Students will learn how to convert difficult repeating decimals to fractions.

Type: Tutorial

Converting repeating decimals to fractions :

This tutorial shows students how to convert basic repeating decimals to fractions.

Type: Tutorial

Converting a fraction to a repeating decimal:

Students will learn how to convert a fraction into a repeating decimal. Students should know how to use long division before starting this tutorial.

Type: Tutorial

Adding and Subtracting Numbers in Different Formats:

In this example, we will work with three numbers in different formats: a percent, a decimal, and a mixed number.

Type: Tutorial

Changing a Fraction to Decimal Form:

In this video, you will practice changing a fraction into decimal form.

Type: Tutorial

Multiplying and Dividing Even and Odd Numbers of Negatives:

You will learn how multiplication and division problems give us a positive or negative answer depending on whether there are an even or odd number of negative integers used in the problem.

Type: Tutorial

Simplifying Expressions with Rational Numbers:

In this tutorial, you will simplify expressions involving positive and negative fractions.

Type: Tutorial

Making Sense of Complex Fractions:

In this tutorial, you will see how to simplify complex fractions.

Type: Tutorial

Multi-Step Word Problem :

Solve a multi-step word problem in the context of a cab fare.

Type: Tutorial

Rational Number Word Problem with Fractions:

In this example, you determine the volume of frozen water and express the answer as a fraction.

Type: Tutorial

Rational Number Word Problem with Decimals:

This video demonstrates adding and subtracting decimals in the context of an overdrawn checking account.

Type: Tutorial

Negative Signs in Numerators and Denominators:

In this tutorial, you will evaluate fractions involving negative numbers and variables to determine if expressions are equivalent.

Type: Tutorial

Dividing Negative Fractions:

In this tutorial, you will see how to divide fractions involving negative integers.

Type: Tutorial

Multiplying Negative and Positive Fractions:

In this tutorial you will practice multiplying and dividing fractions involving negative numbers.

Type: Tutorial

Multiplying Positive and Negative Numbers:

In this tutorial, you will learn rules for multiplying positive and negative integers.

Type: Tutorial

Dividing Positive and Negative Numbers:

In this tutorial you will learn how to divide with negative integers.

Type: Tutorial

Why a Negative Times a Negative Makes a Positive:

In this tutorial you will use the repeated addition model of multiplication to help you understand why multiplying negative numbers results in a positive answer.

Type: Tutorial

Why a Negative Times a Negative is a Positive:

In this tutorial, you will use the distributive property to understand why the product of two negative numbers is positive.

Type: Tutorial

Dividing Fractions Example 2:

This video demonstrates dividing fractions as multiplying by the reciprocal.

Type: Tutorial

Dividing Whole Numbers and Fractions: T-shirts:

This video demonstrates dividing a whole number by a fraction by multiplying by the reciprocal.

Type: Tutorial

Substitution with negative numbers:

Practice substituting positive and negative values for variables.

Type: Tutorial

Finding the absolute value as distance between numbers:

In this video, we will find the absolute value as distance between rational numbers.

Type: Tutorial

Even More Negative Number Practice:

This video uses the number line to find unknown values in subtraction statements with negative numbers.

Type: Tutorial

Adding Negative Numbers on Number Line Examples:

This video asks you to select the model that matches the given expression.

Type: Tutorial

Negative Number Word Problem:

Use a number line to solve a word problem that includes a negative number.

Type: Tutorial

Finding Initial Temperature from Temperature Changes:

In this video, we figure out the temperature in Fairbanks, Alaska by adding and subtracting integers.

Type: Tutorial

This video demonstrates how to add and subtract negative fractions with unlike denominators.

Type: Tutorial

This video demonstrates use of a number line and absolute value to add negative numbers.

Type: Tutorial

This video demonstrates use of a number line to add numbers with positive and negative signs.

Type: Tutorial

Subtracting a Negative = Adding a Positive:

Find out why subtracting a negative number is the same as adding the absolute value of that number.

Type: Tutorial

Negative Number Practice:

This video demonstrates adding and subtracting integers using a number line.

Type: Tutorial

Examples of Evaluating Variable Expressions:

This video tutorial shows examples of writing expressions in simplified form and evaluating expressions.

Type: Tutorial

Pre-Algebra - Fractions and Rational Numbers:

The first fractions used by ancient civilizations were "unit fractions." Later, numerators other than one were added, creating "vulgar fractions" which became our modern fractions. Together, fractions and integers form the "rational numbers."

Type: Tutorial

Pre-Algebra - Multiplying Negative Numbers:

When number systems were expanded to include negative numbers, rules had to be formulated so that multiplication would be consistent regardless of the sign of the operands.

Type: Tutorial

Pre-Algebra - Commutative & Associative Properties of Addition:

A look behind the fundamental properties of the most basic arithmetic operation, addition

Type: Tutorial

Students will be able to see examples of addition of integers while watching a short video, and practice adding integers using an online quiz.

Type: Tutorial

Multiplying Fractions:

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

Type: Tutorial

## Video/Audio/Animation

Converting Fractions to Decimal Numbers:

Any fraction can be converted into an equivalent decimal number with a sequence of digits after the decimal point, which either repeats or terminates. The reason can be understood by close examination of the number line.

Type: Video/Audio/Animation

## Parent Resources

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

Distances on the Number Line 2:

The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.

Comparing Freezing Points:

In this task, students answer a question about the difference between two temperatures that are negative numbers.

Operations on the Number Line:

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers. There is a subtle distinction between a fraction and a rational number. Fractions are always positive, and when thinking of the symbol ab as a fraction, it is possible to interpret it as a equal-sized pieces where b pieces make one whole.

Repeating Decimal as Approximation:

The student is asked to complete a long division which results in a repeating decimal, and then use multiplication to "check" their answer. The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation.

Sharing Prize Money:

Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.