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.

**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

**Grade:**7

**Domain-Subdomain:**The Number System

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Educational Games

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Teaching Ideas

## Tutorials

## Video/Audio/Animations

## Virtual Manipulative

## Student Resources

## Original Student Tutorials

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

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

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

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

## Problem-Solving Tasks

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

## Tutorials

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

Type: Tutorial

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

Type: Tutorial

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

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

Type: Tutorial

This video demonstrates dividing fractions as multiplying by the reciprocal.

Type: Tutorial

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

Type: Tutorial

Practice substituting positive and negative values for variables.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

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

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

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

Type: Tutorial

## Video/Audio/Animation

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

## Problem-Solving Tasks

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

## Tutorials

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

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

Type: Tutorial