- Describe situations in which opposite quantities combine to make 0.
*For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.* - Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
- Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
- Apply properties of operations as strategies to add and subtract rational numbers.

### Clarifications

**Fluency Expectations or Examples of Culminating Standards**

Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in grade 7 depends on rational number arithmetic, fluency with rational number arithmetic should be the goal in grade 7.

**Subject Area:**Mathematics

**Grade:**7

**Domain-Subdomain:**The Number System

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (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 Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

**Assessment Limits :**N/A

**Calculator :**Neutral

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**A number line is shown.

Use the Add Point tool to plot a point that is 14.5 units from 8 on the given number line.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

**Test Item #:**Sample Item 2**Question:**An expression is shown.

What is the value of the expression?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 3**Question:**A number line is shown.

Jack knows that a + b = 0.

Which statement is true?

**Difficulty:**N/A**Type:**MC: Multiple Choice

**Test Item #:**Sample Item 4**Question:**An expression is shown.

Kendrick is using number lines to find the value of the expression. His first two steps are shown.

A. Use the Add Arrow tool to show the last two steps.

B. Select the value of the expression.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

**Test Item #:**Sample Item 5**Question:**An expression is shown.

What is the value of the expression?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 6**Question:**The sum of

*a*and*b*is*c*. The number line shows*a*and*b*.Which statements about

*c*are true?**Difficulty:**N/A**Type:**MS: Multiselect

**Test Item #:**Sample Item 7**Question:**An expression is shown, where a < 0 and c > 0.

a + b = c

Drag the two points to the number line to show possible locations of a and b.

**Difficulty:**N/A**Type:**GRID: Graphic Response Item Display

## Related Courses

## Related Access Points

## Related Resources

## Assessments

## Educational Games

## Educational Software / Tool

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Tasks

## Teaching Idea

## Tutorials

## Video/Audio/Animation

## Virtual Manipulatives

## STEM Lessons - Model Eliciting Activity

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.

## MFAS Formative Assessments

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

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

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

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

## Original Student Tutorials Mathematics - Grades 6-8

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.

## Student Resources

## 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.

Type: Original Student Tutorial

## Educational Games

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

This addition game encourages some logical analysis as well as addition skills. This particular circle game uses positive and negative integers. There is only one way to combine all the given numbers so that every circle sums to zero.

(source: NLVM grade 6-8 "Circle 0")

Type: Educational Game

This virtual manipulative provides students with practice adding positive and negative integers. Students are given an addition problem and using one-to-one correspondence, the student is able to see what happens when adding negative integers. The addition problems can be computer generated or teacher generated and there is a free play mode which allows the student to practice with the chips and become familiar with the process of moving the chips around the page and creating a visual representation of an addition problem with integers.

Type: Educational Game

## Educational Software / Tool

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

## 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 in the Florida Standards 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

## Tutorials

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

Type: Tutorial

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

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 tutorial will help you understand the concept of absolute value. Take the quiz after the lesson to practice!

Type: Tutorial

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

Type: Tutorial

This tutorial will help the learner to understand the concept of subtracting the positive and negative integers with the help of a number line. Learners can also take a quiz after the concept is internalized.

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

## Virtual Manipulative

This virtual manipulative guides the student in the use of color counters to model subtraction of integers.

Type: Virtual Manipulative

## Parent Resources

## Educational Games

This addition game encourages some logical analysis as well as addition skills. This particular circle game uses positive and negative integers. There is only one way to combine all the given numbers so that every circle sums to zero.

(source: NLVM grade 6-8 "Circle 0")

Type: Educational Game

This virtual manipulative provides students with practice adding positive and negative integers. Students are given an addition problem and using one-to-one correspondence, the student is able to see what happens when adding negative integers. The addition problems can be computer generated or teacher generated and there is a free play mode which allows the student to practice with the chips and become familiar with the process of moving the chips around the page and creating a visual representation of an addition problem with integers.

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 in the Florida Standards 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

## Tutorials

This tutorial will help you understand the concept of absolute value. Take the quiz after the lesson to practice!

Type: Tutorial

This tutorial will help the learner to understand the concept of subtracting the positive and negative integers with the help of a number line. Learners can also take a quiz after the concept is internalized.

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

## Virtual Manipulative

This virtual manipulative guides the student in the use of color counters to model subtraction of integers.

Type: Virtual Manipulative