Explore the concept of absolute value in terms of distances traveled. This video focuses on a real world application of absolute value and visualizes the problem by graphing points on coordinate plane.

Brush up on your math skills relating to absolute value then try some practice problems to test your understanding.

This site is a tutorial for students in algebra 2 or for those who need a refresher. The site has explanations, definitions, examples, practice problems and practice tests are found covering topics such as linear equations, graphing, quadratic equations, and rational expressions.

In this interactive math game, students use absolute value to determine how many feet below sea level Carl must be to stay away from the shark.

Great resource to practice and strengthen math skills pertaining to integers. Math worksheets are printable, may be customized, and include answer keys.

Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems with positive rational numbers.
Plot positive rational numbers on a number line.
Understand the equal sign.
Use the greater than and less than symbols with positive numbers (not variables) and understand their relative positions on a number line.
Recognize the first quadrant of the coordinate plane.

Lesson Flow

The first part of this unit builds on the prerequisite skills needed to develop the concept of negative numbers, the opposites of numbers, and absolute value. The unit starts with a real-world application that uses negative numbers so that students understand the need for them. The unit then introduces the idea of the opposite of a number and its absolute value and compares the difference in the definitions. The number line and positions of numbers on the number line is at the heart of the unit, including comparing positions with less than or greater than symbols.

The second part of the unit deals with the coordinate plane and extends student knowledge to all four quadrants. Students graph geometric figures on the coordinate plane and do initial calculations of distances that are a straight line. Students conclude the unit by investigating the reflections of figures across the x- and y-axes on the coordinate plane.

Students revise their work on the Self Check based on feedback from the teacher and their peers.Key ConceptsConcepts from previous lessons are integrated into this assessment task: integers, absolute value, and comparing numbers. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply your knowledge of integers, absolute value, and comparing numbers to solve problems.Track and review your choice of strategy when problem solving.

Students watch a dot get tossed from one number on a number line to the opposite of the number. Students predict where the dot will land each time based on its starting location.Key ConceptsThe opposite of a number is the same distance from 0 as the number itself, but on the other side of 0 on a number line.In the diagram, m is the opposite of n, and n is the opposite of m. The distance from m to 0 is d, and the distance from n to 0 is d; this distance to 0 is the same for both n and m. The absolute value of a number is its distance from 0 on a number line.Positive numbers are numbers that are greater than 0.Negative numbers are numbers that are less than 0.The opposite of a positive number is negative, and the opposite of a negative number is positive.Since the opposite of 0 is 0 (which is neither positive nor negative), then 0 = 0. The number 0 is the only number that is its own opposite.Whole numbers and the opposites of those numbers are all integers.Rational numbers are numbers that can be expressed as ab, where a and b are integers and b ≠ 0.Goals and Learning ObjectivesIdentify a number and its oppositeLocate the opposite of a number on a number lineDefine the opposite of a number, negative numbers, rational numbers, and integers

Students revise their work on the assessment task based on feedback from the teacher and their peers.Key ConceptsConcepts from previous lessons are integrated into this assessment task: the opposite of a number, integers, absolute value, and graphing points on the coordinate plane. Students apply their knowledge, review their work, and make revisions based on feedback from the teacher and their peers. This process creates a deeper understanding of the concepts.Goals and Learning ObjectivesApply knowledge of the opposite of a number, integers, absolute value, and graphing points on the coordinate plane to solve problems.Track and review a choice of strategy when problem solving.

Students analyze whether given statements are possible or impossible using their definitions of absolute value and the opposite of a number. If the statements are possible, students give an example of a pair of numbers that fit the statement. If the statements are impossible, students explain why.Key ConceptsA number and the opposite of the number always have the same absolute value.In general, taking the opposite of n changes the sign of n. For example, the opposite of 3 is −3.In general, taking the absolute value of n gives a number |n|, which is always positive. For example, |3| = 3 and |−3| = 3.Since the opposite of 0 is 0 (which is neither positive nor negative), therefore −0 = 0. The number 0 is the only number which is its own opposite.Goals and Learning ObjectivesFind pairs of numbers that satisfy different statements about absolute values and/or the opposites of numbers.State when it is impossible to find a pair of numbers that satisfies the statement and explain why.

Working With Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Compare and order positive and negative numbers and place them on a number line.
Understand the concepts of opposites absolute value.

Lesson Flow

The unit begins with students using a balloon model to informally explore adding and subtracting integers. With the model, adding or removing heat represents adding or subtracting positive integers, and adding or removing weight represents adding or subtracting negative integers.

Students then move from the balloon model to a number line model for adding and subtracting integers, eventually extending the addition and subtraction rules from integers to all rational numbers. Number lines and multiplication patterns are used to find products of rational numbers. The relationship between multiplication and division is used to understand how to divide rational numbers. Properties of addition are briefly reviewed, then used to prove rules for addition, subtraction, multiplication, and division.

This unit includes problems with real-world contexts, formative assessment lessons, and Gallery problems.

Students find the distance between points on a number line by counting and by using subtraction. They then use subtraction to find differences in temperatures.Students discover that the distance between any two points on the number line is the absolute value of their difference, and apply this idea to solve problems.Key ConceptsStudents know from earlier grades that the distance between two positive numbers on the number line can be found by subtracting the lesser number from the greater number. For example, the distance between 5 and 11 is 11 – 5, or 6. We can also state the rule for finding distance as “The distance between two positive numbers is the absolute value of their difference.” With this version of the rule, we don’t have to consider which number is greater; the result is the same either way. Using the example of 5 and 11, the distance is |11 – 5| or |5 – 11|, both of which are equal to 6.This idea extends to the entire number line, including numbers to the left of 0. That is, the distance between any two numbers is the absolute value of their difference. For example, the distance between –5 and 3 is |–5 – 3| = |–8| = 8 or |3 – (–5)| = |8| = 8, and the distance between –12 and –7 is |–12 – (–7)| = |–5| = 5 or |–7 – (–12)| = |5| = 5.Goals and Learning ObjectivesUnderstand the relationship between the distance between two points on the number line and the difference in the coordinates of those points.Find distances in real-life situations.

What is a number line? How can you use one to compare large and small numbers? Find the answers to these questions, play with an interactive number line, and follow links to information on adding, subtracting, and understanding absolute value using a number line.

Here is a site that clearly and thoroughly explains many topics related to absolute value, including solving equations and inequalities involving absolute values. There are example problems solved, problems for the student to attempt, and answers to the student problems. Point this site out to students who have been absent or who need additional instruction on this or many other topics.

Given a, b, and c shown on the number line, Sal determines if statements like -b < c are true. [4:54]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Students extend the operations of addition, subtraction, multiplication, and division to include positive and negative rational numbers, and build fluency with evaluating numerical expressions.

An algebra "cheat sheet" to use as a reference when completing algebra homework. Lists basic facts, properties, operations, formulas, and functions, as well as common errors.

Students learn how to solve equations and inequalities. Topics examined are linear equations, quadratic equations, linear inequalities, and absolute value inequalities. The class notes are available in pdf format.