It is also true for all of the opposite numbers between —2 and 0. When you graph this on a number line, the closed dots at —2 and 2 indicate that those numbers are included.
One way to think about it is, you're still getting two sets of values the "negative" set and the "positive" set , but because they meet at zero, they converge into one set. These inequalities can be rewritten without absolute value signs by writing the expression inside the absolute value as falling between two numbers:. Preparation: If you don't have a commercially prepared number line, draw one either on the chalkboard or on a long preferably thin sheet of paper.
If teaching remotely, share an absolute value number line that the entire class can see. Include at least —20 to Prerequisite Skills and Concepts: Students need to be familiar with the inequality symbols and how to make and use a number line.
They also need to be able to compute with negative numbers. You are looking for questions such as: What was the temperature in degrees Fahrenheit? How do I get to Lake Erie from here? If appropriate for you and your students, compare the different ways that signed numbers and direction appear in student answers. For example, a temperature value only has "direction" because degrees in Fahrenheit include negative and positive values, so a sign is needed for clarity.
Directions to Lake Erie would require a variety of signed numbers: where to travel east positive vs. You are looking for questions such as: How far above zero degrees Fahrenheit was the temperature? How far north is Lake Erie from here? Have the teams alternate going first, thinking of questions that require a signed or absolute number to answer, and then having the other team revise the question.
Encourage students to be creative with their questions. Discuss why the direction of the comparison symbol changed, using the large number line to illustrate what the students and you say. Do several more examples until you are satisfied that students can compare both signed numbers and absolute values. Materials: Index cards or digital "cards" that can be distributed among the class.
Each Absolute Value Card listed has two values for x. These values overlap so that each Variable Value Card satisfies two of the given absolute value equations the first and second values satisfy the first equation, the second and third values satisfy the second equation, and so on, until the last and first values satisfy the last equation.
Distribute the cards or equations equally. Be sure they've all been distributed. Choose a student to say "I have" and then read the value or equation on their card. Then have the student say "Who has a match for my card?
Absolute Value Equations - Concept. Sometimes we need to use only positive numbers, and the absolute value is a useful tool for this purpose. When you see an absolute value in a problem or equation, it means that whatever is inside the absolute value is always positive. Absolute values are often used in problems involving distance and are sometimes used with inequalities. Later we will discuss graphs of absolute value equations and inequalities. Absolute Value is a funny concept in Math that a lot of people have a hard time getting used to but the important thing to keep in mind when you're working with Absolute Value is to remember that Absolute Value just means distance away from zero, I'm going to say that lots of time.
So like for example if I were looking at a problem that looks like this where it said "the Absolute Value of x equals 2. The symbol for absolute value is two vertical bars:.
Finding the absolute value of a number is one of the most important nonbinary operations. The absolute value doesn't pay attention to whether a number is positive or negative — only how far that number is from zero. How do you find the absolute value equation? Step 3: Solve for the unknown in both equations.
Step 4: Check your answer analytically or graphically. What are the rules for absolute value? When we take the absolute value of a number, we always end up with a positive number or zero. Whether the input was positive or negative or zero , the output is always positive or zero.
What is the absolute value of negative one and one third? Which number is greater than the absolute value of? The absolute value of any number is either zero 0 or positive. It makes sense that it must always be greater than any negative number.
Show 4 more comments. Michael Hoppe Michael Hoppe And once you can measure distances to zero you may calculate the distance of any two numbers by taking the absolute value of their difference.
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