# Absolute Value Worksheets

Many times in math we will need to understand how two different things relate and/or differ. We will often refer to the concept of absolute value when creating relationships between values. The absolute value refers to a numbers distance from zero on a numbers line regardless of direction. In this way the absolute value of 10 and -10 are the same because both of them are exactly 10 ticks from the zero position. When we begin to write more complex equations and expression the absolute value comes in handy to describe conditional situations. We will help students understand how to calculate absolute value and simplify all types of different math applications of it.

### Aligned Standard: Grade 6 Numbers - 6.NS.C.7c

- Absolute Value Step-by-step Lesson- In this one we focus on the application with positive numbers. It is explained with the help of a numbers line.
- Guided Lesson - We refresh you on the skill and then we start using it in operations.
- Guided Lesson Explanation - We work on the true value of absolute numbers.
- Practice Worksheet - This is the definitive on the coverage of the skill.
- Absolute Value Equations Five Pack - This will help kids overcome their fears of the value of equations and show them that there is little difference between equations and integers.
- Skills Focused Five Pack - A nice grab bag of questions for you.
- Matching Worksheet - Match the problems to their final values.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Using number lines, raw sums and differences can be found in these.

- Homework 1 - Absolute values focus on the size or magnitude of a number. They do not leave any regard for the sign of the number, as a result the results are positive or zero.
- Homework 2 - It is important to understand the basic measure we are working with here the measure is that of a number is its distance from 0.
- Homework 3 - Again, it does not matter if the number is negative or positive.

### Practice Worksheets

These sheets will help students build up some confidence.

- Practice 1 - These measures are always positive or zero. You will classify the end result of operations and numbers themselves.
- Practice 2 - Give yourself some more practice with this through a practice exercise. Focus on the || symbols first, then move on to the operations.
- Practice 3 - Simplify each equation and work to make sense of it all. Process the numbers in the symbols first and then move on.

### Math Skill Quizzes

The first one involves algebra and is only for advanced students.

- Quiz 1 - Where the negative symbol lies is important. We bring algebra into this one. You will need to solve for x.
- Quiz 2 - This is a really nice mix of problems for you to concentrate on. You will work on problems like these: If the domain is the set of signed numbers, find the solution set for: |x| = 12. Find the value of x.
- Quiz 3 - These are tricky on purpose. Do well here and you will show that you know your stuff.

### What Is Absolute Value?

In mathematics, an absolute term or commonly referred to as the modulus is denoted by placing the value inside bars such as: |x. This is also without any indication of the sign associated with it. The absolute value is a measure of the distance of a number from zero. For example, in the case below, the absolute value of 4 is 4 ticks or places from zero. Yes, it may seem a bit obvious; why wouldn't be the distance between 0 to 4 is 4. But this values really shows their true colors when the distance is not measured from 0. For example, the absolute value of -4 is also 4. The symbol used to denote this is a | which is placed on each side of the number. For example, in regard to a -6 it would be denoted as a |-6|. The end result of this would be 6 as well because it is 6 places from 0. It is important to remember that this measure for 5 and -5 is 5. So, it can be written as both |-5| or |5|.

There is a wide range of applications where the generalization of this concept takes place such as for quaternions, complex numbers, fields, ordered rings, and vector spaces. You find this when in the real world when you are trying to gauge finances especially changes in it, temperature, speed.

### When and How is Absolute Value Used in The Real World?

This measure is constantly used in situation where we are attempting to assess a difference, change or rate. The common example is when a car is pulled over for speeding. If the zone the car passed through was marked for 45 miles per hour and a state trooper clocked the car travelling at 58 miles an hour, the difference is 13 miles per hour. All penalties and fines are based on this value. We find this measure being determined and handy when we are exploring the concept of altitude. This measure is based on the standard distance from sea level. Which is a theoretic measure of the surface of the ocean. The Dead Sea in Israel is considered to below the Earthâ€™s lowest point on land. It measures 1,388 feet below sea level (-1,388). This sea is super salty, it is so salty that many living things can not inhabit it. Mount Everest located in Nepal and Tibet is thought to be the highest point on land. The highest recorded peak on Everest measures 29,029 feet above sea level. If we were asked to calculate the difference in height between these two world wonders, we would express it as 30,417. We eventually realize that without the concept of absolute value the negative value of global mean sea level, would throw off our calculations. This measure is super helpful in healthcare and pharmacology when dosages and temperatures are critical to maintain health.