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The Constructing and interpreting absolute value exercise used to appear under the Pre-algebra Math Mission. This exercise practices using the absolute value in context and as a distance measurement.

## Types of Problems

There are two types of problems in this exercise:

1. Select the correct answer: This problem provides a situational problem and asks for information. The answer choice is provided in a multiple choice format on the right side of the screen.
2. Enter the correct answer: This problem gives a word problem and this time the student is asked to find the answer and type it in the space provided.

## Strategies

Thinking of absolute value as a distance (rather than "turning things positive") can make these problems easier, although it is not necessary.

1. The expression $|x-y|$ means the magnitude of the distance between x and y.
2. The answer to the multiple choice type problem is almost always the expression that has the absolute value of a difference. The only exception research has found is where the answer was "is equal to $|x-y|$" as opposed to being smaller or greater than this amount.
3. If one object is above zero and the other is below zero, the distance between them can be found by adding their magnitudes.
4. Decimals and fractions are permitted interchangeably.
5. Remember that moving in a negative direction can be represented by a negative number. This is necessary on some of the Enter the correct answer problems.

## Real-life Applications

1. Absolute value can be used in applications connecting algebra to geometry.
2. The absolute value function is an example of a continuous but non-differentiable function (specifically at zero).
3. Absolute value extends into the concept of modulus for complex numbers.