Absolute Value
 Absolute value can be a bit confusing for students who are just learning about signed numbers. First, you tell them that numbers not only have a value, but they have a direction from zero. Then, as they're trying to grasp that, you tell them that even directed numbers have an absolute value. Things will be much easier if you emphasize throughout your discussions of both rational numbers and absolute value the differences between distance and direction.
 Encourage students to check their work by testing some values in both directions from a proposed solution to an absolute value inequality.
 Help students to see that the way problems are worded will indicate whether their answer should be a directed (signed) number or an absolute value. If, for example, they're asked to show change in value, they should expect to use signed numbers to show the direction of the change. If they're asked to show increase or decrease, those words give away direction, so a second direction on the number itself is redundant and may produce a double negative (a negative decrease would logically be an increase).
 
