Why should I bother learning this?
Tell them that they need to be able to answer questions using numbers that make sense in context. Ask students to compare their responses to How do I get to ______ from here? and How far is it to ______? Fill in the blank with some well-known local place that requires just a right or left turn out of the parking lot and a short (straight) drive or walk. Extend the discussion into a clear differentiation between direction and distance.
What's so important about closed and open dots in an absolute value graph?
The issue here is not really absolute value. It's the distinction between the inequality symbols <, > and , . Use time as a way to model comparisons that include a number and those that exclude it.
Today is Tuesday. You have less than a week until your exam. Could that exam be next Tuesday? E < 7
It will take at least an hour to cook tonight's dinner. Could it possibly take exactly an hour? D 60 min.
Help students to see that the symbols that have two parts (including half of an equals symbol) are the ones that include the compared number and so require a closed dot.