Number Line Sums

The number line below shows the location of a, b, and 0. All of the other information has been hidden. The three gray diamonds are located at (a + b), (a - b), and (b - a). Unfortunately, the labels are hidden!

Using just the location of a and b, can you identify which gray point is (a + b), which is (a - b), and which is (b - a)? If you need a hint, you can show the numbers on the number line as well as arrows for a and b. When you think you know the answers, click the buttons to show the labels.

Make a game of this!

Player 2 looks away while Player 1 moves a and b to a new location. Then, Player 2 will try to guess which diamond is (a + b), which is (a - b), and which is (b - a). After guessing, click the button to show the answers.

What strategies can you use to guess correctly the first time?

SERP, 2 October 2013, Created with GeoGebra