In one of the middle school sessions at TMC12 we were talking about integers and how students struggle especially with subtraction. We were brainstorming different strategies (chips, number lines, rules, etc.) This is the distance strategy I shared with the group.
When working with students it is important for them to understand that subtraction is more than just "take away". Yes, we can figure 25 - 3 as "You have 25 candies in your hand and you eat 3. What do you have left?" but that limits us when we expand to include integers.
Using a number line students can also recognize that the distance between 25 and 3 is also 22. Continue building on what students know.
13 - 4 = 13 take away 4 but also the distance between 13 and 4
So what happens when you switch it?
4 - 13
Many students will intuitively notice the result would have to be negative. What is the distance between 4 and 13? It is the same as 13 and 4 only it is negative because the smaller number is first.
*Students have to understand the above to be able to move forward.
9 - (-2) = the distance between 9 and -2, notice 9 is larger than -2 = 11
-2 - 9 = the distance between -2 and 9, notice the -2 is smaller than 9 = -11
-3 - (-8) = the distance between -3 and -8, notice the -3 is larger than -8 = 5
If students have trouble determining the distance, provide a number line. Counting on to determine how far apart numbers are is another strategy that some students might need practice with.
-135 - 124 =
(the distance from -135 to 0 is 135, the distance from 0 to 124 is 124 so the distance from -135 to 124 is 135 + 124)