So I made a handout about adding and subtracting integers that’s a visual nightmare so I’m not even sharing it. In the process, I’ve got a hypothesis about why every semester students seem to get adding integers reasonably well and then explode when subtraction gets dumped on them.
I realized that there are four possibilities when you’re adding integers if students understand the commutative property: putting two positives together — old school –, putting two negatives together (not a positive; the biggest hurdle here…), putting a big positive and small negative together, and putting a big negative and a small positive together. I’m thinking for the big picture people that it might just be peachy to show them that.
With subtraction, there are five possibilities — and five’s too big for lots of people… unless you chunk it up. It’s also coming right smack ON TOP of the adding negatives. It’s kinda like how much harder it is to juggle “just one more thing.”
So I’m wond’ring if starting out with “big minus little” and “little minus big” and getting that down pat … and *then* “negative minus positive” as being the same as negative plus negative — more negative, thank you…
and *finally,* the (-)(-) situations… where either it’s a positive number in front — so you just add — or negative, the nastiest… but *hopefully* if this has been done systematically, by now the student will have adding different signed integers at least hovering near the elusive mastery/automaticity.
So… assuming I’ll successfully breach what was my nemesis developing the app the first time, and be able to construct quizzes and store that information, etc… that’s my plan.