How can we carefully choose our words when introducing signed numbers in 7th grade so that we do not cause unnecessary confusion? Let me first say that it is very important how a topic is introduced. Inevitably, that first experience with the new topic will stick with the students for a long time. I introduce negative numbers through the idea of money (not using a number line). We simply ask the question: “When is it possible to have less than nothing?” The next day, we talk briefly about debt. Very soon thereafter, they can work work with problems like:
5 – 3 + 10 – 8
Every one of these problems is a story problem about a checking account. Beth opened her account and deposited $5, then wrote a check for $3, then deposited $10, then wrote a check for $8. What is her ending balance? (We assume that it’s okay for the balance to go under 0.)
Then I make a big deal about how, in algebra, we don’t usually talk about adding and subtracting numbers, but rather combining positive and negative numbers. Then I write a simple problem on the board: 9 – 4
Then I say (somewhat dramatically) that from an algebra standpoint, we don’t see this as 9 minus 4, but rather combining positive 9 with negative 4. In that light, we could have just as well written it as -4 +9. It’s the same thing! I really try to be strict with my language through the remainder of the block, trying to use the word “combining” rather than “plus” or “minus” or “subtract.” In 8th grade, (and hopefully there’s not too much algebra) or 9th grade, the words “plus” or “minus” may creep back in, but it’s okay because the students have grasped the general concept.