J Crabtree says: >The use of the '-' and '+' signs as both verbs (take away and add) as well as adjectives (negative and positive) result in confusion. As mentioned, I use a model of bumps and holes for integers. While -7 - -4 confuses most adults in society, 7 holes take away 4 holes leaves 3 holes confuses nobody. I will expand on this later.
OK - let's have a bit of fun. Holes and bumps are OK, but "3 holes take away three bumps" still seems a bit recondite.
Let make a positive number forward facing: 3 (or +3) shall be officially 3->, and have length 3 units with arrow facing RIGHT (correct, proper, richtig). A negative 3, (shame!!!), for example, shall be written <-3 and have length 3 on the number line with arrow pointing LEFT (how gauche! again shame!!).
To ADD these numbers the rule is: place the tail of (either one -- call it "second") to the head of the other (whose tail is at the origin). Read off the mark at the pointer of the second arrow.
To subtract one from the other, (now order matters) the second is flipped in direction and then added (placed at the head of) the first. Read the final marker on the number line.
OK - tastes great, less filling. Lets trim the notation for ease of writing. Since positive numbers are typically introduced first without explicit signs, lets leave it that way (i.e, 3-> = 3). For the negative numbers: <-1, <-2, <-3, ...etc., since they are the only numbers left with all the ornaments, lets just shorten, for our ease, "<-N" to just "-N", OK?