Integers and the four operations revisited
At Stage 8 the four sign rules should feel automatic β here they are gathered in one place.
By now the number line is a familiar friend. At Stage 8 the aim is fluency: calculating with integers quickly and without second-guessing the signs.
Two ideas carry all of it. First, adding and subtracting β two signs sitting next to each other combine into one. A plus and a minus make a minus; two minuses make a plus. So and .
Second, multiplying and dividing β look only at the two signs. Same signs give a positive, different signs give a negative.
The new skill is keeping all of this steady inside a longer calculation. Take it one operation at a time and rewrite the whole line after each step β that habit alone removes most slips.
- Two signs together combine: .
- Same signs multiply or divide to a positive answer.
- Different signs multiply or divide to a negative answer.
- Rewrite the full line after each step to stay accurate.