Students might feel that the concept of numbers less than zero just doesn’t make sense. They wouldn’t be alone. There have been several classifications of numbers, including negative numbers, that were not been well received initially. Negative numbers have existed in various forms for a couple of thousand years, but didn’t really catch on in europe until the 1500s. The greek mathematician Diophantus (c. AD 250) considered equations that yielded numbers less than zero to be “absurd.”1 So, it is understandable if students today take a while to warm up to them. It is true that numbers less than zero do not make sense in every context, but there are plenty of places where they do.

Numbers less than zero exist in various areas: Temperature (temperatures below zero), golf scores (shots under par), money (being in debt), bank accounts (being overdrawn), elevation (being below sea level), years (AD vs bc), latitudes south of the equator, the rate of inflation (falling prices), electricity (impedance or voltage can be negative), the stock market (the Dow was down 47 points), and bad Jeopardy scores. launches of rockets run through the number line. T minus 3 means it’s 3 seconds before the test. T minus 3, T minus 2, T minus 1, 0, 1, 2… counts the seconds before and after liftoff: –3, –2, –1, 0, 1, 2…

Those real life examples can be used to make sense of some of the rules for computation. The fact that 4 + (–9) = (–5) can make sense to students because they know that dropping 9 degrees from a temperature of 4 degrees makes it 5 degrees below zero. Also, if it is currently 17 degrees, but the temperature is dropping 5 degrees a day for the next 7 days, that is the same as saying that 17 + 7(–5) = –18. That same situation can show that two negatives multiplied together make a positive. Again, suppose this day it is 17 degrees and the temperature is dropping 5 degrees a day. going back in time, four days ago it must have been 17 + (–4)(–5) = 37 degrees.