Natasha Glydon

It is easy to recognize numbers in the real world.  For example, highways have posted speed limits that are represented in numbers.  People who have obtained a driver’s license understand this system of numbers.  They know that if the posted limit is 110 km/h and they drive 120 km/h, they could be fined.  We see numbers on clocks and use them to understand time.  There are numbers on doors and buildings that state identifications.  Maps have numbers to give directions and information.  Positive integers are included in the set of whole numbers {0, 1, 2, 3, …}.  It is relatively easy to see how positive integers affect the world.  The implications of negative integers however, may be less obvious.

Going Down

In general, negative integers represent decreasing or downwards movement, or to the left (in relation to the number line).  If we are describing a car slowing down for a stop sign, its acceleration is represented with a negative value because its speed is decreasing.  If you were digging a hole, your depth could be represented using negative integers.

The Thermometer

A common example of negative integer usage is the thermometer.  Thermometers are similar to number lines, but vertical.  They have positive integers above zero and negative integers below zero.  Commonly, people recognize a temperature of -25°C as cold.  People use this number system to measure and represent the temperature of the air.   Also, if it -23°C outside, and the temperature drops 3 degrees, what is temperature now?  -26°C.  If we picture the thermometer, we know that as the temperature drops, we look downwards on the thermometer.

Image reproduced with permission of CasellaCEL

Hockey

Negative integers are commonly seen in sports as well.  Consider hockey.  Each line of players records a plus/minus.  If the other team scores on your line, that is a minus.  If someone on your line scores a goal, that is a plus.  If neither team scores, the result is zero.  Let’s look at an example.  During your time on the ice, you score one goal (+1).  One of your line mates also scores a goal (another +1).  However, in the last seconds of the game, a goal is scored against your team while you are on the ice (-1).  Your plus/minus score would be +1 at the end of the game.  However, during your next game, your line did not score through out the entire game (0) and the other team scored twice on your line (-2).   Your plus/minus score for that game would be –2.  Similarly, plus/minus scores can even out to zero if your line scores and is scored on an equal number of times in a game.  Considering that goal scoring is one of the important elements of hockey, it is imperative that players understand this system of numbers.

Altitude            

Geographically, we represent sea level with integers.  Obviously, below sea level is represented with negative integers.  For example, Death Valley (pictured below) in California is located at 86 m below sea level.  This can be represented numerically as –86 m.  Antarctica is  2,538 m below sea level
(-2,538).  When geography specialists study the difference between say the top of Mount Everest in Tibet, which is 8,848 m above sea level, and the bottom of the Dead Sea (409 m below sea level), they use negative representations of integers.

Image reproduced with permission of Alan Levine

Banks

Finally, banks and credit unions frequently use negative integers.  Negative integers can be used to represent debits and positive integers represent credits.  For example, let’s say I deposit $100 into my personal bank account.  My balance is then $100.  If I buy two $20 sweaters, I will need $40.  If I buy both sweaters, my account will decrease by $40.  This is often represented mathematically as -$40.  My account balance is then at $60.  I decide I also need a pair of jeans to go with my new sweaters and I find a pair I like for $65.  If I buy the pants, my account balance will be -$5.  It is easy to see how banks and credit unions use positive and negative integers to show whether money is being put into an account or taken out. 
Sometimes, negative integers are used to represent the following English words:

below

under

down

south

left

debit

ago