Bobby's Encounter with Integers
By: Ilona Kusz
Bobby was very excited to begin his second year of middle school. Bobby enjoys learning new things and was excited to learn new and challenging facts in seventh grade. Everything was going well for Bobby until he came across multiplying and subtracting integers in math class.
Bobby did very well with adding an d subtracting integers. Bobby enjoyed integer addition and subtraction because both operations could be easily related to real life. For example, Bobby related positive integers to gaining money and negative integers to losing or borrowing money.
All was going well for Bobby until his teacher introduced the rules for multiplying and dividing integers. Bobby was a visual learner and he would often use the number line to illustrate integer addition and subtraction. Bobby’s teacher taught him that when multiplying or dividing integers with the SAME signs, the result will be positive. When multiplying or dividing integers with DIFFERENT signs, the result will be negative.
Bobby went home very puzzled. He just recently mastered the rules for adding and subtracting integers and then his teacher introduced two new operations. Bobby had his mother check his homework one night and he discussed with her how he might remember the rules for multiplying and dividing integers.
Bobby’s mother had an idea. She told Bobby to think of a positive sign as a “good thing” and a negative sign as a “bad thing”. She then went through a few scenarios with Bobby.
Think of it this way Bobby “when good things happen to good people, that’s good”. This could be used when multiplying and dividing two positive integers.
(+) x (+) = +
AND
(+) / (+) = +
Bobby’s mother went on to explain “when good things happen to bad people, that’s bad”. This could be used when multiplying and dividing a positive and a negative integer.
(+) x (-) = -
AND
(+) / (-) = -
Bobby stopped his mother before she could explain the next scenario. “I got it” Bobby said. “When bad things happen to bad people, that’s good”, said Bobby. This could be used to remember the rules for multiplying and dividing two negative integers.
(-) x (-) = +
AND
(-) / (-) = +
Bobby was very happy that he not understood the rules for multiplying and dividing signed numbers as a result of the funny situations that his mother taught him about good and bad things and what happens when they mix. Bobby repeated these funny reasons in his head each time he multiplied and divided positive and negative numbers.