Note Taking Using Index Cards for Signed Numbers

In this series we will discuss how to prepare for a test using note taking as a strategy. If you are preparing for a math test that involves memorizing rules for the purpose of solving a problem, then index cards would be a helpful tool. On one side of the index card write down the rule. On the other side of the card, work out a problem using the rule. You can make up the numbers yourself or use the textbook that provides the answer key, (that way you know for sure you did the problem correctly). For example, a lot of students may have trouble memorizing the rules for adding and subtracting signed numbers. Write down the rule for how to simplify when the signs are the same. The rule is "add and keep the common sign". On the other side of the card write down an example or two. -25 + -12. Work out the problem using the rule of adding to get 37 and keeping the common sign of both numbers (-) and our solution is -37. The rule for adding signed numbers that have opposite signs is "first subtract, then take the sign of the number that has the larger absolute value". Absolute value is the distance a number is from zero on a number line. We can not have a negative distance so absolute value is always positive. Let's use -25 + 12. The signs are opposite so we subtract to get 13. Then we look at each number, -25 and 12. -25 has the larger absolute value because the absolute value of -25 is 25 and the absolute value of 12 is 12. So we take the sign of -25 and our solution will be -13. So far we looked at addition problems, now we will look at when the problem involves subtraction. If the problem involves subtraction, first change the subtraction sign to an addition sign. Then change the sign of the second number. For example, 12 - 25. Use your pencil to change the subtraction to addition and now make 25, negative 25. So now we have, 12 + -25 which is an addition problem! So, use the rules for addition to finish the problem.  The signs are opposite so subtract and keep the sign of the number with the larger absolute value and we get -13. What if we were subtracting a negative number such as 25 - -12? We will still change the subtraction sign to an addition sign, then change the sign of the second number thus making negative 12, a positive 12. Now the expression is 25 + +12, which we all know is +37. Of course we know that practice makes perfect so memorizing the rules may take some time but being organized with well written rules and and numeric examples will only benefit you in the end.