THESE ARE TEACHER ERIC ELIASON’S TIPS ON HOW TO TEACH MATHEMATICS
I have the privilege of preparing students for the GRE/GMAT at Nomen Global English School. Here is my strategy for arithmetic.
I introduce various types of numbers as needed; natural, whole, integer, positive, negative, even, odd, consecutive, prime and composite. We understand what each number is like and how to perform arithmetic on them.
For example, we draw a number line. Positive means the number is to the right and negative means the number is to the left. Adding means to go to the right and subtracting means to go to right in reverse or to go to the left. However, subtracting a negative means to reverse its leftward direction and therefore to go right. Likewise, when we multiply or divide, multiplying a negative by a negative means to count a negative a negative amount of times, so it is going to the right.
With the number line, we also cover absolute value. We explain that it means the positive version of a number. When we have two numbers and we want the distance between them, it is the absolute value of subtracting them. That is because if you want the distance from x to y, if y is bigger, it is y-x and if x is bigger, it is x-y. x-y and y-x are opposites, so taking the absolute value of (x-y) will provide us with the positive distance.
With even and odd, we give the students the option to either memorize the rules or understand them. If the number can be divided by 2 it is even, otherwise odd. Evens and odds are next to each other.
With consecutives, we teach how to add them. There is a formula for starting at 1 and a strategy for adding them when they are in a range but not starting at 1.
We take order of operations one operation at a time.
For Least common multiple and greatest common factor, I explain that we factor the numbers into primes. Then for LCM we take each prime the most it appears and that contributes to the LCM. For GCF we take each prime the least it appears and if there is a number that doesn’t have it, we don’t include it.
With fractions, I use pizzas. For instance, if you had 2 1/8 it would be 2 full pizzas and 1 1/8th slice or in other words 17 pieces (17/8). I teach them how to go back and forth.
To add and subtract fractions, I show to use the LCM to get the denominators in sync and the GCF to simplify the end result. Multiplying is easy and division is when you just flip the fraction you are dividing by and multiply instead.
Decimals are just more place values of multiples of 10 smaller than 1. We add them and subtract them place by place just like normal numbers. When we multiply them, we pretend there’s no decimal and then count how many numbers to the right of the decimal there are afterwards and put the decimal accordingly. When we divide, we move the decimals to the right one at a time until we are just dividing numbers. We keep dividing after we get past the decimal point.
For percentages, we have an equation for every statement they can make. For ratios, we look at marbles that are in that ratio.
To convert between decimals, fractions, ratios and percentage we just express them in a certain way and simplify.
And that is how I teach arithmetic at Nomen Global.