When I first started working at the Math Forum, I was given the task to complete packets for Primary students. I had to think of various methods on how to prove that 3 - 2 = 1. After having many years of mathematics, I simply wanted to use subtraction in my head to solve this problem, but I could not. When creating primary packets, besides creating a numerical equation using counting which would be just setting up 3-2 = 1, I also used other methods such as drawing a picture, using a number line, and using manipulatives. Using manipulatives is just a fancy way to say using counters.
I then started working on other packets for Pre-alg and Math Fundamental packets. I found coming up with methods for these problem a bit more difficult. When creating these packets, I first solved the problem myself, giving me one method to work with. I then thought very hard and looked through other students solutions while also comparing with my co-workers on methods they could come up. In many of the Pre-alg problems I used Algebra as a method, such as coming up with an equation using a variable, but then I also started using algebraic reasoning. Algebraic reasoning is almost identical to algebra, except instead of using a variable such as x or y, you would put the actual thing you are solving for in the equation. Say for example you have a problem where x represents the number of adults at a carnival and y represents the number of childen and the total is 100. Instead of writing:
x + y = 100
You would write:
adults + children = 100
It’s very simple, but its just an easier way to understand/read the problem.
Besides these methods, you can also use logical reasoning as a method, which is basically just gathering the facts you have and making a conclusion with little to no math involved. It’s almost like a guess, but definitely more educated and supported.
Creating a table or a list became very popular methods that I began using frequently. They are both easy ways to organize all of your information making the problem easier to understand. You may have one method as algebra and then another as creating a table, where the math may be the same, but it is organized in a table making it easier for someone to read.
An example of a table would be: