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: