In working with mathematics, I love finding
alternate ways of solving a problem. If something
doesn't make sense, there should be another way to work it out.
What makes me happy? Discovering another method.
The girls who I tutor are just entering that new
world of Algebra. It's a land of mystery that either
inspires adventure through problem solving, or
tears through confusion.
You have an equation like:
2x + 4 = 4
Now, the way I solve it, is to work on isolating
my variable, X. I do this by working my way
backward through the order of operations;
ie, I multiply to get rid of the divisor 6.
So, multiplying each side by 6, gives me:
2x + 4 = 24
Then, I get subtract 4 from each side.
2x = 20
Finally, I divide both sides by 2, which gives me:
x = 10
This is the method I was taught, and it works for me,
but there it can be a frustrating method to teach.
This is the new-to-me method the girls I work with
were shown in school:
You take your equation:
2x + 4 = 4
and you use a template to create a sort of map that follows the journey of x.
On the left hand side, you have X. X is multiplied by 2, then has 4 added to it, and then is divide by 6.
Then, we write the inverse function of each operation along the bottom of the template.
What I like about this method is that it breaks down
the algebraic process into steps that are easy to follow.
There is less mystery as to where to start. You start
with your variable, and follow the mathematical actions
that are done to it. For the beginner who is intimidated
by the idea of variables, and who struggles with order of
operations, it is a confidence builder.
I am waiting to see if this method can be expanded to
more complicated equations, but I love how quickly
my students absorbed it. It is a much better beginning
than I had.