Inspiration in algebra for adults

To understand algebra you must first understand numbers.  First understand the integers (positive and negative whole numbers), then rational numbers, then the real numbers.  The integers should be simple: There are five sheep, I have two pens.  The negative numbers can be understood thinking of money.  I have $1000 in the bank and a $500 debt, so my worth is $500.  That debt plays the role of a negative number.

After the integers are understood, rational numbers are the next step.  You should be able to add and multiply them together without a calculator or much effort (for simple problems).  After that the really silly stuff begins.  The rational numbers kind of have gaps in them.  They don't explain every magnitude that one might consider.  For example there is no rational number whose square is 2.  The real numbers fill in these gaps.  Once real numbers are understood, with all their operations then algebra can be a target of study.

Our discussion of algebra will involve grandmother's house.  Say your grandmother moved to a house 120 miles away.  You get in your car and drive at 60 miles an hour.  How long will it take you to get to grandmother's house?  The great thing about algebra is that it will actually answer this question.  It'll take two hours.  The point is that you can actually find out stuff you didn't know using the stuff you do.

This example is rather simplistic, but that's the catch 22 of math.  More interesting things take more interesting (harder) math.  The more interesting math is not accessible until the simpler math is understood.

Another hurdle of mathematics is the language aspect of math.  Math really creates its own language.  There are ideas that are deemed important, and words are created to help express the ideas.  Also, there's the aspect that letters are used to represent quantities.  For our grandmother's house example could have been stated as: Let d be the distance from your house to grandmother's house, r be the speed you travel, and let t be the time it takes to travel to grandmothers house.  Since we know that these quantities are related by the relation d=rt we have 120=60*t for our case. Solving this equation yields that t=2.

The reason one would use such verbose language is because it is more precise. The line of reasoning is easier to follow once this type of language has been adjusted to. Also the use of the equation "d=rt" is crucial in explaining how to solve similar problems.

Don't sell yourself out. Don't go into the fight thinking you will lose. You can do it, the fact that you're reading this suggests that you are the type that can.