Learning Algebra

Date: 03/02/97 at 18:01:40
From: McArthur
Subject: I need a lot of help with Algebra!

Hi, 

I am a grade 10 math student who has the greatest trouble learning
algebra. I will need a lot of help understanding the concepts if I am
going to survive the year-end exam.  If it is possible, could you 
explain algebra to me so it is simple for me to understand?

Help would greatly be appreciated. 

Thank you,
Robyn McArthur

Date: 03/03/97 at 13:38:56
From: Doctor Mike
Subject: Re: I need a lot of help with Algebra!

Hi Robyn,    

You are not alone.  Algebra is not easy.  Also, it often happens that 
a student doesn't start to get worried until the second half of the 
year.  Better late than never.  Let's go.
  
I cannot explain algebra in an e-mail.  I can give you some hints and 
pointers.  Then, you will just have to crank up your effort for the 
rest of the year.  You are going to be busy.
  
1. The concept at the top of my importance list is that if you have an 
equation and you do EXACTLY the same thing to each side of the 
equation, what you wind up with will be a true equation.  Here is a 
very simple example.  Given 2*x+6 = 32, if you subtract 6 from both 
sides, you get 2*x = 26.  If you then divide both sides by 2 you get 
x = 13.  Since the first equation is given to be true, the equation 
x = 13 is also true.

2. Write everything down.  Don't do stuff in your head.  You may be 
tempted for the previous example to say, "Okay, I'll subtract 6 and 
divide by 2 and get ummmmmm...x = 14".  Paper is cheap.  Write it 
down.  Go step-by-step.  Don't cut corners.  There are two reasons to 
take this advice. It is good advice because it helps you solve 
problems when you can see everything on paper that you're working 
with.  Also, teachers really love to see work. Really!

3. Always check your answer.  If you get the answer 14, go back and 
check to see if it really is a solution.  Do the math! Find 2*14+6 and 
see if it really is 32.  If it is not, you have messed something up 
and it's your responsibility to find out what.  

4. Check each step.  It's really easy even for a Ph.D. in math to 
multiply 6*7 and get 56 if (s)he is not being careful. These are just 
details, but alot of math IS details.  There are some important 
concepts, but there are lots of details. In order to learn the 
concepts, you must sweat the details.

5. It's okay to think.  If you are asked to answer "What is the square 
root of 2357*2357?" then you should be able to do that in your head.  
If you really understand about square roots, then the answer is 
obvious (2357). The area of exponents is a prime opportunity to use 
this hint. For example, to simplify "four to the 1.5 power" you might 
think "calculator time", but that's NOT the best way.  This problem is 
an opportunity to actually use one of the math concepts you learned.  
Since 1.5 is 3/2, the problem is really "four to the 3/2 power".  Now 
you MUST review the definition of fractional powers.  Taking something 
to the 3/2 power MEANS to "cube it to get a result, then square root 
that result". No calculator needed yet, just words and what they mean.  
Now we know what the problem is really asking;  Simplify : 
  
       Square root (4 cubed)
  
What's 4 cubed?  64, right?  What's the square root of 64? You 
probably know that, but I suppose you COULD use your calculator to 
get 8.  A good rule of thumb for use of your calculator in algebra is 
to use it at most once per problem. Save that one time for when you 
really need it.  

6. I have mentioned it before, but this is important enough to get its 
own number.  SWEAT THE DETAILS.  If you make "silly" arithmetic 
mistakes in doing an exercise about a new concept you are learning, 
then you might think you do not understand the new concept.  Algebra 
has some interesting ideas and techniques, but if you are not careful 
and don't use the tool of arithmetic reliably, you are not going to 
see what algebra has to offer.  It's like if you have been given a 
good car to take on a vacation.  If you know how to drive and take 
care of the car, you will have a great time.  If you go over a big 
pothole in the road at 60 miles per hour, you may bust a CV joint and 
the car will spend the vacation in the hospital.  Enough said.

7. I have given some simple examples in order to illustrate the advice 
I am giving.  What you will have to do is to start getting serious 
about doing problems - lots of them.  That's where we can help out 
here at Dr. Math.  We can help you with specific problems that are 
giving you fits.  But pick your questions for us well.  If we get an 
e-mail saying, "Please work these 15 exercises, my homework's due 
tomorrow," then we will not be able to help you.  It's much better for 
you to pick one problem about which you can say "Gee, if I could just 
figure out what the heck's going on here, I'd be able to do all my 
other problems". Then write us about that problem and tell us how far 
you got on it.  If you take my hints (above), and send in questions 
like this a few times, you will be back on track.  Good luck.

8. Re-read this e-mail at least once a week for the rest of 
   the year.  This WILL help you in algebra. 

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/