Learning AlgebraDate: 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/ |
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