Math Tips


matbusters tips

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Math is different from other subjects

At MathBusters, we have a lot of experience teaching and tutoring math. And you know what? Some of us weren’t always good at it. Some of our tutors learned the hard way that they kept making the same kinds of mistakes over and over. We’ve seen our students make these mistakes over and over again, too. The following is a list of math tips for students who are struggling.

Math is learned by doing

You may be used to doing well in many classes such as history, social studies, even biology by simply paying attention in class and absorbing the information through osmosis. Or you may learn better by reading. You read your book, the information goes in your memory bank, and you spit the information back out on the test.

Unfortunately this will probably not help you succeed very well in most math classes. Maybe when you were learning your multiplication tables in elementary school this worked, but in order to learn any math beyond basic arithmetic (algebra and up) you’ll need to be more actively engaged with the material. That means it is not enough just to pay attention in class or read the chapter. You have to practice, practice, practice. That means doing lots and lots of problems. At MathBusters, our experience has taught us that learning math is is like learning to ride a bike or play the guitar. You can watch someone ride a bike or play the guitar till the cows come home, but that doesn’t mean you will know how to do it yourself. The only way you will learn is by actually practicing.

Try to see the big picture

When you’re solving a math or physics problem, you may forget what it is you were even trying to do in the first place. Always keep asking yourself, “What am I being asked to do?”

Are you being asked to find x? Are you being asked to find the perimeter of a shape? Are you being asked to prove a statement like “A square is a rhombus?” Write your goal in big letters at the top of the paper you’re working on and put big circle around it.

WANT: X
 

When you feel lost or like you’re not sure what to do next, take a look at that big WANT. You may find yourself surprised at how much time and frustration having this simple reminder will save you.

Divide and conquer!

Break harder problems up 2 or more easier problems. Break longer problems up into smaller problems.

For example, I might be trying to find the area of a parallelogram on a high school geometry test. I know there’s a formula for the area of a parallelogram, but for the life of me I can’t remember it. That means I just have to skip that problem and get 0 points, right?

Nope! I can break that parallelogram up into two triangles, find the area of each one using the formula \large \frac{1}{2} \times \text{base} \times \text{height} and then add the two areas together to get the area of the whole parallelogram. Many, many, many hard problems in math can be broken up into easier problems like this.

Work backwards

Many times you will be asked a question that you can’t answer until you first answer a question that wasn’t even asked! The rule of divide and conquer is sometimes optional, but in a situation like this it’s mandatory.  

For example, a question on a physical science homework assignment might say

“Ted started jogging at 2pm and finished jogging at 4pm. Find Ted’s average speed in miles per hour if he jogged a total distance of 10 miles.”

Since this is a physical science class, let’s assume I’ve already learned that I can divide the total distance travelled by the time spent travelling to find the average speed. The problem is that I don’t know what the time spent travelling is. So now I have a new sub-problem: find the time spent travelling. Fortunately this is pretty easy to do, I just subtract the time from the ending time to  find that I spent 2 hours jogging.  Now that my sub-problem has been answered, I can use the answer to my sub-problem to find the answer I really want. (Divide 10 miles by 2 hours to get 5 miles per hour)

Whenever you are asked to find something and you have no idea how you’re supposed to do that, ask yourself whether you need to solve a sub-problem first. Write down on your paper something like this:


To get X, I need to find Y.
New Problem: Find Y.

WANT: Y


 

Once you’ve found Y, You can use Y to get X. And then you’re done!

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