A Cat Word Problem

Date: 08/23/2001 at 00:52:09
From: rachel
Subject: Word problems

Hi, 

I am bad at word problems - I don't understand how to take out the 
infomation you don't need. Here's the problem:

You have 5 cats and they all are 6 and all weigh 10 pounds. How much 
do they weigh altogether?

What do you take out?

Date: 08/23/2001 at 13:02:02
From: Doctor Peterson
Subject: Re: Word problems

Hi, Rachel.

The way to decide what information you don't need, is to list all the 
information you have, and all the information you DO need. To find 
what you do need, you'll need a plan for solving the problem. And that 
idea of planning is probably the main point of this sort of exercise.

What do you know?

    There are 5 cats.
    Each cat is 6 (years old?).
    Each cat weighs 10 pounds.

What is the goal?

    How much do they weigh altogether?

How can you find that out? You know the weight of one cat, and how 
many cats there are, so you can multiply. That's your plan. (You can 
often make a plan by just taking one fact and thinking about what you 
could do with it, then seeing if any other facts will help. When you 
find a way to the goal, you can retrace your steps and see which facts 
you used.)

Now you can check off the information you used in your plan; that will 
leave one item that is not needed, and that is the answer to the 
problem.

It's entirely possible that you might have a different way to solve 
some problems than your teacher would, so you might come up with a 
different answer that would still be valid for your method of solving 
it. Usually a problem like this will be pretty straightforward; but in 
real life, there might be several tricks you could use - sometimes you 
have redundant (extra) information, and can choose to take the short 
way (using the best information you are given), or the long way (using 
a different set of information), or the safe way (using both methods 
and comparing).

For example, suppose you had some more information: that cats always 
weigh four pounds when they are born, and gain one pound a year for 
the first ten years. Then if you want to take the long way, you could 
figure out for yourself that each cat weighs 10 pounds; you would be 
using all my new information, but would not need to have been given 
the cats' weight.

I myself tend to want to use all the information I am given, in order 
to check that it all agrees. If we had been told that each cat weighed 
12 pounds, we would have inconsistent information, and would know we 
had to go back and check the numbers we were given. So in real life, 
there may be no information you WON'T use, even though there is some 
you don't HAVE to use.

If you do well in all subjects except math, you can use your other 
abilities to strengthen your math skills. Problem solving, you may 
have noticed, involves more than just numbers. It requires a good 
understanding of language, an ability to imagine yourself in a 
situation, and perhaps even some background information about cats or 
whatever. If you ever read mystery books, they are all about problem 
solving. Which of the facts the detective knows are useful, and which 
are "red herrings" that are only there to confuse you? That's the same 
thing you're doing here. You might find you can improve your problem- 
solving skills by not thinking of it as math, but as fun! Be a 
detective, and look for different ways to think through a problem. 
Eventually, you'll find that all math is really problem solving, and 
is fun if you look at it the right way.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/