"I am not what happened to me, I am what I choose to become." Carl Jung
Systematic Problem Solving: Prelude
Who hates word problems? Well, most people do actually. There's a pretty good reason for this too: no one ever teaches us how to work with word problems! It's one of those little things where some people are good at them, while others look upon them with a sense of dread. Without extended encounters with problems like these, many people fail to really grasp the methods involved in solving them. What we're going to do is teach you, or maybe just give you a little refresher course on, how to demystify this type of problem and effectively apply your skills towards finding a solution.
What are word problems, really? Simply put, they are applications. What they are applications of depends on where you are encountering them. I suspect many of you who are reading this have taken at least a few classes in mathematics, certainly one area where you are likely to encounter these situations, but if you expand how you are thinking about them just a little, it is not hard to see that they are quite abundant and so there is real purpose in learning to master them.
Another way to think of word problems is to call them "real world" problems. Just how real depends on where you are getting the questions from. Our first examples will come from a basic intermediate algebra textbook, and so they will be simple and applying the principles we are looking at will be straightforward since the problems are generally fictional and selected by the authors for their simplicity. Later examples will become more challenging, yet you will see that even without extensive background in the fields that those problems come from, you will still be able to apply good systematic problem solving techniques to be able to attempt a solution.
The earlier problems will be largely mathematical in nature, or drawn from the realm of physics, but don't be surprised when you find some fun riddles in the mix. Some of those should come to be quite enjoyable. Later problems will begin to grow much broader in scope, with problems in fields ranging from business and computer science to medicine and information theory. Don't let anything scare you, you will have all the necessary tools to tackle each problem by the time you approach it.
The other, most important thing of all, is to have fun and enjoy a more enriched way of handling problem solving and becoming better prepared to handle all kinds of "real world" problems, many of which you might not have thought you would be able to approach before.
Good luck to you and feel free to comment and ask questions for help or clarification if you need it.
Best wishes,
Tristen
What are word problems, really? Simply put, they are applications. What they are applications of depends on where you are encountering them. I suspect many of you who are reading this have taken at least a few classes in mathematics, certainly one area where you are likely to encounter these situations, but if you expand how you are thinking about them just a little, it is not hard to see that they are quite abundant and so there is real purpose in learning to master them.
Another way to think of word problems is to call them "real world" problems. Just how real depends on where you are getting the questions from. Our first examples will come from a basic intermediate algebra textbook, and so they will be simple and applying the principles we are looking at will be straightforward since the problems are generally fictional and selected by the authors for their simplicity. Later examples will become more challenging, yet you will see that even without extensive background in the fields that those problems come from, you will still be able to apply good systematic problem solving techniques to be able to attempt a solution.
The earlier problems will be largely mathematical in nature, or drawn from the realm of physics, but don't be surprised when you find some fun riddles in the mix. Some of those should come to be quite enjoyable. Later problems will begin to grow much broader in scope, with problems in fields ranging from business and computer science to medicine and information theory. Don't let anything scare you, you will have all the necessary tools to tackle each problem by the time you approach it.
The other, most important thing of all, is to have fun and enjoy a more enriched way of handling problem solving and becoming better prepared to handle all kinds of "real world" problems, many of which you might not have thought you would be able to approach before.
Good luck to you and feel free to comment and ask questions for help or clarification if you need it.
Best wishes,
Tristen