You may recall getting very nervous when your teacher said “OK class, today we’re going to do some word problems to help you learn math.” I use to break out into a cold sweat! But it doesn’t need to be thaat way for you or your children. Check out this article written by Joe Pagano. Perhaps your view of word problems will change!
In Mathematics, Word Problems Can Be Fun
By Joe Pagano
One of the biggest hurdles your youngster has to overcome in school is the terrible bugaboo which is a math word problem. During my many years of private instruction, the one complaint I have heard all too many times is that of the inability to conquer the word problem. Yet word problems can be tackled successfully. This article outlines how.
Word problems are more difficult that “regular” math problems because the solution requires one to first determine what has to be done and then how to do it. Thus a word problem, unlike the solution of an equation such as x + 3 = 4, and then asking for the value of x, requires one to determine what equations can be extracted from the words, and then how to solve those specific equations.
Another difficulty lies in a student’s inability to read at a level necessary to make sense out of the words that make up the problem. Poor readers will generally make poor word problem solvers. This is why I teach students critical reading skills, among which are techniques such as “anticipatory reading” and other active reading competencies. Such methods not only give students a tremendous boost in their mathematical abilities but cross over into other disciplines requiring reading, such as social studies and English.
In order to better understand these strategies, we will look at a specific word problem at the pre-algebra/algebra level, and then see how to implement such techniques. The problem we shall discuss is on the topic of systems of equations in algebra.
Word Problem Example: Five hockey sticks and three hockey pucks cost $23. Five hockey sticks and one hockey puck cost $20. How much do two pucks cost?
Word Problem Strategies:
First Pass: This is the stage at which we just read the problem to get a “feel” for what is going on within. During this stage, we are not trying to solve the actual problem but just get an overall sense of what the problem deals with.
Second Pass: This is the stage when we re-read the problem, paying careful attention to the situation at hand, what the problem deals with, who the main players are, and so forth. During this stage, we start to mull over some problem solving strategies and start to plan our attack.
Third Pass: This is the brainstorming stage. At this point we clearly determine what the nature of the problem is, what we know, and what we are asked to do. This is when we start to convert words to numbers and equations and quantify everything within the problem.
Fourth Pass: This is the stage at which we begin to solve the problem using the information we gathered in the third pass. At this stage, we also double check our brainstorming phase to insure that we took the right approach.
Fifth Pass: This is the final stage at which we check the solution obtained in the fourth pass for consistency.
Let us go through these stages with the problem at hand. During the first pass, we read the problem and see that it has something to do with hockey sticks and hockey pucks and the price of two pucks. Note we have been thrown a curve ball here in that we are asked to state the price of two pucks not one. Keep this in mind for the end of the problem.
Now during the second pass, we notice that indeed we are dealing with the sport of hockey, that we are limited to the two pieces of equipment, pucks and sticks, and that we are given the prices for certain combinations of the two, and that we are asked specifically for the price of two pucks.
At the third pass, we start to create the initial mathematics. We have that 5 sticks and 3 pucks cost $23. We also know that 5 sticks and 1 puck cost $20. At this point, we should even take a guess at some numbers that might work just to make sure we have a good feel for the problem. For example, you may guess that a stick might be $4 and a puck $1. Then 5 sticks and 3 pucks would cost $23 so this seems like a good choice. However, those values do not satisfy the second condition, that of 5 sticks and 1 puck costing $20. Remember the final values have to satisfy both conditions in order to be the correct ones. But at least we are in the ballpark with our initial guess.
In our fourth pass, we choose letters to represent our items in the problem, and we then put our equations together. Since we are dealing with pucks and sticks, a good choice of letters would be S for stick and P for puck. Gee. Really? Okay, so now we have the following two equations:
5S + 3P = $23
5S + 1P = $20
Now you see that you are looking at a simple system of linear equations. You can solve by using the method of elimination. Thus if we subtract equation 2 from equation 1, we end up with 2P = $3, or by simple division, that P = $1.50. If we plug this value for P back into either equation 1, we get that S = $3.70. Now going back to what was asked for, the price of two pucks, we have 2x$1.50 = $3.00.
At the fifth pass, we should ask ourselves if our answer is reasonable. It seems that the cost of the stick should be more than that of the puck, even if the price of the stick seems a bit inexpensive. If we plug these values for S and P into equation 2, we get a check and thus we can feel comfortable that our solution is correct.
By using this simple step strategy, your children can confidently conquer word problems. No matter whether the problem involves hockey pucks and sticks, or giraffes and elephants, or whether the solution involves systems of equations or mixed rate problems. Reading critically, solving actively, and applying this five step process will insure impressive success in the oft regarded ghoulish realm of word problems. Goblins beware!
Joe is a prolific writer of self-help and educational material and is the creator and author of over a dozen books and ebooks which have been read throughout the world. He is a former teacher of high school and college mathematics and has recently returned as a professor of mathematics at a local community college in New Jersey.
Joe propagates his Wiz Kid Teaching Philosophy through his writings and lectures and loves to turn “math-haters” into “math-lovers.” See his website http://www.mathbyjoe.com for more information and for testimonials, and try out one of his ebooks here http://www.mathbyjoe.com/page/page/2924777.htm to achieve better grades in math.
Joe breaks down the process very well – eh? So simple that a child could do it! (Well after a little coaching. 🙂 )
By the way, I found this article at ezinearticles .com. They have some very interesting reading on many different and varied topics.
Hope you have a wonderful Thanksgiving if you live here in the USA!