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Simple Strategy for Word Problems

A basic strategy for getting started on word problems, story problems and modeling.
by

Garry Carpenter

on 2 December 2014

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Transcript of Simple Strategy for Word Problems

Word Problems. We call them story problems, word problems, modeling problems and sometimes HEADACHES. They strike fear into the hearts of even the bravest of math students. They cause endless frustration for the unprepared. But... THERE IS HOPE! A basic strategy when solving "word" problems. Step 1: Read the problem. Step 2: Read the problem. Step 3: Identify any unknown quantities and
assign variables to represent them. Step 4: Write an equation. Step 5: Solve the equation. See, here it is! Didn't we already do this? In this step, you should RECORD relevant information as you read.
Then it's on to Step 3. Yes. But now we're reading for DETAILS. Times Distances Variables Names Formulas Equations Numbers Dates Speeds Questions Amounts Relationships Measurements Unknowns Values Expressions Quantities Having a variable that represents the quantity you want to know allows you to move on to Step 4. Unknown quantities often are found in the form of a question. Your variable answers the question. How far did he go? What was her speed? How much money was in the account? Find the number of bricks. When did they arrive? Determine the height. Sometimes the "question" is hidden as a directive...Find, determine, evaluate, calculate, show, analyze....and words like that. How many pounds of peanuts? How fast was the car going? How much money did you earn? This step is a "look before you leap" sort of step. You read the problem once to get a big picture. What is it talking about?
Are we dealing with distance and speed, or width and area, or money and interest....what? Once you have a general idea of what the problem is about, it's time to move on to Step 2. x = number of pounds of peanuts. s = the speed of the car in mi/h w = the amount of money, in $, earned Once you've written an equation to describe the situation, it is on to Step 5. Often, seeing the problem in a picture can help you to see the relationships that can form an equation. Try drawing a picture. Use a known formula. Using your variable, write an equation. Here are some strategies. For most people, this is the most difficult step in solving a word problem. Use a chart, a table of values, or a list to put the information into a more organized format. Depending on the situation, you may be able to find a formula to relate the quantities. d=rt , A=bh, P=2w+2l, I=Prt
F=ma, and many more are available. Organize the information. Begin by writing out in words any relationships that you can identify. This can form the basis for the beginning of your equation. Write a verbal model first. Classify the type of problem. Shared work problem? Use a rational equation. Mixture problem? Use quantity and value. Distance problem? Use a chart. Knowing the type of problem can point the way toward an equation. There is no single strategy for writing equations from information presented as a "word problem". As you practice, you will continue to add more and more strategies to your toolbox so that you can tailor your strategy to the problem. Many, many more. Amount of 10% acid solution. + Amount of 15% acid solution. = 2 liters of 13% acid solution. Use all the tools of solving equations you've learned to solve the equation you wrote. Don't forget the possibility of solving by graphing. You've found it! You have the solution. You can now rest from your labors....unless there is a Step 6. By this time you've successfully translated the word problem into a mathematical model. Time to do the math. Disclaimer: you've been "doing the math" this whole time. Math is far more than just solving equations. Step 6: Write your answer. See, when you SOLVE the equation in Step 5 you end up with something like
x=3 But what does that have to do with the price of tea in China? The SOLUTION to the equation needs to be interpreted and reported as the answer to the original question. So if x=3 is the solution, then maybe the price of tea was $3 per pound. Or maybe it was 3 yuan per bushel. Your final answer should completely answer the question, and should include appropriate units. Hey! Maybe the word problem was actually asking you what the price of tea in China is. It's possible. What are you waiting for? GO TRY IT!
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