Dealing with Word Problems Study Guide (page 2)
Introduction to Dealing with Word Problems
A mathematician is a blind man in a dark room looking for a black cat, which isn't there.
—CHARLES R. DARWIN, English naturalist (1809–1882)
Word problems abound both on math tests and in everyday life. This lesson will show you some straightforward approaches to making word problems easier. The practice problems in this lesson incorporate the various kinds of math you have already studied in this book.
A word problem tells a story. It may also present a situation in terms of numbers or unknowns or both. (An unknown, also called a variable, is a letter of the alphabet that is used to represent an unknown number.) Typically, the last sentence of the word problem asks you to answer a question. Here's an example: Last week, Jason earned $57, and Karen earned $82. How much more money did Karen earn than Jason? Word problems involve all the concepts covered in this book:
- Arithmetic (whole numbers, fractions, decimals)
- Ratios and proportions
- Probability and counting
Doing all the problems in these two chapters is a good way to review what you have learned in the previous lessons.
Steps to Solving a Word Problem
While some simple word problems can be solved by common sense or intuition, most require a multistep approach as follows:
- Read a word problem in chunks rather than straight through from beginning to end. As you read each chunk, stop to think about what it means. Make notes, write an equation, label an accompanying diagram, or draw a picture to represent that chunk. You may even want to underline important information in a chunk. Repeat the process with each chunk. Reading a word problem in chunks rather than straight through prevents the problem from becoming overwhelming, and you won't have to read it again to answer it.
- When you get to the actual question, it. This will keep you more focused as you solve the problem.
- If it's a multiple-choice question, glance at the answer choices for clues. If they're fractions, you probably should do your work in fractions; if they're decimals, you should probably work in decimals; and so on.
- Make a plan of attack to help you solve the problem. That is, figure out what information you already have and how you're going to use it to develop a solution.
- When you get your answer, reread the circled question to make sure you've answered it. This helps you avoid the careless mistake of answering the wrong question. Test writers love to set set traps: Multiple questions often include answers that reflect the most common mistakes test takers make.
- Check your work after you get an answer. In a multiple-choice test, test takers get a false sense of security when they get an answer that matches one of the given answers. But even if you're not taking a multiple-choice test, you should always check your work if you have time. Here are a few suggestions:
- Ask yourself if your answer is reasonable, if it makes sense.
- Plug your answer back into the problem to make sure the problem holds together.
- Do the question a second time, but use a different method.
If a multiple-choice question stumps you, try one of the backdoor approaches, working backward or nice numbers, explained in the next lesson.
Translating Word Problems
The hardest part of any word problem is translating from English into math. When you read a problem, you can frequently translate it word for word from English statements into mathematical statements. At other times, however, a key word in the word problem hints at the mathematical operation to be performed. The translation rules follow this explanation.
When reading a word problem, cross out all the unnecessary words that do not directly pertain to the math. They only serve as a distraction, and your process will be more visible when they're removed.
EQUALS Key words: is, are, has
|Bob is 18 years old.||B = 18|
|There are 7 hats.||h = 7|
|Judi has 5 books.||J = 5|
ADD Key words: sum; more, greater, or older than; total; altogether
|The sum of two numbers is 10.||x + y = 10|
|Karen has $5 more than Sam.||K = 5 + S|
|The base is 3" greater than the height.||b = 3 + h|
|Judi is 2 years older than Tony.||J = 2 + T|
|Al threw the ball 8 feet further than Mark.||A = 8 +M|
|The total of three numbers is 25.||a + b + c = 25|
|How much do Joan and Tom have altogether?||J + T = ?|
SUBTRACT Key words: difference; fewer, less, or younger than; remain; left over
|The difference between two numbers is 17.||x – y = 17|
|Jay is 2 years younger than Brett.||J = B – 2 (NOT 2 – B)|
|After Carol ate 3 apples, r apples remained.||r = a – 3|
|Mike has 5 fewer cats than twice the number Jan has.||M = 2J – 5|
MULTIPLY Key words: of, product, times, twice
|25% of Matthew's baseball caps||0.25 × m, or 0.25m|
|Half of the boys|
|The product of two numbers is 12.||a × b = 12, or ab = 12|
|Murray has twice as many cards as Tina.||M = 2T|
|[Notice that it isn't necessary to write the times symbol (×) when multiplying by an unknown.|
DIVIDE Key word: per
|15 blips per 2 bloops|
|60 miles per hour|
|22 miles per gallon|
Converting Decimals and Fractions into Time: Remember, decimals are based on units of 10, while seconds and minutes are based on units of 60, so be careful when converting information in word problems! When faced with time as a decimal or fraction, multiply the fraction or decimal portion by 60 to convert it into seconds.
Today on Education.com
- Coats and Car Seats: A Lethal Combination?
- Kindergarten Sight Words List
- Signs Your Child Might Have Asperger's Syndrome
- Child Development Theories
- 10 Fun Activities for Children with Autism
- Social Cognitive Theory
- Why is Play Important? Social and Emotional Development, Physical Development, Creative Development
- GED Math Practice Test 1
- Problems With Standardized Testing
- The Homework Debate