Problem Solving Mentor

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MATH MENTOR: Solving Word Problems

Many people hate word problems. They can read the problem, they can understand it, but they can't find the missing part: the solution!

There are two steps to solving math word problems:

Turn the words into numbers. A number problem is called an equation. Take the numbers and produce an equation. Example: Words: How much is 10 - 6? Equation: 10 - 6 = X
Solve the equation!

Which is harder, number 1 or number 2? For most people, number one is the most difficult: turning words into numbers in an equation.

Read the whole problem - Get a feel for the problem. What is it talking about? What information does it lack or want? What information is given?
Decide how the information presented: miles, minutes, inches, centimeters, etc...)
Define what answer you need, and how it needs to be stated: miles, yards, meters, gallons, etc..
Look for "key" words and decide if some information is not needed. Following are some key words that have a numerical partner.

Addition	Subtraction	Multiplication	Division	Equals
increased by more than combined together total of sum added to	decreased by minus, less difference between/of less than, fewer than	of times, multiplied by product of increased/decreased by a factor of (this one is both addition/subtraction AND multiplication!)	per, a out of ratio of, quotient of percent (divide by 100)	is, are, was, were, will be gives, yields sold for

Vocabulary

"Per" means "divided by" - "I drove 340 miles on 10 gallons of gas, so I got 34 miles per gallon" (340/10 = 34 or 34/gallon)
Also 30 miles/gallon

"a" sometimes means "divided by" - "I just paid $10.00 for 4 gallons of gas! That means gas is $2.50 a gallon." 2.50/gallon

"less than" - "John paid $750.00 less for his car than Jan. Jan's payment minus John's.

Examples

Wording	Math expession	If Y is 30
What is the sum of 12 and y?	12 + y	12 + 30
12 less than y	y - 12	30 -12
y multiplied by 12	12y	12 X 30
the quotient of y and 12	y/12	30 ¸ 12
the difference of 12 and y	y - 12	30 - 12

Try these two different types of problems. The more you practice, the better you'll get. At first, you may feel lost. Later, you'll be writing problems yourself!

1. Problems that take a few steps to solve

Example: A machinist completes 9 parts in three days. How many parts can he complete in 8 days?

The answer will be in parts. I know how many parts in three days but not for one. I need to find out how many parts the machinist completes in one day. She will complete fewer parts in one day. If I divide 9 by 3, I will have the amount I want.

9 ¸ 3 = 2

Now I know how many parts she completes in 1 day. If I multiply that number by 8 days, I'll have the answer!

2 x 8 = 16 parts in 8 days.

Your turn:

The shop can repair 22 bikes a week. How many bikes can it repair in 12 days?

2. Problems that have extra information

Example: Jackson bought a 5 pounds of hamburger for $9.50, 2 loaves of bread bread for $ 4.75, a dozen eggs for $ 3.25, and a toy for his dogs for $3.84. How much did Ralph spend on food?

Always look at the question carefully. "How much did Ralph spend on food?"
The toy for his dog is extra information. You won't use that amount to solve the problem.
Solve the problem using only the information you need.
I need to add all of the amounts that are for food. The answer willl be in dollars. Toys aren't food, so I won't add that amount.

$9.50 + $ 4.75 + $ 3.25 = $17.50 (Ralph spent $17.50 on food.)

Your Turn

Marty enrolled at City Community College. He final bill included $765.00 in tuition, $35.00 in lab fees, and $ $40.00 in gym fees. On his way home, he bought 2 tickets for the Game Emporium in town. How much did Marty pay to complete his enrollment?

Links to practice more:

http://www.homeschoolmath.net/other_topics/teach-solve-word-problems.php

http://library.thinkquest.org/4471/learn.htm