Solving Math Word Problems

    One of the biggest struggles for math students each year is solving word problems – especially if they involve setting up equations.  Below I have included a few tips on successfully attacking these problems.

First: Read the problem!

This seems so obvious, but many students only read a small portion of the problem.  I believe that many students anticipate what the problem is asking and try to solve before they know all the facts.  Some students are intimidated by word problems and give up before they even read the problem. 

Second: What is the question? What does the problem want to know?

            It is hard to answer a question if you don’t know what is being asked.  The question usually is found at the end of a problem.  For example:

            Three friends go to a restaurant and spend $30 on food. The tax on the food is 5%. The friends leave a combined $5 tip.  How much will each person spend at the restaurant?

            The problem wants to know “how much each person spends at the restaurant.”

Third: Play detective and look for clues.

            What are the important pieces of information found in the problem? In the above problem we know the following information:

·         3 friends

·         Spent $30 on food

·          5% tax

·         A combined $5 tip

A very effective strategy is to highlight or underline these key pieces of information.

Fourth: Decode the clues

            As you look at the different clues you should look for tips about what each is asking.  For example, the word “each” is telling us we will probably need to divide.  The word “combined” is telling us we are adding.  A list of key words is found at the end of this article.

Fifth: Sketch out the clues

            Once you have found the clues to the problem it is very helpful to write down and organize.  There are all sorts of ways to sketch out this info. Flow charts, Venn Diagrams, arrows, symbols such as > or <, circles, tables, operations symbols, and many others.

            On our sample problem we can organize the clues this way:

($30 for food) + (5% tax) + ($5 tip) ÷ (the three friends) = cost for each friend

Sixth: Solve the mystery (Compute)

            Once you organize the information you see that you really only need to find the tax of 5% on the $30 meal. You then find that 5% of $30 is $1.50. After you find the tax you are now ready to solve the problem.

($30 food) + (5% tax) + ($5 tip)

(3 friends)

 

 

             In this problem the cost of food, tax and tip equals $36.50. After you divide the $36.50 by 3 (number of friends) you get $12.166… which is about $12.17 after rounding.

Key words for Operations and Symbols

Below are some Math Operation Words for Addition:

SUM	Add	Addition	Total	Plus	More than
In addition to	Increased by	Enlarged by	Exceeds by	Gain	Rose
Greater	Greater than	Together	Grouped	In all	Altogether
Bought	Join	Both	How many	In excess	Combine

 

Below are some Math Operation Words for Subtraction:

DIFFERENCE	Subtract	Subtraction	Minus	Take away	Decreased by
Deduct	Less than	Reduced by	difference	Loss of	How many left
Fewer than	Dropped	How many more than?	How many less than?	How many fewer?	How much taller?
How much shorter?	How much left?	How many are not?	Diminished	Reduce

 

Below are some Math Operation Words for Multiplication:

PRODUCT	Multiply	Multiplied by	Times	By	Of
At	Groups of	Each	Every	In all	Altogether
Each shared

 

Below are some Math Operation Words for Division:

QUOTIENT	Evenly	Each	Divide	Divided	Into
Per	Ratio	Parts	Dividend	Divisor	Fractions
Each	Every	How much for each?	How many groups?

 

Below are some math symbols and matching words:

(  )	Quantity
=	Equals, Equal, Is, Was, Will be, Results
>	Greater than
>	Greater than or equal to
<	Less than
<	Less than or equal to

 

 

Below are some examples of translating words into Algebraic Expressions:

Five more than x	x + 5
A number added to 7	7 + x
A number increased by 11	x + 11
5 less than 8	8 – 5
A number decreased by 3	x – 3
Difference between x and 5	x – 5
Twice a number	2x
Twenty five percent of a number	0.25x
Ten times a number	10x
Quotient of x and 4	x ÷ 4 or x/4
Quotient of 4 and x	4 ÷ x or 4/x
8 is three more than a number	8 = x + 3
The product of 2 times a number is 20	2x = 20
One half a number is 5	x/2 = 5
3 times the difference of a number  and 5	3(x – 5)
9 is greater than x	9 > x

Todd Hawk is a middle school math teacher and the co-founder of the Land of Math website (www.landofmath.com). You can reach him at landofmath2@gmail.com or follow him on twitter: @landofmath2.