This document provides guidance on solving word problems in mathematics. It presents 5 sets of basic word problems and their key terms as examples. It also outlines the steps to take in solving word problems: 1) familiarize yourself with the situation, 2) translate the problem into a mathematical equation, 3) solve the equation, 4) check the answer, and 5) state the answer clearly. An example problem is worked through demonstrating these steps.
2. SOLVING WORD PROBLEMSSOLVING WORD PROBLEMS
Organize the word problem into steps
1.Read the problem, carefully
2.Underline all math facts, leaving out
information/numbers which are not useful
3.Draw a picture of the problem
4.Write a number sentence
5.Solve the sentence
3. Basic Word Problem Set 1Basic Word Problem Set 1
Let’s do this basic word problem together
Brad has 3 violet shirts and 1 red shirt. How many
shirts does Brad have total?
Now try this one on your own
To get to Jill's house, you need to first go 3 miles
on 2nd
Street. You then turn on 4th
Street for 4
miles and you will read Jill's house. How far in all
is it to Jill's house?
KEY + WORDS: Both, Altogether, In all, Total,
Sum, Increased by
4. Basic Word Problem Set 2Basic Word Problem Set 2
A set of drapes requires 23 yd of material. The drape
maker has 10 yd of material. How much more material is
needed?
It is 134 miles from Los Angeles to San Diego. A driver
has gone 90 miles of the trip. How much farther does the
driver have to go?
KEY - WORDS: Many more, Much more
Much _______er (shorter, longer, fatter, hotter, taller...)
Left, Less, Change, Difference, Fewer, Decreased by,
More than, Farther than
5. Basic Word Problem Set 3Basic Word Problem Set 3
A jogger runs 4 mi on each of 8 days. How many miles are
run in all?
A band is arranged rectangular in 12 rows with 20 members
in each row. How many people are in the band?
KEY x WORDS: Per, Each, Groups, Set, Product, Times,
Twice
6. Basic Word Problem Set 4Basic Word Problem Set 4
A candy factory made 176 lb (pounds) of
chocolates. They put them in 4 lb boxes. How
many boxed did they fill?
A family divides an inheritance of $184,000
among its children, giving each of them $23,000.
How many children are there?
KEY (division) WORDS: Quotient, Split, Divided
by, Given an amount of many and finding one,
when sharing, cutting, splitting
7. Basic Word Problem Set 5Basic Word Problem Set 5
Ty Cobb hit 3052 singles in his career. Stan
Musial hit 2641. How many did they hit together?
It takes Venus 225 days to rotate about the sun.
It takes the earth 365 days. How much longer
does it take the earth?
You wrote checks of $45, $78, $and $32. Your
balance before that was $246. What is your new
balance?
A customer buys 8 suits at $195 each and 3
shirts at $26 each. How much is spent?
How many 16 oz bottles can be filled with 608
oz of catsup?
8. SOLVING PROBLEMSSOLVING PROBLEMS
FAMILIARIZE yourself with the situation. If it
is described in words, read carefully. In any case,
think about the situation. Draw a picture
whenever it makes sense to do so. Choose a
letter, or variable, to represent the unknown
quantity. To be solved for.
TRANSLATE the problem to an equation.
SOLVE the equation.
CHECK the answer in the original wording of
the problem
STATE the answer to the problem clearly with
appropriate units.
9. Solving Problem ExampleSolving Problem Example
The John Hancock Building in Chicago is
1107 ft tall. It has two 342 ft antennas on
top. How far are the tops of the
antennas from the ground?
10. Solving ProblemSolving Problem
JOHN HANCOCK BUILDINGJOHN HANCOCK BUILDING
FAMILIARIZE: make a drawing
Height of the antenna is 342
ft
Height of building 1107 ft
What is the height of top of
the
antennas from the ground?
h
11. Solving ProblemSolving Problem
JOHN HANCOCK BUILDINGJOHN HANCOCK BUILDING
TRANSLATE:
We translate the problem to the following
addition sentence using the variable h
1107 + 342 = h
12. Solving ProblemSolving Problem
JOHN HANCOCK BUILDINGJOHN HANCOCK BUILDING
SOLVE
To solve the equation, we carry out the
addition sentence:
1107
+342
1449
Therefore, 1449 = h, or h = 1449
13. Solving ProblemSolving Problem
JOHN HANCOCK BUILDINGJOHN HANCOCK BUILDING
CHECK
We check the height of 1449 ft in the original
problem. We can repeat the calculation.
We can also check the reasonableness of
the answer. We would expect our answer
to be larger than either of the heights, which
it is. We can also find an estimated answer
by rounding:
1107 + 342 ~ 1100 + 300 = 1400 = 1449
14. Solving ProblemSolving Problem
JOHN HANCOCK BUILDINGJOHN HANCOCK BUILDING
STATE
The height of the top of the antennas from
the ground is 1449 ft.
