Strategies for Solving Math
Problems
Carolyn Carter
GED Prep
Introduction TaskProcess
Resources Evaluation
Conclusion Teacher
Notes Additional Comments
INTRODUCTION
Students who take the GED exam almost always take
one of the tests last. Do you know which one it is? It’s math. Why does
math seem so hard? I think it’s because students have not learned
strategies for solving problems. To them math looks like a bunch of
numbers with no purpose. Would it be easier to solve problems if you
knew different ways to take the problems apart?
TASK
During this Webquest you will be introduced to
nine different strategies for solving math problems. It will be your job
to review the sample problems given, find another problem that uses the
same strategy and then enter the new problem to the class book.
PROCESS
1. Review the nine strategies presented below for solving math problems.
Read each strategy carefully and follow the sample problem.
2. Analyze the strategies. Which ones were new to you? Which ones have
you already used?
3. Did you understand each strategy? If not, consult another person in
the class who could help you understand, and reread strategy.
4. When you understand all the strategies, find an example problem for
seven of the nine strategies. It is your choice. Record your response in
your class notebook.
5. Your problems will be evaluated according to the rubric at the end of
this exercise.
6. You do not need to complete all of the exercises at one time. It is
more important to learn each of them well, so take your time.
_________________________________
THE NINE STRATEGIES
1.
Make a model
Make a model or representation using the data given in the problem.
Problem – Rachel had 28 blocks. If she stacked them in rows starting
with seven blocks and subtracted one block from each new row, how many
rows would she need to use all the blocks?
Using the model Rachel would need
seven rows.
2.
Use smaller numbers
Using smaller numbers can make the problem easier to imagine and then
solve.
Problem – Jose lives 3000 miles away from his family. If you drive 600
miles a day, can you estimate how many days it will take into drive?
3000 total miles
600 miles per day
Cross out the extra zeroes making sure you cross out the same number of
zeros from the numerator as the denominator.
300 total miles
6 miles per day = 5 days
It will take Jose five days to drive to his family’s house.
3. Use a graph
A graph is another way of picturing a problem so it can be solved.
Graphs have two dimensions; the X axis is horizontal and the Y axis is
vertical.
Problem –Adrienne took a typing class to improve
for speed on the computer. Each week she improved by 15 more words per
minute. How many weeks will it be before she can type 80 words per
minute?
At the end of six weeks she will be able to type 80 words per minute.
4. Draw a picture
Students often get stuck when they try to solve problem before they
understand it. Trying to picture helps you visualize the problem and
makes it easier to solve.
Problem – Casey had six cats. Two of the cats had litters of three cats
each. She gave away four of those kittens. How many cats and kittens
were still left after she gave away the kittens?
Count the number of cats in the
pictures. Then subtract four. How many cats are left?
Casey still had 8 cats! Here kitty kitty!
5. Use graph paper to trace a route
Graph paper can be used to solve problems especially those involving
directions.
Problem – Graham went for a walk one day. He started at the corner of
Harrison & 2nd. First he walked five blocks north, then three blocks
east and then four blocks south. He got tired and called a sister for
ride. She asked him where he was. What is the name of the intersection
where Graham stopped?
Graham was at the intersection of Garfield and 4th.
6. Look for a pattern
Patterns are everywhere. When you see a pattern in math, you can then
predict what is coming next.
Problem – James runs every week. He adds 2 miles to his weekly run each
week. If he ran 3 miles the first week, how far did he run in week
eight?
WEEK 
1 
2 
3 
4 
5 
6 
7 
8 
MILES 
3 
5 
7 
9 
11 
13 
15 
17 
In the eighth week James ran 17
miles.
7. Make an organized list
Another way to solve a problem is to list all the parts in an organized
way and then cross up the duplicates.
Problem – There are five flavors of ice cream. How many different
combinations of cones can be made if each column has two different
scoops?
The flavors are:
V = vanilla C = chocolate
S = strawberry B = banana
R = raspberry

V 
C 
S 
B 
R 
V 
X 
V+C 
V+S 
V+B 
V+R 
C 
V+C 
X 
S+C 
B+C 
R+C 
S 
V+S 
C+S 
X 
B+S 
R+S 
B 
V+B 
C+B 
S+B 
X 
R+B 
R 
V+R 
C+R 
S+R 
B+R 
X 
To solve the problem list every possible combination of two scoops, then
cross out the duplicates. The x in a square represents combinations that
are the same ice cream flavor.
There are 10 possible combinations.
8. Work backwards
When working backwards is the strategy, start with the facts at the end
of the problem and work backed work the beginning.
Problem – Charlie had some pennies. He had six more than Rosie and Rosie
had five more than Harry. Harry had four pennies. How many pennies does
Charlie have?
Harry 
4 



Rosie 
4 
5 

9 
Charlie 
4 
5 
6 
15 
When solving the problem, start with
the information you know. The first thing you know in this problem is
that Harry had 4 pennies. The next thing you know is that Rosie had five
more than Harry so 5 would be added to Harry’s 4. Continue on with the
problem by adding the number of pennies Charlie has to the number Rosie
has.
Charlie has 15 pennies.
9. Guess and check
Guess and check is exactly what it sounds like. You guess a number, plug
it into the problem and see if it works. If not, guess again.
George took a $20.00 bill to grocery store. He bought the following
items:
Bread $2.87
Milk $3.39
Hamburger $4.55
Chili beans $1.79
Licorice $2.50
Deodorant $5.55
Does George have enough money to pay
his bill? I guess that he does.
By rounding the numbers we can get a better idea if he has enough money.
Bread $3.00
Milk $3.00
Hamburger $5.00
Chili beans $2.00
Licorice $3.00
Deodorant $6.00
The total of all the estimates is
$21.00.
Since George still has to pay sales tax after purchasing the items, he
will not have enough money. (George better put the deodorant back).
RESOURCES
The following resources are
available to you.
SteckVaughn GED study guide
GED math practice books
Newspapers
Magazines
Life experience stories (make it up)
Interview with a neighbor or friend
GED web sites –
www.mathacademy.com/pr/prime/articles/storprob/index.asp
www.ket.org/ged2002/math/mathlesson14a.htm
www.aaamath.com/b/est.htm
www. Mcdonaldpublishingcatalog.com/solving_word_
_problems_smart_bookmarks_p128775.html
Evaluation Rubric
Score 
3 
2 
1 
Information needed to solve the
problem was complete 
All information was included 
Missing some information 
Not enough information to solve the
problem 
Strategy was identified 
Strategy clearly identified 
Strategy identified but misapplied 
No strategy identified 
Grammar punctuation and spelling meet GED standards 
No errors 
A few errors that did not detract from
the problem 
Many errors made it hard to read the
problem 
Problem was well written 
Language was easy to understand 
A little confusing but could work on
the problem 
Parts were confusing; did not
understand the problem 
Solution presented used the named
strategy. Pictures graphs tables were included. 
The strategy was correct and the
visuals were included. 
The strategy was correct. Most of the
visual information was included. 
Either the strategy or the visual
information was missing. 
Strategy was appropriate for the
problem. 
Strategy matched the problem. 
Strategy OK but a better one could
have been chosen 
Strategy did not match the problem 
Contributed required number of
problems 
Contributed seven or more problems 
Contributed 4 to 6 problems 
Contributed three or less problems 
CONCLUSION
Congratulations! You’ve just
reviewed nine different strategies for solving math problems and you’ve
contributed seven new problems. By studying these approaches you’re much
better prepared to take the GED exam and pass. In addition, you’ve
helped others prepare for the exam. Good for you!
TEACHER NOTES
During this exercise I’ve tried to
take the bugaboo out of math. The strategies are presented with simple
problems. The focus is on the student understanding how the strategy
works.
In my classes I always offer students a choice. I’ve found that students
are more motivated by choices and frequently will complete all of the
work. For adults with busy lives completing less than 100% of the
problems gives them a break.
The reading level of these exercises is 5.6 grade equivalents on the
Kincaid scale. Because of this, these exercises are also appropriate for
preGED students.
Additional Comments
This Webquest was designed for my
students at the jail who do not have access to computers. Although
references are given for web sites, they would not be able to use them.
Fairy tales are an important part of our culture and can be confusing to
ESL students. References are constantly made such as, “she’s waiting for
her prince charming,” or “here comes the big bad wolf”. One of the
variations for this exercise could be to rewrite the problems using
different fairy tales as a source of information. Students could
collaborate in groups to study culture as well as math.
