Transcript Problem Solving Strategies: Story Problems

Learning The Language:
Word Problems
STEP ONE
 Read the word problem and identify the important
information you will need to solve the problem.
STEP TWO
 Identifying what type of arithmetic you will need to do
 Addition
 Subtraction
 Multiplication
 Division
Addition
 Addition story problems often use words like:
 Increased by
 More than
 Combined
 Together
 Total of
 Sum
 Added to
EXAMPLE:
• Jane has 10 Barbie's and for her
birthday she gets 3 more. How many
Barbie’s does Jane have now? (10+3=?)
Subtraction
 Subtraction story problems often use words like:
 Decreased by
 Minus
 Difference
 Less than
 Fewer than
 Away/loose
 “Subtract from”
EXAMPLE:
• If there are 10 cars in one parking and
6 less cars in the second parking lot.
How many more cars are there in the
second parking lot? (10-6=?)
Multiplication
 Multiplication story problems often use words like:
 Of
 Times
 Multiplied by
 Product of
EXAMPLE:
• If Mary has 3 pets and Annie has 2
times as many pets as Mary. How
many pets does Annie have? (3x2=?)
Division
 Division word problems often
use words like:
 Per
 Out of
 Ratio of
EXAMPLE:
• If Bobbi had 15 cookies and ate the
same amount each day for 5 days how
many did she eat per day? (15 / 5=? )
 Quotient of
 “a”
EXAMPLE:
John ate a total allowance of $250. If he
spends $25 a day, how many days
will the allowance last?
STEP THREE
 Solve the Problem
Using one of the many problem solving strategies
Choose a Strategy to Solve the
Problem:
 Working Backwards
 Drawings and illustrations
 Making an equation
 Visualizations
 Make a Table
 Guess and Check
 Or use your own strategy
WORKING BACKWARDS

A problem you would use the working backward method on would be
something like this:

Mary Ann flew from Marquette, Mi to Los Angeles , CA . It took her 2 hours to
get from Marquette to Chicago, Il and 4 hours to get from Chicago to Los
Angeles. If she arrived at 4:00 pm what time was it when she left?
1.
2.
3.
Figure out what you are trying to find. In this case it is the time in which she
left Marquette.
Make a plan of action. In this case you would take the time she arrived and
work backwards by subtracting the hours she was in flight.
4:00 (when she arrived in LA) – 4 hours (it took to go from Chicago to LA)
= 12:00 (time she left Chicago).You would then take that time and subtract
the time it took to go from Chicago to Marquette.
12:00pm – 2 hours = 10:00 am (your answer)
DRAWINGS AND ILLUSTRATIONS

Drawing a picture is a great way to solve word problems.You not only get
the answer but it is easy to see WHY you get the answer. A good example of
a problem you would want to make a drawing for would be a problem like:

For Stacie's birthday she got a bag of marbles from her friend Amy. The bag has 6
red marbles, 10 blue marbles, 4 yellow marbles, and 1 green marble. How many
marbles does she have in her bag?
1. Figure out what you are trying to find: How many marbles there are in the
bag.
2. Make a plan: Draw out each set of marbles and count them up.
3. There are a total of 21 marbles!
MAKE AN EQUATION

Making an equation of story problems is also a great way to solve story problems.
You just take the numbers from the problem and turn them into an equation.
This problem would be a good example of when to use an equation:
 For a school bake sale 5 students each brought in something to sell. Keri
brought 2 dozen cookies, Rachel brought 3 dozen brownies, Max brought 5
dozen muffins, Michelle brought 1 dozen cupcakes, and Sarah brought 4
dozen rice crispy bars. How many treats did they have to sell?
1. Decide what you are trying to find in this case: How many treats they
will have to sell.
2. Make a plan or in this case an equation. We know that there are 12
treats in a dozen and we know how many dozen cookies we have so
here are some sample equations you could use:
1. 2(12)+3(12)+5(12)+1(12)+4(12)=180
2. (2+3+5+1+4)12=180
Then just simply solve the Problem Mathematically
VISUALIZATIONS/HANDS ON
 This problem solving strategy can be the most fun and it is very simple.You
actually use visuals to do the problem much like when using drawings but
instead of using pencil and paper you use the actual things. Say you have a
problem like this:
At the beginning and the end of every day Mrs. Smith collects and hands back papers.
On Monday at the beginning of the day she hands back 25 and collects 18. At the end of
the day she hands back 17 and collects 15. How many papers will the teacher have
collected on Monday and how many will the students have gotten back?
To do this problem hands on is very simple. I would actually take the class and do
exactly what the story problem says. Hand out some papers, collect some paper, and
repeat the process. As if it were the beginning and end of the day. Then when you are
finished count the papers the students have and how many the teacher has.
MAKE A TABLE
 Making a table is a very organized and
simple way to solve some story
problems. It is best used when dealing
with problems like:
 Andy and his parents decided that
for his allowance would go up one
dollar and 50 cents every week for 3
consecutive weeks. If he starts out at
getting 6 dollars how much would
he make week 5?
 Find: What will his allowance be
week 5?
 Plan: Make a chart of what his
allowance will be each week 
$12.00
Week
$ allowance
1
$6.00
2
$7.50
3
$9.00
4
$10.50
5
$12.00
GUESS AND CHECK

They guess and check method isn’t the fastest but it is very effective.You
would usually use it on problems like this:

If two sisters ages add up to 22 years and one is 4 years older than the other what
are there two ages?
1. You are trying to find what: Their Ages
2. Plan: Select random numbers that add up to 22 until you find two that are 4
apart.
3. 10 and 12: 10+12=22 but 12-10=2 not 4; 8 and 15: 8+15= 22 but 158=6; 9 and 13: 9+13=22 and 13-9=4 so there ages are 9 and 13!
STEP FOUR
 Writing your answer to the story problem is the final step
 When writing the answer there are a few things you have to
remember
 What are you trying to find
 If your answer should be in units such as (mph, cups, or inches)
 Your answer should be in complete sentences
Examples of Answers
If Keri has 3 apples and 5 oranges how many more oranges does she have than
apples?
Wrong way to Answer this Story Problem:
 2 (it is the right answer but when working with story problems you have to
explain your answer)
Right Way to Answer this Story Problem:
 Keri has 2 more oranges than apples.
Now that you are familiar with Solving Story Problems lets test
your memory with some worksheets and a quiz!
PROBLEM
 Read this problem and use the information to answer the
questions.
 Dwayne Johnson’s net earnings for last month was $726. During that
month he spent 10% on tithes, $150 on gas, 25% on rent, $90 on
cellphone, 15% on groceries, 5% on entertainment, and $300 on his car
payment.
QUESTION #1
What was Dwayne’s gross earnings last month?
A
B
C
• $3,249
• $2,813
• $1,756
QUESTION #2
How much money did he spend on groceries and
rent?
A
• $1,125.20
B
• $3,500.46
C
• $937.15
QUESTION #3
If Dwayne did not pay his car payment, how much
would he have in net income?
A
• $1,026
B
• $1,214.33
C
• $426
Principal and Interest
A total of $20,000 was invested between two accounts one
paying 4% simple interest and the other paying 3% simple
interest. After 1 year the total interest was $720. How much
was invested at each rate?
I = Prt
Using a Table
Accounts
P
r
t
=I
4%
x
.04
1
.04x
20,000 - x .03
1
.03(20,000 – x)
3%
I1 + I2 = $720
.04x + .03(20,000 – x) = 720
.04x + 600 - .03x = 720
.01x = 120
x = 12,000
Furthermore 20,000 – 12,000 = 8,000
Thus the amount invested at each rate is
$12,000 at 4%
and
$8,000 at 3%
Mixture Problems
How many ounces of 30% alcohol solution
that must be mixed with 10 ounces of a
70% solution to obtain a solution that is
40% alcohol?
30% alcohol
+
70%alcohol
40% alcohol
=
Using a Table
Alcohol
Ounces
Concentration
30% of
x
Alcohol
Percent
Solution
.30
.30x
70% of
Alcohol
10
.70
.70(10)
40% of
Alcohol
x + 10
.40
.40(x + 10)
.30x + .70(10) = .40(x + 10)
.30x + 7 = .40x + 4
3 = .10x
30 = x
Furthermore 30 +10 = 40
Thus, the amount of alcohol at each concentration is
30 ounces at 30%
40 ounces at 40%
Solving Mixture Problems
Example:
The owner of a candy store is mixing candy worth $6 per
pound with candy worth $8 per pound. She wants to obtain
144 pounds of candy worth $7.50 per pound. How much of
each type of candy should she use in the mixture?
1.) UNDERSTAND
Let n = the number of pounds of candy costing $6 per
pound.
Since the total needs to be 144 pounds, we can use 144  n
for the candy costing $8 per pound.
Continued
Solving Mixture Problems
Example continued
2.) TRANSLATE
Use a table to summarize the information.
Number of Pounds
Price per Pound
Value of Candy
$6 candy
n
6
6n
$8 candy
144  n
8
8(144  n)
144
7.50
144(7.50)
$7.50 candy
6n + 8(144  n) = 144(7.5)
# of
pounds
of $6
candy
# of
# of
pounds of pounds of
$8 candy
$7.50
candy
Continued
Solving Mixture Problems
Example continued
3.) SOLVE
6n + 8(144  n) = 144(7.5)
6n + 1152  8n = 1080
1152  2n = 1080
2n = 72
n = 36
Eliminate the parentheses.
Combine like terms.
Subtract 1152 from both sides.
Divide both sides by 2.
She should use 36 pounds of the $6 per pound candy.
She should use 108 pounds of the $8 per pound candy
(144  n) = 144  36 = 108
Continued
Solving Mixture Problems
Example continued
4.) INTERPRET
Check: Will using 36 pounds of the $6 per pound candy
and 108 pounds of the $8 per pound candy yield 144
pounds of candy costing $7.50 per pound?
?
6(36) + 8(108) = 144(7.5)
?
216 + 864 = 1080
?

1080 = 1080
State: She should use 36 pounds of the $6 per pound
candy and 108 pounds of the $8 per pound candy.
Distance and Rate
Two cars are 350km apart and travel towards each other on the
same road. One travels 110kph and the other travels 90kph.
How long will it take the two cars to meet?
Distance = (Rate) (Time)
d = rt
Using a Table
Rate
Time
Distance
Car 1
110
x
110x
Car 2
90
x
90x
D1 + D2 = Total Distance apart
110x + 90x = 350
200x = 350
x = 1.75
Hence, the cars will meet in 1¾ hours