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Slide 1
Slide 2
Learning The Language: Word Problems
Slide 3
STEP ONE Read the word problem and identify the important
information you will need to solve the problem.
Slide 4
STEP TWO Identifying what type of arithmetic you will need to
do Addition Subtraction Multiplication Division
Slide 5
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 Barbies does Jane have now? (10+3=?)
Slide 6
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=?)
Slide 7
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=?)
Slide 8
Division Division word problems often use words like: Per Out
of Ratio of Quotient of a EXAMPLE: John ate a total allowance of
$250. If he spends $25 a day, how many days will the allowance
last? 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=? )
Slide 9
STEP THREE Solve the Problem Using one of the many problem
solving strategies
Slide 10
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
Slide 11
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. Figure out what you are trying to find. In this case it is the
time in which she left Marquette. 2. 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. 3. 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)
Slide 12
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!
Slide 13
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
Slide 14
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.
Slide 15
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 Week$ allowance 1 2 3 4 5
$6.00 $7.50 $9.00 $10.50 $12.00
Slide 16
GUESS AND CHECK They guess and check method isnt 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 15- 8=6; 9 and 13: 9+13=22
and 13-9=4 so there ages are 9 and 13!
Slide 17
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
Slide 18
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!
Slide 19
PROBLEM Read this problem and use the information to answer the
questions. Dwayne Johnsons 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.
Slide 20
QUESTION #1 What was Dwaynes gross earnings last month? $3,249
$2,813 $1,756 C A B
Slide 21
QUESTION #2 How much money did he spend on groceries and rent?
$1,125.20 $3,500.46 $937.15 A B C
Slide 22
QUESTION #3 If Dwayne did not pay his car payment, how much
would he have in net income? $1,026 $1,214.33 $426 A BB C
Slide 23
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
Slide 24
AccountsPrt = I 4%x.041.04x 3% 20,000 - x.031.03(20,000 x)
Using a Table
Slide 25
I 1 + I 2 = $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%
Slide 26
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?
Slide 27
+ = 30% alcohol 70%alcohol 40% alcohol
Slide 28
Using a Table AlcoholConcentrationOuncesPercentSolution 30% of
Alcohol x.30.30x 70% of Alcohol 10.70.70(10) 40% of Alcohol x +
10.40.40(x + 10)
Slide 29
.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%
Slide 30
Solving Mixture Problems 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. Example: Continued
Slide 31
Solving Mixture Problems Example continued 2.) TRANSLATE
Continued Use a table to summarize the information. Number of
PoundsPrice per PoundValue of Candy $6 candy n66n6n $8 candy 144 n
8 8(144 n) $7.50 candy 1447.50144(7.50) 6 n + 8(144 n ) = 144(7.5)
# of pounds of $6 candy # of pounds of $8 candy # of pounds of
$7.50 candy
Slide 32
Solving Mixture Problems Example continued Continued 3.) SOLVE
6 n + 8(144 n ) = 144(7.5) 6 n + 1152 8 n = 1080 1152 2 n = 1080 2
n = 72 Eliminate the parentheses. Combine like terms. Subtract 1152
from both sides. n = 36Divide 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
Slide 33
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? State: She should use 36 pounds of the $6 per pound candy
and 108 pounds of the $8 per pound candy. 6(36) + 8(108) = 144(7.5)
? 216 + 864 = 1080 ? 1080 = 1080 ?
Slide 34
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
Slide 35
Using a Table RateTimeDistance Car 1 110x110x Car 2 90x90x
Slide 36
D 1 + D 2 = Total Distance apart 110x + 90x = 350 200x = 350 x
= 1.75 Hence, the cars will meet in 1 hours