The key words here are "each" and "trips" which indicates multiplication.

1. UNRAAVEL a Math Problem
Sure-Fire Steps to Becoming a Math Genius!
URL
NOTES
UNRAAVEL
File Name: F:TeachingNorth East Carolina Prep SchoolLesson PlansMathAssigments6 -- Problem Solving 1997 PPT & URL

2. Sometimes it can be difficult
to figure out what to do when
you are faced with a word problem.
Even Albert Einstein said:
“Do not worry about your
difficulties in Mathematics. I
can assure you mine are still
greater.”

3. If he had known about UNRAAVEL…..
…..he may have
been able to do
even more with
Math!
Are you ready to
learn how to
UNRAAVEL a math
problem?

4. U = Underline the question
b) Allison is buying five sets of
markers for each of her twelve art
Find the question and students. If each set of markers
Underline it! costs $5.75, how much will she
spend on markers?
We are going to practice
UNRAAVEL with this one! c) Sid has $50.00. He bought
two video games that cost
a) The soccer team scored six $14.00 each. He also bought a
times as many goals during the poster for $5.69. How much
regular season as they did during money did he have left after his
playoffs. The team scored forty-two purchases?
goals during the regular season.
How many goals were scored
during the playoffs?

5. Sid has $50.00. He bought two video
games that cost $14.00 each. He also
bought a poster for $5.69. How much
money did he have left after his purchases?

6. N = Now Predict
What Do You Think
You Need to Do
to Solve the Problem?
Do you think the answer
will be larger or smaller?
Do you think you will
need to add, subtract,
multiply, or divide? Are
there any hints that you
may need to estimate?

7. I predict that I will
need to
subtract. I saw the
words: HAVE LEFT
in the question.

8. R = Read the Word Problem
Read the
entire
problem!!!!

9. Read it, Dudes and Dudettes!
Sid has $50.00. He bought
two video games that cost
$14.00 each. He also bought
a poster for $5.69. How
much money did he have left
after his purchases?

10. A = Are the Important Words Circled?
(especially the clue words?)
Sid has $50.00. He bought two
video games that cost $14.00
each. He also bought a poster for
$5.69. How much money did he
have left after his purchases?

11. A = Apply the Steps You Chose to
Solve the Problem
$14.00
X 2 Video Games
$28.00
$28.00 Video Games Plus Poster
+ 5.69
$33.69
Tota
l Am
oun
t Sp
ent

12. Sid has $50.00. He bought two
video games that cost $14.00
each. He also bought a poster for
$5.69. How much money did he
have left after his purchases?

13. y
ne
s Mo
Sid’
$ 50.00
- 33.69
t
hes
p en
$16.31
at
Wh
Le
fto
ver
!

14. V = Verify Your Answer.
(Is it reasonable? Does it Make Sense?)
$16.31 IS reasonable
because it is smaller than
$50.00. It would make
sense to have this amount
left after buying games and
a poster.

15. E = Eliminate Wrong Answers.
a. $66.31 Too big.
b. $15.00 Can’t End in two Zeroes.
c. $55.76 Too big.
d. $16.31

16. L = Let the Answer Stay or Rework the
Problem
I got that one
correct, but I
may have to
rework the
next one!

17. How do you UNRAAVEL?
U nderline the question
N ow predict what you think you need to do to
solve the problem
R ead the word problem
A re the important words circled?
(especially clue words)
A pply the step(s) you chose to solve the problem
V erify your answer (is it reasonable; does it
make sense?)
E liminate wrong answers
L et the answer stay or rework the problem
Double check your work!

18. UNRAAVEL Strategy Adapted from the Work and
Property of Larry Bell. (http://www.larry-bell.com/ )

19. Elements
www.animationfactory.com

20. http://www.softschools.com/quizzes/math/4th_grade

21. Problem Solving Strategies:
Story Problems

22. STEP ONE
 Read the story problem and identify the
important information you will need to solve
the problem.

23. STEP TWO
 Identifying what type of arithmetic you will
need to do
– Addition
– Subtraction
– Multiplication
– Division

24. 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=?)

25. Subtraction
 Subtraction story problems often use words like:
– Decreased by
– Minus, less than
– Difference
– Less than
– Fewer than
– Away/loose
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=?)

26. 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=?)

27. Division
 Division word problems
often use words like:
– Per
– Out of
– Ratio of
– Quotient of
– “a”
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=? )

28. STEP THREE
 Solve the Problem
– Using one of the many problem solving strategies

29. 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

30. 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 4:00pm 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)

31. 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!

32. 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

33. 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 29 and collects 26. How many papers will the teach 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.

34. 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: Week $ allowance
– Andy and his parents decided that
for his allowance would go up one 1 $6.00
dollar and 50 cents every week for
3 consecutive weeks. If he starts 2 $7.50
out at getting 6 dollars how much
would he make week 5?
– Find: What will his allowance be 3 $9.00
week 5?
– Plan: Make a chart of what his 4 $10.50
allowance will be each week 
5 $12.00
$12.00

35. 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 15-
8=6; 9 and 13: 9+13=22 and 13-9=4 so there ages are 9 and 13!

36. 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

37. 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!

38. Problem Solving Tool:
KFC

39. What is Problem Solving?
• Problem solving is when you are
presented with a math problem and
you have to figure out a way to
answer the question that the problem
is asking you.

40. Problem Solving can be tough
but not if you use…
•K
•F
•C

41. No, not fried chicken!
• K- stands for “What information do I
know?”
• F- stands for “What am I trying to
find out?”
• C- stands for “Come up with a plan!”

42. The PLAN you come up with
must have two parts!
What operation will I need to
use?
• Addition, subtraction, division or
multiplication
• What problem solving
strategy will I choose to use?

43. Problem solving
strategies!
• Act it out • Make an Organized
• Draw a picture List
• Solve a Simpler • Make a Table /
Problem Chart / T-Chart
• Use Logical Reasoning • Use Estimation
• Work Backward • Use Mental Math
• Write an Equation • Make a Number Line
• Write a Number • Find a pattern
Sentence • Guess and Check

44. Let’s try it!
• Here’s the problem:
• Paul received four postcards from each of
his father’s 11 trips. How many postcards
did Paul receive from the 11 trips?

45. First is “K” or “What do you
know and need to solve the
problem?”
• Paul received four postcards from each of his
father’s 11 trips. How many postcards did Paul
receive from the 11 trips?

46. Know:
Received 4
postcards
Each of 11 trips

47. Next is “F” or “What am I
trying to find out?”
• Paul received four postcards from each of
his father’s 11 trips. How many postcards
did Paul receive from the 11 trips?

48. Know: Find out:
Received 4 How many
postcards postcards did Paul
receive from the
11 trips?
Each of 11 trips

49. Last is “C” or “Come up with a
plan!”
Remember the plan must have
two parts:
• What operation will I need to use?
• Addition, subtraction, division or multiplication
• What problem solving strategy will I
choose to use?

50. How do we choose an
operation?
Look for KEY words!
Addition Subtraction Multiplication Division
add subtract multiplied by divided by
in all difference times share equally
total how much more each part
sum decreased by product distribute
plus minus total evenly
how much less area average
perimeter less than out of
increased by fewer than per
more than have left quotient
both exceed split
together take away separated
all together are not cut up
remain
change left

51. Know: Find out: Come up
with a plan!
Received 4 How many
postcards postcards did Paul
receive from the
Operation:
Each of 11 trips 11 trips?
Multiplication
Strategy:
Draw a picture

52. Now solve!
OOOO OOOO
OOOO OOOO
OOO OOO
OOOO OOOO
OOOO OOOO
OOO OOO
Four groups of 11 is 44.
4 x 11 = 44
Paul received 44 postcards.

53. Easy right?!
Now you try it!
• Solve the following problems using KFC!
Remember to draw the three column chart
and to show your work!
1. There were 6 chickens and 8 horses on Mr. Johnson’s farm. What is
the total number of legs on Mr. Johnson’s farm? (hint: include Mr.
Johnson)
2. Ringo, John, Paul, and George are singing in a band. John and Paul
have on glasses. Paul and Ringo are standing beside of John.
George doesn’t want to stand beside John because he sings off
key. Ringo is standing on the end. What order are they standing on
stage?

54. Problem Solving can be tough
but not if you use…
K F C

56. Problem 1
• Using the graph to
the right; which
activity is…
…most popular
…least popular

57. Problem 1
• Using the graph to
the right; which
activity is…
…most popular
BASEBALL
…least popular
CHEER LEADING

58. Problem 2
Bailey went to the Bailey went to the
grocery store with grocery store with
$10.00. She bought $10.00. She bought
$7.61 in groceries.
$7.61 in groceries.
How much is her
change? How much is her
change?

59. Problem 2 Do you think you
will need to add,
PREDICT subtract, multiply,
or divide
Bailey went to the Bailey went to the
grocery store with grocery store with
$10.00. She bought $10.00. She bought
$7.61 in groceries.
$7.61 in groceries.
How much is her
change? How much is her
change?

60. Problem 2 READ
Bailey went to the
grocery store with
$10.00. She bought
$7.61 in groceries.
How much is her
change?

61. Problem 2 ARE
Bailey went to the
grocery store with
$10.00. She bought
$7.61 in groceries.
How much is her
change?