UNRAAVEL a Math ProblemSure-Fire Steps to Becoming a Math Genius!

UNRAAVEL

URL

NOTES

File Name: F:\Teaching\North East Carolina Prep School\Lesson Plans\Math\Assigments\6 -- Problem Solving 1997 PPT & URL

Sometimes it can be difficultto 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.”

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?

U = Underline the question

Find the question and Find the question and Underline it!Underline it!

b) Allison is buying five sets of markers for each of her twelve art students. If each set of markers costs $5.75, how much will she

spend on markers?

c) 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?

a) The soccer team scored six times as many goals during the

regular season as they did during playoffs. The team scored forty-two

goals during the regular season. How many goals were scored

during the playoffs?

We are going to practice We are going to practice UNRAAVEL with this one!UNRAAVEL with this one!

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?

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?

I predict that I will need to

subtract. I saw the words: HAVE LEFT

in the question.

R = Read the Word Problem

Read the

entire problem!!!!

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?

A = Are the Important Words Circled? (especially the

clue words?)

Sid has $50.00. He bought two Sid has $50.00. He bought two

video games that cost $14.00 video games that cost $14.00

each. He also bought a poster for each. He also bought a poster for

$5.69. $5.69. How much money did he How much money did he

have left after his purchases?have left after his purchases?

A = Apply the Steps You Chose to Solve the Problem

$14.00

X 2$28.00

$28.00+ 5.69

$33.69

Video Games

Video Games Plus Poster

Total Amount Spent

Sid has $50.00. He bought two Sid has $50.00. He bought two

video games that cost $14.00 video games that cost $14.00

each. He also bought a poster for each. He also bought a poster for

$5.69. $5.69. How much money did he How much money did he

have left after his purchases?have left after his purchases?

$ 50.00

- 33.69$16.31

Sid’s Money

What he spent

Leftover!

Leftover!

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.

E = Eliminate Wrong Answers.

a. $66.31

b. $15.00

c. $55.76

d. $16.31

Too big.

Too big.

Can’t End in two Zeroes.

L = Let the Answer Stay or Rework the Problem

I got that one correct, but I may have to rework the next one!

How do you UNRAAVEL?

UU nderline the questionNN ow predict what you think you need to do to solve the problem RR ead the word problemAA re the important words circled? (especially clue words)AA pply the step(s) you chose to solve the problemVV erify your answer (is it reasonable; does it make sense?)EE liminate wrong answersLL et the answer stay or rework the problem Double check your work!

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

Elementswww.animationfactory.com

http://www.softschools.com/quizzes/math/4th_grade_word_problems/quiz682.html

Problem Solving Strategies: Story Problems

STEP ONE

Read the story 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, 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=?)

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 – 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=? )

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 4:00pm 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)

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 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.

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

$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 15-8=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 Solving Tool:Problem Solving Tool:Problem Solving Tool:Problem Solving Tool:

KFCKFC

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.

Problem Solving can be tough but not if you use…

•K•F•C

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!”

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?

Problem solving strategies!

• Act it out• Draw a picture• Solve a Simpler

Problem• Use Logical

Reasoning• Work Backward• Write an Equation• Write a Number

Sentence

• Make an Organized List

• Make a Table / Chart / T-Chart

• Use Estimation• Use Mental Math• Make a Number Line• Find a pattern• Guess and Check

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?

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?

Know:

Received 4 postcards

Each of 11 trips

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?

Know:

Received 4 postcards

Each of 11 trips

Find out:

How many postcards did Paul receive from the 11 trips?

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?

How do we choose an operation?

Look for KEY words!Addition Subtraction Multiplicatio

nDivision

addin alltotalsumplushow muchperimeterincreased bymore thanbothtogetherall together

subtractdifferencehow much moredecreased byminuslessless thanfewer thanhave leftexceedtake awayare notremainchange left

multiplied bytimeseachproducttotalarea

divided byshare equallypartdistribute evenlyaverageout of perquotientsplitseparatedcut up

Know:

Received 4 postcards

Each of 11 trips

Find out:

How many postcards did Paul receive from the 11 trips?

Come up with a plan!

Operation:Multiplication

Strategy: Draw a picture

Now solve!

O O O O O O O O O O O

O O O O O O O O O O O

O O O O O O O O O O O

O O O O O O O O O O O

Four groups of 11 is 44. 4 x 11 = 44

Paul received 44 postcards.

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?

Problem Solving can be tough but not if you use…

K F C

Problem 1• Using the graph

to the right; which activity is…

…most popular…least popular

Problem 1• Using the graph

to the right; which activity is…

…most popular BASEBALL

…least popularCHEER LEADING

Problem 2

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

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

Problem 2PREDICT

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

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

Do you think you will need to add, subtract, multiply, or divide

Problem 2 READ

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

Problem 2 ARE

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