UNRAAVEL a Math Problem Sure-Fire Steps to Becoming a Math Genius! URLNOTES UNRAAVEL File Name: F:TeachingNorth East Carolina Prep SchoolLesson PlansMathAssigments6 -- Problem Solving 1997 PPT & URL
Sometimes it can be difficult to figure out what to do whenyou are faced with a word problem.Even Albert Einstein said: “Do not worry about yourdifficulties in Mathematics. Ican 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 b) Allison is buying five sets of markers for each of her twelve artFind 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 hisplayoffs. The team scored forty-two purchases? goals during the regular season. How many goals were scored during the playoffs?
Sid has $50.00. He bought two videogames that cost $14.00 each. He alsobought a poster for $5.69. How muchmoney 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 answerwill be larger or smaller?Do you think you willneed to add, subtract,multiply, or divide? Arethere any hints that youmay need to estimate?
I predict that I will need tosubtract. I saw thewords: HAVE LEFT in the question.
R = Read the Word Problem Read the entireproblem!!!!
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. Howmuch 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 video games that cost $14.00each. He also bought a poster for $5.69. How much money did he have left after his purchases?
A = Apply the Steps You Chose to Solve the Problem$14.00X 2 Video Games$28.00$28.00 Video Games Plus Poster+ 5.69$33.69 Tota l Am oun t Sp ent
Sid has $50.00. He bought two video games that cost $14.00each. He also bought a poster for $5.69. How much money did he have left after his purchases?
y ne s Mo Sid’ $ 50.00 - 33.69 t hes p en $16.31 atWh Le fto ver !
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 Too big. b. $15.00 Can’t End in two Zeroes. c. $55.76 Too big. d. $16.31
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?U nderline the questionN ow predict what you think you need to do to solve the problemR ead the word problemA re the important words circled? (especially clue words)A pply the step(s) you chose to solve the problemV erify your answer (is it reasonable; does it make sense?)E liminate wrong answersL et the answer stay or rework the problem Double check your work!
UNRAAVEL Strategy Adapted from the Work andProperty of Larry Bell. (http://www.larry-bell.com/ )
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 Barbies 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 theProblem: 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 Stacies 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: 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
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 AnswersIf 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!
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 • 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
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?
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: Find out:Received 4 How manypostcards postcards did Paul receive from the 11 trips?Each of 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 Multiplication Divisionadd subtract multiplied by divided byin all difference times share equallytotal how much more each partsum decreased by product distributeplus minus total evenlyhow much less area averageperimeter less than out ofincreased by fewer than permore than have left quotientboth exceed splittogether take away separatedall together are not cut up remain change left
Know: Find out: Come up with a plan!Received 4 How manypostcards postcards did Paul receive from the Operation:Each of 11 trips 11 trips? Multiplication Strategy: Draw a picture
Now solve!OOOO OOOOOOOO OOOOOOO OOOOOOO OOOOOOOO OOOOOOO OOO 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 2Bailey went to the Bailey went to thegrocery store with grocery store with$10.00. She bought $10.00. She bought$7.61 in groceries. $7.61 in groceries.How much is herchange? How much is her change?
Problem 2 Do you think you will need to add, PREDICT subtract, multiply, or divideBailey went to the Bailey went to thegrocery store with grocery store with$10.00. She bought $10.00. She bought$7.61 in groceries. $7.61 in groceries.How much is herchange? How much is her change?
Problem 2 READBailey went to thegrocery store with$10.00. She bought$7.61 in groceries.How much is herchange?
Problem 2 AREBailey went to thegrocery store with$10.00. She bought$7.61 in groceries.How much is herchange?