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POWER MATH 6 TH GRADE THE PROBLEM SOLVING PLAN & PROBLEM SOLVING STRATEGIES 6th Grade Old Crow, LLC 2009 Please do not copy

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THE PROBLEM SOLVING PLAN Read and Understand the Problem Make a Plan: Choose a Strategy Estimate Carry out the Plan: Apply the Strategy Estimate for Reasonableness: Does it make sense? 6th Grade Old Crow, LLC 2009 Please do not copy

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PROBLEM SOLVING STRATEGIES Brainstorm. Draw a picture. Look for a pattern. Make a table. Guess and Check. Make an organized list. Make it simpler. Work backwards. Use logical reasoning. Act it out or use objects. 6th Grade Old Crow, LLC 2009 Please do not copy

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BRAINSTORM The Brainstorm strategy is often used when all else fails! Brainstorming means looking at a problem in new and inventive ways. Use your imagination, be creative, and by all means, be flexible in your thinking. Eventually the light bulb will go on and you will find a solution. 6th Grade Old Crow, LLC 2009 Please do not copy

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DRAW A PICTURE There are many types of problems where it helps to draw a picture. Work this problem: 1. It takes 6 cubes to build a staircase with 3 steps. How many cubes will be needed for 11 steps. 6th Grade Old Crow, LLC 2009 Please do not copy

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DRAW A PICTURE 2. In the old days there were elevator operators to transport passengers. Don Downs always started his day in the basement. He went up 20 floors to take his boss some coffee. Then he went down 8 floors to take a Danish to his friend. He went up 7 floors to check things out. This was the halfway point in the building. How many floors are in this building? Draw a diagram to show how you would figure this out. 6th Grade Old Crow, LLC 2009 Please do not copy

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DRAW A PICTURE 3. A team of scientists found that there were 4 oak trees for every 10 pine trees. How many oak trees were there if they counted 36 more pine than oak? 6th Grade Old Crow, LLC 2009 Please do not copy

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DRAW A PICTURE 4. Choose 3 geometric solids to build a model house. What solids did you choose? How many vertices are there? From an aerial view of your structure, how many vertices can you see? Draw a picture of the aerial view. 6th Grade Old Crow, LLC 2009 Please do not copy

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LOOK FOR A PATTERN Solve this problem with your partner: Find the pattern to solve. You finally get an allowance! You put $2.00 away in January, $4.00 away in February, $8.00 away in March, $16.00 away in April and followed this savings pattern through to December. How much money do you have in 12 months? 6th Grade Old Crow, LLC 2009 Please do not copy

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LOOK FOR A PATTERN 2. Find the next three terms in each sequence and explain your pattern (rule) in a sentence. A. 2; 5; 10; 17… B. 128; 64; 32; 16… C. 5; 10; 9; 18; 17; 34; 33… D. 1; 3; 7; 13; 21… 6th Grade Old Crow, LLC 2009 Please do not copy

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LOOK FOR A PATTERN 3. Kazuko has a beach ball. It is colored with six vertical stripes, in order: white, orange, yellow, blue, red, and green. She spins the beach ball on the surface of the water in her swimming pool, and she notices that the colors whir by very fast. If the first color to go by is white and the ball spins around so that 500 colors go by, what is the 500th color? 6th Grade Old Crow, LLC 2009 Please do not copy

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LOOK FOR A PATTERN 4. This problem is about pentagonal numbers. Find the pattern in the sequence of diagrams shown below, and determine how many dots would be in the seventeenth diagram. 6th Grade Old Crow, LLC 2009 Please do not copy

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GUESS AND CHECK Sometimes the only way to solve a problem is to guess and check until you find an answer that makes sense. Solve this problem with your group: 1. Mr. and Mrs. Simpleton are shopping for carpet for their living room and dining room. Their living room is 21 feet by 15 feet and their dining room is 12 feet by 9 feet. They have looked at two different priced carpets. One for $14.95 a square yard installed and another for $19.99 a square yard installed. How much would they save by choosing the cheaper carpet? What are some other things besides money that they should consider before making their choice? After you find out how much carpet they need, figure out the savings in one calculation. Explain. 6th Grade Old Crow, LLC 2009 Please do not copy

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GUESS AND CHECK 2. Mabel and her mom are going shopping on Saturday. They bought at least one item from each of the 3 departments that they visited. Mabel gave the clerk $120 and she got back $11.76 change. What items did they buy? Think about how much they spent. NO TAX TODAY! HOUSEWARES Dishtowels: $11.38 Curtain Rods: $12.98 Bath Mats: $29.58 CLOTHING Shirt: $30.98 Dress: $49.90 Slacks: $39.90 TOOLS Hammer: $17.90 Saw: $23.90 Drill: $ th Grade Old Crow, LLC 2009 Please do not copy

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GUESS AND CHECK 3. Tom had a platter of chocolate wafers. He ate 5 of them and then gave his brother 3, he then handed them to his ball team of 8 members. The first player to arrive took 1, the second player took 3, the third player took 5 and so on. When the last player took his, the platter was empty. How many chocolate wafers did Tom start with? 6th Grade Old Crow, LLC 2009 Please do not copy

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GUESS AND CHECK 4. I’m thinking of two numbers, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What is the other number I am thinking of? 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE AN ORGANIZED LIST Lists are a great way to solve some problems! But, make sure you organize your list so that you don’t get confused or leave something out. Solve this problem with your partner: Groups of campers were going to an island. On Sunday 10 went over and 2 came back. On Monday, 12 went over and 3 came back. If this pattern continues, how many would be on the island at the end of a week? How many would be left? 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE AN ORGANIZED LIST 2. How many times in a 12 hour period does the sum of the digits on a digital clock equal 6? Try to think of a way to solve this without going through every single time. Describe what you did. 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE AN ORGANIZED LIST 3. An ice cream stand has 9 different flavors. A group of children come to the stand and each buys a double scoop cone with 2 flavors. If none of the children chooses the same combination of flavors and every combination is chosen, how many children are there? Show how you got your answer. 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE AN ORGANIZED LIST 4. Liberty is going to flip four coins at once: a penny, a nickel, a dime, and a quarter. How many ways are there for the four coins to come up? Make a list of all the possible results. 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE A TABLE Use a table to solve this problem with your group: 1. Sadie went to the store with a $10 bill. She spent $4.76. Give 6 possible ways she could get her change. She cannot use the same number of coins twice. (You cannot say 5 one dollar bills, 2 dimes, 4 pennies, and then a $5 bill 2 dimes and 4 pennies.) She must use each type of United States coin at least once. 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE A TABLE 2. The Prestage family wants to take another vacation. They have decided to drive their van to a destination 600 miles away. If they drive at a reasonable speed, how much time should they set aside for the trip? Create a table that shows various driving speeds (in miles per hour). 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE A TABLE 3. A rectangle has an area measuring 120 square centimeters. Its length and width are whole numbers of centimeters. What are the possible combinations of length and width? Which possibility gives the smallest perimeter? 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE A TABLE 4. Holley scored 10 points in a basketball game. She could have scored with one-point free throws, two-point field goals, or three-point field goals. In how many different ways could she have scored her ten points? 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE IT SIMPLER Solving a Simpler Problem means to break down a bigger problem into smaller ones so it is easier to solve. Solve this problem with your group: 1. What is the sum of the first one hundred whole numbers? 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE IT SIMPLER 2. In China each calendar year is given one of 12 names, which rotate year after year. The year 2000 was the year of the Dragon. The year 2001 was the year of the Snake. The subsequent years are, in order, the year of the Horse, Sheep, Monkey, Rooster, Dog, Boar, Rat, Ox, Tiger, and Rabbit. After the year of the Rabbit, the Year of the Dragon will occur again and the whole cycle will repeat. What will the year 2100 be? How old will you be? 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE IT SIMPLER 3. Have everyone in your class line up. How many different combinations can you come up with? Make sure to give each student a turn to be first, second, and so on. 6th Grade Old Crow, LLC 2009 Please do not copy

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MAKE IT SIMPLER 4. Simon has decided to be a one-man band, complete with a harmonica, and accordion, and a drum. Identify the sub- problems and the easier related problems Simon must master to be able to play “The Star Spangled Banner” using all three instruments while twirling three hula hoops. 6th Grade Old Crow, LLC 2009 Please do not copy

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WORK BACKWARDS Sometimes working a problem backwards helps you find the solution. Solve this problem with your partner: Bad Bargle sneaked into Homer’s pigeon loft one day. He took half of the pigeons. He decided that wasn’t bad enough, so he took one more and left. Later, Homer opened the door of the loft to exercise his prize possessions. Half of the remaining flock flew out, leaving six inside the pen. How many pigeons did Homer have before Bad Bargle did his dirty deed? 6th Grade Old Crow, LLC 2009 Please do not copy

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WORK BACKWARDS Dad was paid on Wednesday. On Thursday morning my brother borrowed half of Dad’s money to open a checking account with, because he was always short of money. On Friday I needed some money for a date, so I borrowed half of what remained. Sister came along next and borrowed half of the remaining money. Dad then went to gas up the car and used half of the rest of his money, and he wondered where it all went so fast. He had only $5 left. How much money did he start with in his wallet? 6th Grade Old Crow, LLC 2009 Please do not copy

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WORK BACKWARDS 3. Mr. Phil T. Rich left half of his estate to his wife, $30,000 to his daughter, half of what was left to his butler, half of what remained for the care of his goldfish, and the remaining $8,000 was left to charity. What was the value of his estate? 6th Grade Old Crow, LLC 2009 Please do not copy

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WORK BACKWARDS 4. A man competing on a game show ran into a losing streak. First, he bet half of his money on one question and lost it. Then he lost half of his remaining money on another question. Then he lost $300 on another question. Then he lost half of his remaining money on another question. Finally, he got a question right and won $200. At this point the show ended and he had $1,200 left. How much did he have before his losing streak began? 6th Grade Old Crow, LLC 2009 Please do not copy

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USE LOGICAL REASONING Logical reasoning is when you use clues to help you solve a problem. Solve this problem with your group. 6th Grade Old Crow, LLC 2009 Please do not copy

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USE LOGICAL REASONING 1.Three friends: Elaine, Kelly, and Shannon all start for their high school volleyball team. Each plays a different position: setter, middle blocker, and outside hitter. Of the three, one is a freshman, one a sophomore, and the other a junior. From the clues below, determine each woman’s position and year in school. A. Elaine is not the setter. B. Kelly has been in school longer than the middle blocker. C. The middle blocker has been in school longer than the outside hitter. D. Either Kelly is the setter or Elaine is the middle blocker. E. This is Shannon’s first year in high school. 6th Grade Old Crow, LLC 2009 Please do not copy

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USE LOGICAL REASONING 2.Ted, Ken, Allyson, and Janie each have a favorite sport: running, swimming, biking, and golf. Given the following clues, determine who likes which sport. A. Ted hates golf. He agrees with Mark Twain that golf is nothing but a good walk spoiled. B. Ken wouldn’t run around the block if he didn’t have to and neither would Janie C. Each woman’s favorite sport is featured in a triathlon. D. Allyson bought Ted a new bike for his birthday to use in his favorite sport. 6th Grade Old Crow, LLC 2009 Please do not copy

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USE LOGICAL REASONING 3. Several friends take a fishing trip every year. Each year they have a contest to see who catches the heaviest fish. The loser has to pay for all of the junk food they eat on the trip. (Second and third places are also expected to chip in token amounts.) Determine each friend’s standings in the year’s contest by using the following clues. By the way, in the tradition of fishing trips, every statement quoted here is a falsehood. Marta: Larry was first Sally: Marta beat Woody Woody: I beat Sally. Larry: Woody was second. 6th Grade Old Crow, LLC 2009 Please do not copy

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USE LOGICAL REASONING 4.Two men (Jack and Mike) and two women (Adele and Edna) each like a different type of music (Adele likes Jazz). Their last names are Mullin, Hardaway, Richmond, and Higgins. From the clues below, find each person’s full name and favorite type of music. A. Hardaway hates country-western music. B. The classical music lover said she’d teach Higgins to play the piano. C. Adele and Richmond knew the country-western fan in high school. D. Jack and the man who likes rock music work in the same office building. E. Richmond and Higgins are on the same bowling team. There are no men on their team. 6th Grade Old Crow, LLC 2009 Please do not copy

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ACT IT OUT OR USE OBJECTS This strategy allows you to use visual images of the information in the problem to solve the problem. Acting or moving around objects can help you remember the process you should use to solve the problem. 6th Grade Old Crow, LLC 2009 Please do not copy

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ACT IT OUT OR USE OBJECTS Solve this problem with your group. Act it out and use graphics to help you solve. 1. A farmer grows 196 pounds of potatoes. He sells them to a grocer who divides them into 5 pound and 2 pound bags. If the grocer uses the same number of 5 pound and 2 pound bags, how many bags of each did he use? 6th Grade Old Crow, LLC 2009 Please do not copy

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ACT IT OUT OR USE OBJECTS 2. Carl is given 24 toothpicks and told to construct a geometric solid. He must use all of the toothpicks. Which solid could he make? Draw a picture to support your answer. How many balls of clay would he need to hold his structure together? 6th Grade Old Crow, LLC 2009 Please do not copy

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ACT IT OUT OR USE OBJECTS 3. Use the digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 once each to fill in the blanks of the puzzle. 6th Grade Old Crow, LLC 2009 Please do not copy 4 + ________ X ________ 2 X = 6 - =

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ACT IT OUT OR USE OBJECTS 4. Three playing cards from an ordinary deck of 52 cards lie face down in a row. There is a queen to the right of a jack. There is a queen to the left of a queen. There is a diamond to the left of a heart. There is a diamond to the right of a diamond. What are the three cards? 6th Grade Old Crow, LLC 2009 Please do not copy

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CREATE YOUR OWN Use the previous questions as examples to create your own problem. You will then present your question to the class, choose your strategy, and solve the problem. We will share. 6th Grade Old Crow, LLC 2009 Please do not copy

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WHAT STRATEGY WOULD YOU CHOOSE? 6th Grade Old Crow, LLC 2009 Please do not copy

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THE END! Don’t forget to use the Problem Solving Plan when solving problems. Don’t forget about all of the WONDERFUL strategies you can use! 6th Grade Old Crow, LLC 2009 Please do not copy

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