November Problem Solving


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A fun way to start each math class in November. Emphasis is MP3: Construct viable arguments and critique the reasoning of others. Source: MTMS Menu of Problems,

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November Problem Solving

  1. 1. Problem SolvingMP3: Construct viable arguments and critique the reasoning of others.
  2. 2. 11/1 A Fraction Problem A half is one third of it. What is it?
  3. 3. 11/2 Number of NumbersHow many different 1-, 2-, or 3-digit whole numberscan be made using the digits 2, 5, and 8?No digit may be repeated within any one number. 2 5 8
  4. 4. 11/5 Fractions and the Flu You catch the flu, and your doctor prescribes some medicine. You are to take one pill every 2/3 hour. You have 18 pills to take. How many hours will the pills last?
  5. 5. 11/6 Percent ProblemsYou are going to a sporting goods store to buya pair of tennis shoes and a pair of in-lineskates. The original cost of the tennis shoeswas $150, but today that pair of tennis shoesis 40% off. The original price of the in-lineskates was $200, but today that item is 20%off. What was the percent of discount on thetotal purchase (assuming no taxes areinvolved)?
  6. 6. 11/7 Twin PrimesTwin primes are a pair of prime numbers such that the lesserprime number subtracted from the greater prime number is 2.There are three pairs of twin primes between 100 and 150.How many pairs of twin primes are there less than 100? ..., 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, ...
  7. 7. 11/8 Product of Primes The product of three prime numbers that are less than 30 is 1955. What are the three prime numbers?
  8. 8. 11/9 Mystery NumberI am thinking of a special four-digit number:• All the digits are different.• The digit in the thousands place is 3 timesthe digit in the tens place.• The number is odd.• The sum of the digits is 27.What’s my special four-digit number?
  9. 9. 11/13 The Winner is...The winner of a school election is announced afterschool at 4:00 p.m. One student calls 2 friendsbefore 4:15 p.m., telling the name of the winner.Before 4:30 p.m., those 2 people call 2 more studentsand tell them the name of the winner. Before 4:45p.m., each new student who has been notified calls 2more people, telling them the name of the winner. Ifthis continues and no student is called twice, at whattime will 200 students know the name of the winner?
  10. 10. The Product is Prime?11/14 Find three integers in arithmetic progression (with equal differences between each number) whose product is a prime number. (This is possible.)
  11. 11. From Perimeter to Area11/15When a square piece of paper is folded in half vertically,the resulting rectangle has a perimeter of 39 cm. Insquare centimeters, find the area of the original squaresheet of paper.
  12. 12. The Missing Number11/16 Determine the missing number based on the values in each square.
  13. 13. Hens and Eggs11/19 If 3 hens lay 4 eggs in 5 days, how many days will it take a dozen hens to lay 8 dozen eggs? Please round your answers to the nearest day (or egg, if needed).
  14. 14. Hug a Tree11/20 Several years ago, I planted a 3-foot tree that has grown the same amount each year. At the end of the third year, the tree was 1/5 taller than it was at the end of the second year. The tree is now 18 feet tall. How many years ago did I plant the tree?
  15. 15. Maximize the Regions11/21 What is the greatest number of regions you can get if you draw four straight lines through a circle? Convince someone that you found the greatest number!
  16. 16. 1, 2, 3,...11/26What three consecutive countingnumbers have a sum that is 20% ofthe product of the three numbers?
  17. 17. Alphanumeric Puzzle11/27 Find the digits that represent the letters E, F, G, and H to satisfy the following puzzle. Each letter represents a different digit.
  18. 18. There’s Algebra in There!11/28 Complete the table by determining the value of each letter. Explain what rule is used to relate the numbers in the second column (with the heading of y) with those in the first column (with the heading of x).
  19. 19. Determining Weights11/29 Three boys, Jamal, Hector, and Simon, work together on a farm. They walk into the barn, notice a scale. used to weigh cattle, and decide to weigh themselves. Unfortunately, the scale begins at 100 kg and none of the boys weighs more than 100 kg. They decide to weigh themselves in pairs and found these amounts. Jamal was sure that he weighed the most. What did each boy weigh?
  20. 20. Mystery Number Puzzle11/30 Find an integer between 100 and 200 such that each digit is odd and the sum of the cubes of the digits is equal to the original three-digit number.