September Problems


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A problem of the day for each day in September! Source: NCTM's MTMS publication.

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September Problems

  1. 1. Problem SolvingMP1: Make Sense of Problems and Persevere in Solving Them
  2. 2. 9/5/12 Around the WorldOn November 14, 1889, journalist Nellie Bly set off on atrip around the world. Her goal was to make the trip in lesstime than Jules Verne’s fictional character Phileas Fogg,who went “around the world in 80 days.”It took Bly 72 days, 6 hours, 11 minutes, and 14 seconds tomake the journey by boat, train, and horse. How muchquicker was Bly’s trip than Fogg’s?
  3. 3. 9/6/12 Finding Distance On a line, B is 1 unit to the right of point A, point C is 2 units to the left of point A, point D is 3 units to the right of point B, and point E is 12 units to the left of point D. How many units of distance is it from A to E?
  4. 4. 9/10/12 Fruit BasketsThe kitchen staff was arranging baskets of fruiton the tables. Four baskets contained a total of84 delicious, juicy Florida oranges. The fifthbasket contained 4 fewer oranges than theaverage (mean) of the five baskets. How manyoranges were in the fifth basket?
  5. 5. 9/11/12 Shawna’s CoinsShawna returned some bottles to the store. She received $1.60 inquarters, dimes, and nickels. Use these clues to determine thenumber of each kind of coin. She received at least 1 of each coin.There are more dimes than nickels. There is an even number ofquarters. There are as many quarters and nickels together as thereare dimes.How many quarters, dimes and nickels did Shawna receive?
  6. 6. 9/12/12 Bicycle RacingTwo cyclists were going to race. It takes Mary 6 minutesto ride around the track once. It takes Mike 4 minutes toride around the track. How many minutes will passbetween each of the times that Mike passes Mary?
  7. 7. 9/13/12 Milking Cows A total of 3 holstein cows and 3 guernsey cows give as much milk in 3 days as 2 holstein cows and 4 guernsey cows in 4 days. Which breed of cow is the better milk producer, holstein or guernsey?
  8. 8. 9/14/12 PE Class Coach Crowe has a certain number of students in her PE class. If there had been as many students again as there actually were in the class, plus 1/2 as many more, plus 1/3 as many more, plus 1/6 as many more, plus 8 more students, there would have been 170 students. How many students were actually in the class?
  9. 9. 9/17/12 Arranging Digits Construct an eight-digit number using the digits 1, 1, 2, 2, 3, 3, 4, and 4 and arrange them so that the 1’s are separated by one digit, the 2’s are separated by two digits, the 3’s are separated by three digits, and the 4’s are separated by four digits.
  10. 10. 9/18/12 Peeling PotatoesMiles was peeling potatoes for a big family dinner. He can peel2 every minute. After he had worked for 25 minutes, his wife,Prudence, realized that he would never finish all the potatoesin time for dinner, so she decided to help him. She is fasterthan Miles and can peel 3 potatoes every minute. They finishedin time for dinner, and the two of them peeled exactly 400potatoes. How much time did each person spend peelingpotatoes?
  11. 11. 9/19/12 Cooking Time A recipe for cooking a turkey states to allow 20 minutes for each pound of turkey and to add 5 minutes per pound if the turkey is stuffed. Our turkey weighs 16 pounds and will be stuffed. To have dinner at two o’clock in the afternoon, what time does the turkey need to go in the oven? Allow 1/2 hour for cooling and carving. Explain your answers and your thinking.
  12. 12. 9/20/12 Area ProblemW, X, Y, and Z are midpoints of the sides ofthe rectangle. What part of the rectangle isshaded?
  13. 13. 9/21/12 Fruit Weights A dozen pears weigh the same as 8 oranges. Three apples weigh the same as 2 oranges. How many apples weigh the same as a dozen pears?
  14. 14. 9/24/12 Merry Go Round Someone asked Teri how many children were riding on the merry-go-round with her. Teri plans on being a mathematics teacher so, as do all teachers, she turned the answer into a problem. She said, “If you add 1/3 of the number of children riding ahead of me to 3/4 of those riding behind me, you will know how many were on the merry-go-round.”
  15. 15. 9/25/12 Arranging Seats Suppose that there are 3 empty seats in a classroom. Two new students join the class. How many different ways can they be assigned to the empty seats? How many ways can they be assigned if there were 4 empty seats? Five empty seats? Try to find a rule that will work for any number of empty seats and 2 new students.
  16. 16. 9/26/12 Distance Dilemma Matt is going to a basketball game out of town. If he could travel 75 mph, he would arrive 1 hour early for the game. If he travels 45 mph, he will arrive 1 hour late. How far is his trip to the basketball game?
  17. 17. 9/27/12 Prime Problem Find the sum of the least and greatest two- digit prime numbers whose digits are also prime.
  18. 18. 9/28/12 Division Digits If each letter below stands for a single digit, what are the digits in the division problem?