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

1. Problem Solving
MP1: Make Sense of Problems and
Persevere in Solving Them

2. 9/5/12 Around the World
On November 14, 1889, journalist Nellie Bly set off on a
trip around the world. Her goal was to make the trip in less
time 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 to
make the journey by boat, train, and horse. How much
quicker was Bly’s trip than Fogg’s?

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. 9/10/12 Fruit Baskets
The kitchen staff was arranging baskets of fruit
on the tables. Four baskets contained a total of
84 delicious, juicy Florida oranges. The fifth
basket contained 4 fewer oranges than the
average (mean) of the five baskets. How many
oranges were in the fifth basket?

5. 9/11/12 Shawna’s Coins
Shawna returned some bottles to the store. She received $1.60 in
quarters, dimes, and nickels. Use these clues to determine the
number of each kind of coin. She received at least 1 of each coin.
There are more dimes than nickels. There is an even number of
quarters. There are as many quarters and nickels together as there
are dimes.
How many quarters, dimes and nickels did Shawna receive?

6. 9/12/12 Bicycle Racing
Two cyclists were going to race. It takes Mary 6 minutes
to ride around the track once. It takes Mike 4 minutes to
ride around the track. How many minutes will pass
between each of the times that Mike passes Mary?

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. 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. 9/17/12 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. 9/18/12 Peeling Potatoes
Miles was peeling potatoes for a big family dinner. He can peel
2 every minute. After he had worked for 25 minutes, his wife,
Prudence, realized that he would never finish all the potatoes
in time for dinner, so she decided to help him. She is faster
than Miles and can peel 3 potatoes every minute. They finished
in time for dinner, and the two of them peeled exactly 400
potatoes. How much time did each person spend peeling
potatoes?

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. 9/20/12 Area Problem
W, X, Y, and Z are midpoints of the sides of
the rectangle. What part of the rectangle is
shaded?

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. 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. 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. 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. 9/27/12 Prime Problem
Find the sum of the least and greatest two-
digit prime numbers whose digits are also
prime.

18. 9/28/12 Division Digits
If each letter below stands for a single digit, what are
the digits in the division problem?