Problem Solving

MP1: Make Sense of Problems and Persevere in Solving Them

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?

9/5/12

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?

9/6/12

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?

9/10/12

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?

9/11/12

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?

9/12/12

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?

9/13/12

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?

9/14/12

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.

9/17/12

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?

9/18/12

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.

9/19/12

Area Problem

W, X, Y, and Z are midpoints of the sides of

the rectangle. What part of the rectangle is

shaded?

9/20/12

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?

9/21/12

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.”

9/24/12

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.

9/25/12

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?

9/26/12

Prime Problem

Find the sum of the least and greatest two-

digit prime numbers whose digits are also

prime.

9/27/12

Division Digits

If each letter below stands for a single digit, what are

the digits in the division problem?

9/28/12