Problem Solving Items
THE THREE BEARS COOKIE STORE.
The Bear family decided to open a cookie store that featured bear-sized cookies. Mama
and Baby Bear decorated the cookies, and Papa Bear sold the cookies. Mama Bear could
completely decorate a cookie every 7 minutes. Baby Bear could completely decorate a
cookie every 12 minutes. Unfortunately, Papa Bear was eating one of the cookies every
9 minutes. If they open the store and have no cookies decorated, how long will it take
them to produce 500 decorated cookies that can be sold?
STARTING THE SCHOOL YEAR.
A 24-volume encyclopedia is sitting on a bookshelf in numerical order from left to right.
Each book is the same thickness. The front and back covers of each book are each 0.75
cm thick. The page section inside each book spans exactly 3.25 cm. If a hungry
centimeter bookworm starts eating at page 1 of volume 1 and eats, in a straight line, to
the last page of volume 24, exactly how far will the worm travel?
END OF THE YEAR
You’re thinking back on all that you’ve done, and you complain. “Dad, I’m worn out. I
work too hard! I need a bigger allowance.” Your Dad is really good with numbers. He
says, “Wait one minute. Let’s figure out exactly what you do.” He takes out a paper and
produces the following:
There are 366 days in the year 2000. You sleep 8 hours a day, which is one-third of
the time or 122 days. That leaves 244 days. You spend 8 hours a day having fun or
resting. That’s another 122 days, which leave 244 - 122 = 122 days. You don’t do any
serious work on Saturday or Sunday, so that’s 104 (2 times 52) more days. This leaves
122-104 = 18 days. You get two weeks of vacation (14 days), so now we have 18 - 14 =
4 days. You get a day off for New Year’s, Fourth of July, Labor Day, and Christmas, so
4 - 4 = 0 days. So you see, you don’t even work one day all year! Could your Dad Be
right? Never! Explain to him where he went wrong.
THE FERRIS WHEEL
The Ferris Wheel is named after George Washington Gale Ferris Jr. who designed a
massive, 264 foot diameter “Ferris Wheel” for the World’s Columbian Exposition in
Chicago in 1893. Mr. Ferris’ invention could carry 2,160 persons at one time. The wheel
was later moved to the St. Louis Exposition of 1904 after which it was dismantled.
You are a visitor to the 1904 St. Louis World’s Fair and you just took an exhilarating ride
thanks to George Ferris. You have an idea. Twenty-five years earlier, Thomas Edison
invented the first practical incandescent light bulb (1879). Wow! The Ferris Wheel
would look fabulous at night if its outer edge had light bulbs, one every three feet. How
many of Mr. Edison’s bulbs would be needed to light one side the Ferris Wheel?
KENNEL VOLUNTEERS
Jack, Art, Fran, and Megan work as volunteers at the local kennel. Jack gives the dogs
baths every 4 days; Art cleans out cages every 6 days; Fran feeds the animals in Section
B every 2 days; and Megan helps the receptionist every 3 days. How many times in 12
weeks will all 4 helpers be at the clinic on the same day?
RON’S TV
For a school Project, Ron recorded how much TV he watched in one weekend and what
kinds of programs he watched. This chart shows the time he watched TV:
SATURDAY: 9:30-10:30AM; 1:00-3:30PM; 8:00-10:00 PM
SUNDAY: 1:00-2:30PM; 8:00-10:00PM
Ron watched sports programs for one half of the time. He watched movies for one third
of the time. He watched cartoons with his sister Ronnette the rest of the time. How many
minutes did Ron watch cartoons? Make sure you explain all of the steps and label your
answers.
MOVING ON
Mr. and Mrs. Quigley just moved into a new home with a lot of land. They need to plant
grass seed. The problem is that they are not sure how to figure the new amount that they
need. At their old house, they knew that the lawn was 10 ft. by 20 ft. and needed 5
pounds of seed. Their new lawn is 100 ft. by 50 ft. How will knowing the amount of seed
needed from their old house help them with buying seed for the new lawn? How much
seed will they need now?
ZOOMING ZUCHINNI
Gordon Greenthumbs likes to grow huge plants. He once grew a zucchini that started out
at 6 inches, then grew 9 inches to be 15 inches on the second day. Each day the zucchini
grew by the same amount as the day before plus another 3 inches. On which day would
the zucchini be longer than 11 feet?
BOOTH’S BICYCLE SHOP
Henry counted some bicycles and tricycles. He counted 19. When he counted the
wheels, he got 45. How many tricycles were there?
LIBRARY TABLES
At a local library, 34 students can sit at 7 tables with no empty seats. There are small
tables that hold 4 students and large tables that hold 6. How many small tables are in the
library?
HOW MANY TILES DO I HAVE?
Clues:
I can arrange them into a square and have 3 left over.
I can form a rectangle whose length is 10 more than the width.
I have less than 60.
SCHOOL GARDEN
The agricultural school garden is rectangular in shape and measures 20' x 45'. The
students plant beans in 2/3 of the garden. One half of that contains lima beans. How many
square feet of the garden are planted in lima beans?
VERIZON CELL PHONE PLANS
In 2008, Verizon had the following basic plans available (source: verizon.com):
450 minutes for $39.99 and a $0.45 charge per extra minute.
900 minutes for $59.99 and a $0.40 charge per extra minute.
1350 minutes for $79.99 and a $0.30 charge per extra minute.
Determine which plan is the best for a customer who uses 600 minutes each month.
Other extensions:
At what point will the 450 and the 900-minute plan cost the same?
What are the linear equations for each?
THE PAYOFF
Late one night a burglar somehow got into one of the vaults in Fort Knox and started out
with a big sack of gold coins. No one really knows how much he stole. At any rate, on his
way out, he was stopped by one of the guards, who caught him "holding the bag" so to
speak. Fortunately for him, the burglar was able to talk his way out of trouble by offering
the guard half the money he had taken with a bonus of $2,000 thrown in. Just as he was
walking away, praising his good luck at having gotten free, he was stopped by a second
guard. It took the same bribe, half of all the money he had left, with $2,000 thrown in, to
get by the second guard. Just as he was about to leave, you guessed it, he was stopped by
yet a third guard who let him go only after receiving half of all the burglar had left, with
$2,000 thrown in.
By the time the burglar left the front gate of Fort Knox, he had mixed emotions. After all,
he did leave with $9,000 more than he had when he arrived and he escaped a free man.
But as he thought of all the money he had left behind with the guards, he wept.
Start With a Penny (Frank Schaffer Publications)
Sam had a month’s vacation from school. His parents had many chores for him to do
around the house and yard.
His dad said that Sam would be paid for his work. Sam’s dad offered to pay him $10 a
day for 30 days’ work.
Sam thought about the offer and then made an offer of his own. Sam told is dad that he
would be willing to work for pennies a day. He would work for 1¢ the first day. 2¢ the
second day, 4¢ the third day, and so on with his pay doubling each day. For the 30 days,
Sam would accept the amount he earned on the 30th day.
Compare the plans. Is there a day where Sam’s offer is better than his dad’s plan?
Harder Problems
SWIMMING POOL DECK
A swimming pool measures 14 feet by 40 feet. It has a rectangular deck that is 6 feet
wide around it. If each tile on the deck is 1 foot by 1 foot, how many tiles are needed?
CITY WALL
A certain city has a circular wall around it, and this wall has four gates pointing north,
south, east and west. A house stands outside the city, three miles north of the north gate,
and it can just be seen from a point nine miles east of the south gate. What is the diameter
of the wall that surrounds the city?
CIRCLE GEOMETRY
C is the center of the circle and F is a point on the circle such that BCDF is a 2cm by 3cm
rectangle. What is the area of the shaded region? (in cm2).
QuickTime™ and a
TIFF (Unc ompressed) decompres sor
are needed to see this picture.
The Philly Cheese Steak Sandwich (HOLT ALG 1 textbook)
At Geno’s Steaks, the busiest shift of the week is on Saturday from 11:00 AM to 7:00 PM.
During that time Geno’s makes an average of 1.5 cheese steak sandwiches a minute. Use the
recipe below. How many pounds of steak are needed to get through this shift?
Moving Cows (patterns)
There are cows in each of these pastures. Bridges connect the pastures. The number on
each bridge tells the total number of cows in the 2 connecting pastures. How many cows
are in each pasture? Hint: no pasture has more than 20 or less than 10 cows.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Vocabulary Expected:
Sum
Total
Connecting
More than/Less than
Supplies needed:
Copies of problem for each student
Vocabulary words posted for students
Mathematically correct reasoning:
How does changing the number of cows in one pasture affect the numbers in all the others?
Explain how you know your answer is mathematically correct using the correct mathematical vocabulary.
Class Process:
1) Read through the problem together.
2) Students work 5 minutes alone then write a couple sentences of what they did to start the problem on their data
sheet.
3) Students break into groups (3 is best), write what each student did on the group poster and together agree on an
answer. After group time is done, the group writes what they did to solve the problem together and how they know it
is correct.
4) Send students out to spy on other groups. Have one student stay with each poster. When spies come back, group
discusses if change is necessary.
5) Circle discussion with all groups looking at each others posters and answers. Groups share out answers and
process.