PROBLEM SOLVING
PROBLEMS
Problem #1
Use or Make A Table
Ann and Makiko like to swim laps at the community pool. They are swimming
together today, but they are on different swim schedules. Ann swims every 3
days and Makiko swims every 5 days. How many times will they both be at the
pool on the same day during the next ten weeks?
Problem #2
Use or Make A Table
It’s here, the hottest item of the season, Rodney the Talking Robot! Rodney
can keep anyone company, including the dog or cat. When the robots are made
at the factory, they move along the conveyor belt and every 8th robot gets a
blue control panel, every 3rd robot gets blinking green eyes, and every 4th
robot gets a square head. If 150 robots come off the conveyor belt, how many
will have all three: a blue control panel, blinking green eyes, and a square
head?
Problem #50 TEST
Lupe and Elena were training for a mile swim. Each week they tried to get
better times. The first week the best time for each of them was 70 minutes.
Then Lupe had a best time of 66 minutes the second week, 67 the third week,
63 the forth week, and 64 the fifth week. Elena had a best time of 69 minutes
the second week, 67 the third week, 66 the fourth week, and 64 the fifth
week. If they continued at this same rate, who would have the best time after
12 weeks of training?
Problem #3
Make an Organized List
James ran down the stairs to the subway and got in line for a ticket. If the
line didn’t move fast, he and Tony would be late for the movie. James
fumbled
in his pocket and finally found a dollar. He gave the dollar to the ticket
man, got his change of 36 cents, and sprinted for the subway car. What are
the possible combinations of coins that James could have received for his
change of 36 cents?
Problem #4
Make an Organized List
Senta and Maurice are lab partners in science class. Today they have to weigh
liquid. They have a tray full of 80 weights that they can use. The weights
are of four different kinds: 50 grams, 25 grams, 15 grams, and 5 grams. The
first liquid weighs 85 grams. How many different combinations of weights will
the scale for the first liquid?
Problem #60 TEST
Sidney remembered that next Monday is his favorite Uncle Wally’s birthday.
Sidney addressed a birthday card to Uncle Wally in Australia, and now he
needs 32 cents to send it. At the post office there is a machine that
dispenses stamps in denominations of 10 cents, 7 cents, 5 cents, and 2 cents.
How many different combinations of stamps totaling 32 cents could Sidney put
on the card?
Problem #5
Act Out or Use Objects
Andre’s Blue Ribbon Cars and Trucks is having a big sale. Mike and Don are
setting up the lot. The boss gives them a diagram of a lot and these
directions: “Put the 4-door car in front of the van. Put the jeep between
the
truck and the van. Put the sports car to the left of the 2-door and 4-door
cars.†How did Mike and Don set up the lot?
Problem #6
Act Out or Use Objects
You have been hired to supervise 22 fourth-graders who are visiting a haunted
house at Halloween. You have a diagram of the house showing the “control
booth†where you will be sitting, hidden behind four two-way mirrors. One
mirror is on each wall, and each mirror looks into three rooms. Mirror 1
looks into rooms A, B, C; mirror 2 looks into rooms C, E, H; mirror 3 looks
into rooms F, G, H; mirror 4 looks into rooms A, D, F. What is a possible
arrangement of the 22 students within the room, if you can see nine students
through each of the four mirrors?
Problem #51 TEST
Heidi has a summer job at the Perfect Pie Shop. Benjamin, who runs the
shop, told Heidi to arrange 6 freshly baked pies in the front window in the
following way:
*pumpkin to the right of the chocolate
*chocolate across from the strawberry
*peach to the right of strawberry
*peach and apple not in the same row with the lemon
How did Heidi arrange the pies?
Problem #9
Use or look for a pattern
On July 5, in the area around Center Village, there was great excitement. Six
different people reported to the police that they had seen Big-foot, the
large hairy creature sometimes seen but never captured. The next day, twice
as many people called the police, sure they had seen the creature. Each day
the police received twice as many calls as the day before. After they got a
total of more than 300 call, the police took the phone off the hook! On what
day did the police receive their 300th call?
Problem #10
Use or look for a pattern
On the ancient island of Circulus archaeologist found a series of caves. In
the first cave they found a circle with 560 stones. In the second cave they
found a circle of stones with 8 fewer stones than in the first cave. Each new
cave had a circle with twice as many stones missing from the circle than in
the previous cave. For example, in the third cave there were 16 fewer stones
in the circle than in the second cave. If the stone circles continued in this
way, which cave would have the last stone circle?
Problem #58
Test Problem
Willy the Wizard has a special hobby, Growing huge vegetables. His favorite
is zucchini, which he likes to measure. He has one that started out 6 inches,
then grew by 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
what day would the giant zucchini be larger than 11 feet?
Problem # 13
Make a picture or Diagram
Gino and Mark had found all the things on the list for a treasure hunt and
had only a few minutes to get to the finish point. But they were lost! Gino
said, When we were at the bridge, we were 2 blocks west of the finish point.
Can you remember where we went after that?†Mark recalled that they had
gone
south 3 blocks, then they went to their left 5 blocks, left again for 2
blocks, then north for 1 block. What is the quickest route from where they
are to finish point?
Problem # 14
Make a picture or Diagram
Darryl has a summer job with real ups and downs: he delivers packages in the
Sears Tower in Chicago. On his first day, he is given a box of sandwiches to
deliver during lunchtime. He takes the turkey sandwiches to an office 3
floors above the basement. He delivers the ham and cheese 13 floors above
the turkey and 7 floors below the egg salad. He delivers the pastrami 9
floors below the ham and cheese and 8 floors below the submarine sandwich.
What is the number of the floor to which Darryl delivered each sandwich?