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December Problems
Number Theory | Measurement | Geometry |
Patterns, Algebra, and Functions | Data,
Statistics, and Probability |
Grab Bag
Number Theory
Start out simple...
Family Fun - From Problem Solving
Connections
1. Four families each brought the same number of chairs to a
block party. Three more chairs are needed to seat all 27 of
the participants. How many chairs did each family bring?
Consecutive Numbers
2. An example of consecutive odd numbers is 23, 25, 27, and
29. Find four consecutive odd numbers with a sum of 160.
Show your work.
Now try to work this out...
Opening Day
 
3. It is the grand opening of a local supermarket. Every 5th
customer will receive a coupon for a free turkey and every
7th customer will receive a coupon for a free half gallon of
ice cream. If 400 customers come in on opening day, how many
will get a free turkey and a free half gallon of ice cream?
Kennel Klub
  
4. Four dozen dogs live in 6 different colored kennels. The
smallest kennel has 6 dogs and the orange kennel is the
largest with 10 canines. The yellow kennel and the green
kennel are the only ones with the same number of dogs. The
13 youngest pups are in the red and blue kennels with the
least number of dogs. The purple kennel has 2 more dogs than
the blue kennel. How many dogs are in each kennel? Make a
chart.
This will really challenge
you...
Car Rental
5. Sam needs to rent a car for his upcoming trip.
CheapWheels charges $20.25 per day plus $.14 a mile. Easy
Rider charges $18.25 a day plus $.22 a mile. San plans to do
a lot of driving on his 3-day trip. Which company should Sam
go with? Explain your choice.
Does the difference in cost go up or down as mileage
increases? Support your answer.
Measurement
Start out simple...
Flooring
6. Mr. and Mrs. Corkwood were going to tile their den floor.
They had tiled the kitchen floor earlier in the year with
ceramic tile. The kitchen was 14ft by 10 feet. The den is 20
ft. by 14 ft. The kitchen tile job cost the Corkwoods $1400
including labor. How
will this help them determine the price of the den floor?
Now try to work this out...
Squares
7. Look at this picture of squares. The area of square F is
16 square units. The area of square B is 25 square units.
The area of square H is 25 square units. Find the area for
square D and square E. Explain how you got your answer.
This will really challenge
you...
Try It
8. A rectangular sheet of wood has 4 small squares removed.
It is then cut to make a box that is 5 centimeters by 4 centimeters
with a volume of 60 cubic inches. (Four pieces of wood size
A-4 are removed.) Find the area of the original sheet of
wood.
Geometry
Start out simple...
The Shape of Things
9. Look around your classroom and find as many different
shapes as you can. Make a tally to help you determine which
shapes are used most often. Why do you think this is so?
Now try to work this out...
Map It
 
10. Willy Wonka went to Kandy Korners to see his friend. His
friend told him how the town was set up and where to find
the candy factory.
- Sweet Street, Rocky Road, and Almond Avenue are all
parallel.
- Lollipop Lane is perpendicular to Rocky Road and ends at
Sweet Street.
- Chocolate Boulevard is diagonal to Almond Avenue.
- The candy factory is bordered by Sweet Street, Lollipop
Lane, Sour Patch Place, and Chocolate Boulevard.
Draw a map and put in the candy factory.
This will really challenge
you...
11. Look at this shape. How would you go about finding the
total area of this shape? Show how you would do this and
then find the total area.
Patterns, Algebra, And Functions
Start out simple...
Rafting - From Problem Solving
Connections
12. You are pulling a raft up a river. You can make 15 miles
a day. At night, while you are asleep, however, the current
pushes the raft 3 miles back downstream. If you set out on
Tuesday to get to a town 85 miles upstream, on which day
will you arrive?
Now try to work this out...
Stepping Up
13. Study this picture. How many blocks would you need for a
20-step staircase? Set up an algebraic equation to solve.
This will really challenge
you...
Wacky Walter
 
14. Walter and his parents are a little unusual. If he does
an acceptable job of doing his chores, he gets paid $3.33
for that day. If he does an outstanding job, he gets $3
more. During one 10 day period, Walter received $42.30 for
his work. How many days did Walter earn the extra money?
Data, Statistics, And
Probability
Start out simple...
Happy Halloween
15. Pete went out for Halloween. He got tons of candy. He
put all of his candy in a shopping bag. He got 80 different
things. 30 were chocolate, 20 were gum, 25 were plain, and 5
were cookies. Make a circle graph to display his loot.
Now try to work this out...
Mean or Median
16. Sam made the following scores on unit tests for the
term:
92, 98, 15, 92, 87, 92
Sam's teacher said that his grade would be based on the mean
of his grades. Sam argued that his grade should be based on
the median score of his grades. Find the mean and the median
of Sam's grades. Which do you think best reflects Sam's work
for the term?
Explain your answer.
This will really challenge
you...
Perfection
17. From 11 positive integer scores on a 10-point quiz, the
mean is 8, the median is 8, and the mode is 7. Find the
maximum number of perfect scores possible on this test.
Grab Bag
Be Careful
Tony's father is a driver for Brank's Armoured Truck
Company. They take money from businesses to the bank. His
last stop is at the largest hotel in the city where he
collects a large sum of money. A map of part of the city
showing the location of the hotel and the bank looks like
this:
If Tony's father must take a different route every day to
prevent a robbery attempt, how many different paths
down and to the left can he take from the
hotel to the bank?
December
Solutions
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