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November Problems
Number Theory | Measurement | Geometry |
Patterns, Algebra, and Functions | Data,
Statistics, and Probability |
Number Theory
Start out simple...
Dining Decisions
1. Mrs. Phillpott is a cook for the Thornberry family. She
usually makes a 5 pound roast for dinner on Thursdays. She
knows that it takes 2 1/2 hours to cook this roast. Her boss
is having a dinner party and she needs to make more food.
She decides that
she needs 15 pounds of meat. The problem is that she only
has one
oven and it will not hold a roast bigger than 10 pounds. How
could
she solve this problem? Answer in paragraph form.
Change
2. Sadie went to the store with a $10 bill. She spent $4.76.
Give 6 possible ways she could get her change. She cannot
use the same number of coins twice. (You cannot say 5 one
dollar bills, 2 dimes, 4 pennies, and then a $5 bill 2 dimes
and 4 pennies.) She must use each type of United States coin
at least once.
Now try to work this out...
Bagging Potatoes
3. A farmer grows 196 pounds of potatoes. He sells them to a
grocer who divides them into 5 pound and 2 pound bags. If
the grocer uses the same number of 5 pound and 2 pound bags,
how many bags of each did he use?
Mug-Making Mary (from THE PROBLEM SOLVER
6)
4. Mary McDonald makes mugs in Miami. She makes two sizes of
mugs: a small mug that she sells for $2.50 and a large mug
that she sells for $5.75. Yesterday Mary made $56. Before
she opened her shop in the morning, she had 200 mugs in her
inventory. At the end of the day she has 188. How many mugs
of each price did she sell?
This will really challenge
you...
  
5. Find out how much per ounce each of these sells for. Then
arrange them from the most expensive to the least expensive.
Gas
$1.65 per gallon
Snapple
$1.29 for 16 oz.
Gatorade
$1.59 for 20 oz.
Lipton Iced Tea $1.19 for 16 oz.
Ocean Spray $2.54 for 30 oz.
Evian Water
$1.49
for 9 oz.
NyQuil
$8.35 for 6 oz.
Pepto Bismol
$3.85 for
4 oz.
Whiteout
$1.39
for .8 oz.
Scope
$$.99 for 1.5 oz.
Measurement
Start out simple...
Space Measurement
6. An object weighing 5 pounds on Earth will weigh 2 pounds
on Mercury. The Statue of Liberty weighs 225 tons. What
would it weigh on Mercury?
Now try to work this out...
Garden
7. Farmer Brown is making a garden 14 1/2 feet long and 8
3/4 feet wide. He puts up a fence 23 1/2 feet long and 17
3/4 feet wide. What is the distance from the fence to the
edge of the garden?
This will really challenge
you...
TV Time
8. Gretchen is going to "Best Buy" to get a new TV. She
already has a cabinet and she wants to be sure that the new
TV will fit. Her cabinet is 24 inches wide by 24 inches high
by 12 inches deep. She wants to have 1 inches on each side,
1 inch on top and
1 inch behind so the TV will slide in easily. Which of these
would be her best choice?
- Volume of 5280 cu. in. w = 22", h = 20"
- Volume of 5290 cu. in. d = 10", base and height
the same
- Volume of 5566 cu. in. w = 22", d = 11"
Geometry
Start out simple...
Meow!
 
9. Draw a cat, but you may only use regular polygons and you
must use at least 6 different ones.
Now try to work this out...
Toothpick Fun
10. Carl is given 24 toothpicks and told to construct a
geometric solid. He must use all of the toothpicks. Which
solid could he make? Draw a picture to support your answer.
How many balls of clay would he need to hold his structure
together?
This will really challenge
you...
Painting Problem
11. Brett has an assignment to paint all of the geometric
solids for a museum display. His directions are to use the
least amount of colors on each solid, but no sides that
touch should be painted the same color. Tell how many colors
will be needed for each solid:
cube, triangular prism, hexagonal prism, octagonal
pyramid, pentagonal pyramid. Is it true that the greater
the number of sides, the more colors that are needed?
Explain your answer in a few sentences and draw a picture.
Patterns, Algebra, And Functions
Start out simple...
Round Robin
12. Six teams are involved in a round robin tournament. In
such a tournament, each team plays every other team once and
only once. It does not matter who wins the games. Therefore,
how many games in all are played? You may want to call your
teams A,B,C OR 1,2,3.
Now try to work this out...
Dots
13. Oblong numbers can be represented by rectangular arrays
in which the number of dots in each row is one more than the
number of dots in each column. The first 3 oblong
numbers—2, 6, and 12—are represented below. Show
the next 5 oblong numbers. How many dots are needed to
represent the tenth oblong number?
**
***
****
***
****
****
This will really challenge
you...
Lucky Leaf Lettuce
14. Monday, the Produce manager, Arthur Applegate, stacked
the display case with 80 heads of lettuce. By the end of the
day, some of the lettuce had been sold. On Tuesday, the
manager surveyed the display case and counted the number of
heads that were left.
He decided to add an equal number of heads. (He doubled the
leftovers.) By the end of the day, he had sold the same
number of heads as Monday.
On Wednesday, the manager decided to triple the number of
heads that he had left. He sold the same number that day,
too. At the end of this day there were no heads of lettuce
left. How many were sold each day?
Data, Statistics, And
Probability
Start out simple...
Car Colors
 
15. Raheem, Cary, and Jamar are having a discussion about
which color car is the most popular. Raheem says white, Cary
says black, and Jamar says silver. They stood at the
intersection of Ridge Avenue and Domino Lane for an hour and
kept a count. The results
were: black=40; silver=60; white=80. Show 2 different ways
that they could display their results.
Now try to work this out...
Brrrrrr!!!!!
16. Here are the average temperatures in Hawaii for 7 weeks
in 1999 and the same 7 weeks in 2000. Determine which type
of graph would be the most appropriate and make it. Don't
forget labels, title, and the correct scale. Justify why you
chose that type of graph.
1999
87 92
98 99
98 101
90
2000
91 92
99 102
100 88
89
This will really challenge
you...
Randomly Speaking
17. There are an equal number of pennies, nickels, dimes,
and quarters in a bag. What is the probability that the
combined value of the four coins randomly selected with
replacement will be $.41? Express your answer as a fraction
in simplest form.
November
Solutions
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