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January Problems
Number Theory | Measurement | Geometry |
Patterns, Algebra, and Functions | Data,
Statistics, and Probability
Number Theory
Start out simple...
French Fry Fun
1. There are about 20 potatoes in a 5 pound bag. A
restaurant uses about 2 potatoes per order of French Fries.
They charge $.95 for an order of Fries. How much money does
the restaurant take in on a day that they use 400 pounds of
potatoes?
Odd
2. The object of this activity is to find the sum of the
first 25 odd counting numbers. One way is to add 1 + 3 +
5...continuing
until you have added the first 25 odd numbers. However, this
is too
much work for the problem. Look for patterns and
combinations to
find a much easier way to solve this. Apply what you have
learned
from this problem and find the sum of the first 25 even
counting numbers.
Now try to work this out...
Pump, Pump, Pump...
3. Your heart pumps about 5 quarts of blood through its
chambers
every 60 seconds. A swimming pool (20 ft. x 60 ft.) will
hold about
65,000 gallons of water. This represents the amount of blood
pumped
by your heart in approximately how many weeks?
Going Shopping
4. The Carters are buying a new CD player. Three stores have
the model they want on sale this week. Here are the ads:
Radio Shop: Regular Price=$200, Discount=20% off
Discount City: Regular Price=$180, Discount=30%
off
Ralph's: Regular Price=$210, Discount=10% off and
Extra 20% off
Which store will give the Carters the best buy and what will
the price be? Show all of the steps and label your answer.
This will really challenge
you...
Gas It Up
5. A car dealer claims that by buying a new car, Mike will
pay 1/5 less for gas than he pays for the car he currently
owns.
If the car Mike currently drives costs 1/6 less to gas up
than Dave's car,
and Dave pays $700 per year, what will it cost Mike to put
gas in a new
car for 1 year? Assume all cars will be traveling the same
distance.
Measurement
Start out simple...
To Scale
6. Use 1/4 inch graph paper and make a scale drawing of your
room. Use the scale 1/4" = 1 '.
Now try to work this out...
Farmer Felix's Field
7. Farmer Felix needs to put up a fence around his field.
The dimensions of the field are given in the diagram. But,
he has a problem. He needs to be able to drive his tractor
and needs 10 feet between the field and the fence. How many
feet of fencing should
he buy?
This will really challenge
you...
The Great Flood Of 2000 - From MATH
FORUM
8. On one Sunday in June of 2000, there was a great storm.
Mr. Lui's basement got flooded! Mr. Lui wondered just how
much water had to be cleaned up with his shop vac that held
12 gallons of water.
He knew that there were 7.48 gallons of water in one cubic
foot of water and that he had 2 inches of water in the
backwards `L' shaped section of his basement. (See diagram
below.) How many gallons of water were in his basement and
how many times did he have to empty his shop vac?
Geometry
Start out simple...
Spelling
9. Write the letters M, T, and H on figures 2 and 3 so that
when the figure is folded into a box, it will spell MATH
around the sides of the box. Figure 1 shows the correct
placement of the letters. How did you decide on the letter
placement?
Now try to work this out...
Rotation
10. Find 3 upper case letters that look the same when
rotated 180 degrees. Then, what letter's 90, 180, and 270
degree rotations has this outline? This is also the inside
lines formed by the rotation of what letter?
Patterns, Algebra, And Functions
Start out simple...
Cookies
12. A boy ate 100 cookies in five days. Each day he ate 6
more than the day before. How many cookies did he eat on the
first day?
Now try to work this out...
Walking To School
13. This line represents the line on a graph that shows how
long it took Khalil to walk to school. The horizontal axis
shows the time and the vertical axis shows blocks covered.
Explain what you think happened on Khalil's way to school?
This will really challenge
you...
Surprise, Surprise
14. Extravagant Ellie and Thrifty Tanya each have bank
accounts. Ellie has $500 and Tanya has $200. Ellie
withdraws $15 each weekend while Tanya deposits $12. At the
end of 13 weeks, what is the difference in their bank
accounts? Solve this algebraically. Can you find a week when
there is only a $3 difference? Hint: It is before
the 13th week.
Data, Statistics, And
Probability
Start out simple...
What's In A Name?
A
E I
O U
15. Choose 10 students from your class. Tally the number of
vowels in each person's name. Use this to predict the
results for the rest of the class.
Now try to work this out...
PE Problems
16. Mr. Bulge has to give his class a sit-up test. There are
33 students in his class and he needs to display the data in
such a way that he can easily examine the results. Think of
3 different ways that he could do this and justify your
opinion.
This will really challenge
you...
Things Change
17. Make a double bar graph to show the changes in sales for
albums (1975) and CD's (1995). What conclusions can you
draw?
YEAR: 1975
ALBUMS: 257,000,000
CDs: 0
YEAR: 1980
ALBUMS: 322,800,000
CDs: 0
YEAR: 1985
ALBUMS: 167,000,000
CDs: 22,600,000
YEAR: 1990
ALBUMS: 11,700,000
CDs: 286,500,000
YEAR: 1995
ALBUMS: 4,600,000
CDs: 613,000,000
January
Solutions
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