1. Mathemania for Teachers!
Problem Solving
Sets and Functions
Numeration Systems
Number Theory
Fractions 5 5 5 5 5 10 10 10 10 10 25 25 25 25 25 50 50 50 50 50
100
100
100
100
100
Final Question

2. Problem Solving

3. Problem Solving: 5 Points
True or False: Problem Solving for some may be an exercise for others .
True

4. Problem Solving: 10 Points
Find a pattern in the following sequence and write the next term:
3, 5, 11, 21, 35 53

5. Problem Solving: 25 Points
What is the fifth number in the set of triangular numbers? 15

6. Problem Solving: 50 Points
There are 78 people around a table. Each person shakes hands with the person to his or her immediate right and left. How many handshakes take place? Write an algebraic expression for the number of handshakes.
78 handshakes and n handshakes.

7. Problem Solving: 100 Points
Two men and two boys want to cross a river, using a small canoe. The canoe can carry two boys or one man. What is the least number of times the canoe must cross the river to get everyone to the other side?
9 crossings

8. Sets and Functions

9. Sets and Functions: 5 Points
Given the universal set U= {0, 1, 2, 3, 4, 5, 6,} and sets A = {2, 4, 6} and B = {1, 2, 3, 4} determine the set A  B and A B.
A  B = {1,2,3,4,6} and A  B = {2, 4}

10. Sets and Functions: 10 Points
Sketch a Venn diagram to illustrate the following set: A B A B

11. Sets and Functions: 25 Points
Consider the function that relates the length x of each line segment to f(x), which is half of the length of the segment. Determine the range value f(x) for each of the following domain values: 1, 2, 3, 4, and 5.
For the domain values 1, 2, 3, 4, 5, the corresponding range values are .5, 1, 1.5, 2, and 2.5.

12. Sets and Functions: 50 Points
In a certain town there live 150 men. 85 are married, 70 have a telephone, 75 own a car, 55 are married and have a telephone, 35 have a telephone and a car, 40 are married and have a car, and 30 are married, have a car, and have a telephone. How many men are single and do not have either a car or a telephone?
20 men

13. Sets and Functions: 100 Points
Which of the following sets of numbers is closed under division?
Natural (counting) numbers, Whole numbers, Fractions, Even numbers, Odd numbers or all multiples of 5.
Just the set of all Fractions.

14. Numeration Systems

15. Numeration Systems: 5 Points
Round 6,281,497 to the nearest hundred thousand.
6,300,000

16. Numeration Systems: 10 Points
Use equal products to find a replacement for each number that is more convenient for mental calculation. Show the new numbers and determine the answer for 25 x 28.
25 x 4 x 7 = 100 x 7 = 700

17. Numeration Systems: 25 Points
True or False: The set of whole numbers is closed for subtraction.
False

18. Numeration Systems: 50 Points
Calculate: 4325 x 225
21,1045

19. Numeration Systems: 100 Points
If the number 652 is expanded and written in positional numeration, what is the digit in the units place?
6 is the digit in the units place.

20. Number Theory

21. Number Theory: 5 Points Determine if the following is true or false:
348,025
False

22. No-it is a composite number.
Number Theory: 10 Points
Is 371 a prime number?
No-it is a composite number.

23. Number Theory: 25 Points
Find the GCF (280, 165) and the LCM(12, 210) .
GCF is 5 and LCM is 420

24. Number Theory: 50 Points
Shane has 72 inches of copper wire and 42 inches of steel wire. He wants to cut them into pieces, but wants all the pieces to be the same length. What is the largest length he can cut these wires into so that each piece is the same length? How many pieces of wire will he have?
6 inches and he will have 19 pieces of wire (12 copper and 7 steel).

25. Number Theory: 100 Points 5 years, or 183 weeks or 1830 days
Suppose that Douglas the Decimal Dictator changed our calendar so that there were now ten days in a week (Onesday, Twosday, Threesday, Foursday, etc.) Also, since Douglas was born on February 29th, he declares that every year is a leap year. Furthermore, suppose that January 1st was a Onesday. How many years will it take for January 1st to land on a Onesday again? Assume that there are 366 days in a year. ?
5 years, or 183 weeks or 1830 days

26. Integers/Fractions

27. Integers/Fractions: 5 Points
True or False? The set of fractions is closed for multiplication?
True

28. Integers/Fractions: 10 Points
Use equal quotients to calculate the answer to 800  16.
800  16 = 200  4 = 100  2 = 50

29. Integers/Fractions: 25 Points
Use Fraction Bars to illustrate 2/3 X 1/5 .
2/15

30. Integers/Fractions: 50 Points
A school’s new pump can fill the swimming pool in 5 hours, the old pump takes 10 hours. How long will it take to fill the pool if both pumps are used together?
3 1/3 hours

31. Integers/Fractions: 100 Points
Paula removed 4/5 of the disks from a new box of computer disks, and Sam removed 7/10 of the disks that remained in the box. If Sam removed 28 disks from the box, how many disks did Paula remove?
160 disks – not that anyone uses computer disks anymore…

32. Final Question What are Polya’s 4 steps to problem solving?
Understand the problem
Devise a plan
Carry out the plan
Look back