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

Problem Solving

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

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

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

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.

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

Sets and Functions

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}

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

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.

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

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.

Numeration Systems

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

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

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

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

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.

Number Theory

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

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

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

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).

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

Integers/Fractions

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

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

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

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

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…

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