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Problem Solving

Sets and Functions

Numeration Systems

Number Theory Fractions

Mathemania for Mathemania for Teachers!Teachers!

Problem Solving Problem Solving Problem Solving Problem Solving

HomeHome Check WorkCheck Work

Problem Solving: 5 PointsProblem Solving: 5 PointsProblem Solving: 5 PointsProblem Solving: 5 Points

True or False: Problem Solving for True or False: Problem Solving for some may be an exercise for otherssome may be an exercise for others

..

TrueTrue



Find a pattern in the following Find a pattern in the following sequence and write the next term:sequence and write the next term:

3, 5, 11, 21, 353, 5, 11, 21, 35

5353



What is the fifth number in the set of What is the fifth number in the set of triangular numbers?triangular numbers?

1515



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

78 handshakes and n handshakes. 78 handshakes and n handshakes.



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

9 crossings9 crossings

Sets and Functions Sets and Functions Sets and Functions Sets and Functions


Sets and Functions: 5 PointsSets and Functions: 5 PointsSets and Functions: 5 PointsSets and Functions: 5 Points

Given the universal set U= {0, 1, Given the universal set U= {0, 1, 2, 3, 4, 5, 6,} and sets A = {2, 4, 6} 2, 3, 4, 5, 6,} and sets A = {2, 4, 6} and B = {1, 2, 3, 4} determine the set and B = {1, 2, 3, 4} determine the set A A B and A B and A B. B.

A A B = {1,2,3,4,6} and A B = {1,2,3,4,6} and A B = {2, B = {2, 4}4}



Sketch a Venn diagram to illustrate the Sketch a Venn diagram to illustrate the following set: Afollowing set: A B B

A B


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

For the domain values 1, 2, 3, 4, 5, the For the domain values 1, 2, 3, 4, 5, the corresponding range values are .5, 1, corresponding range values are .5, 1, 1.5, 2, and 2.5.1.5, 2, and 2.5.



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

20 men20 men


Sets and Functions: 100 PointsSets and Functions: 100 PointsSets and Functions: 100 PointsSets and Functions: 100 PointsWhich of the following sets of numbers is Which of the following sets of numbers is closed under division? closed under division?

Natural (counting) numbers, Whole numbers, Natural (counting) numbers, Whole numbers, Fractions, Even numbers, Odd numbers or all Fractions, Even numbers, Odd numbers or all multiples of 5.multiples of 5.

Just the set of all Fractions.Just the set of all Fractions.

Numeration Systems Numeration Systems Numeration Systems Numeration Systems


Numeration Systems: 5 PointsNumeration Systems: 5 PointsNumeration Systems: 5 PointsNumeration Systems: 5 Points

Round 6,281,497 to the nearest Round 6,281,497 to the nearest hundred thousand.hundred thousand.

6,300,0006,300,000



Use equal products to find a Use equal products to find a replacement for each number that is replacement for each number that is more convenient for mental more convenient for mental calculation. Show the new numbers calculation. Show the new numbers and determine the answer for 25 x 28.and determine the answer for 25 x 28.

25 x 4 x 7 = 100 x 7 = 70025 x 4 x 7 = 100 x 7 = 700



True or False: The set of whole True or False: The set of whole numbers is closed for subtractionnumbers is closed for subtraction..

FalseFalse



Calculate: 432Calculate: 43255 x 22 x 2255

21,10421,10455


Numeration Systems: Numeration Systems: 100 Points100 Points

Numeration Systems: Numeration Systems: 100 Points100 Points

If the number 6If the number 652 52 is expanded and is expanded and written in positional numeration, what written in positional numeration, what is the digit in the units place?is the digit in the units place?

6 is the digit in the units place.6 is the digit in the units place.

Number Theory Number Theory Number Theory Number Theory


Number Theory: 5 PointsNumber Theory: 5 PointsNumber Theory: 5 PointsNumber Theory: 5 Points

Determine if the following is true Determine if the following is true or false:or false:

3348,02548,025

FalseFalse



Is 371 a prime number?Is 371 a prime number?

No-it is a composite number.No-it is a composite number.



Find the GCF (280, 165) and the Find the GCF (280, 165) and the LCM(12, 210)LCM(12, 210) . .

GCF is 5 and LCM is 420GCF is 5 and LCM is 420



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


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

again? Assume that there are 366 days in a year.again? Assume that there are 366 days in a year. ??

5 years, or 183 weeks or 1830 days5 years, or 183 weeks or 1830 days

Integers/Fractions Integers/Fractions Integers/Fractions Integers/Fractions


Integers/Fractions: 5 PointsIntegers/Fractions: 5 PointsIntegers/Fractions: 5 PointsIntegers/Fractions: 5 Points

True or False? The set of fractions is True or False? The set of fractions is closed for multiplication?closed for multiplication?

TrueTrue



Use equal quotients to calculate the Use equal quotients to calculate the answer to 800 answer to 800 16. 16.

800 800 16 = 200 16 = 200 4 = 100 4 = 100 2 = 50 2 = 50



Use Fraction Bars to illustrate 2/3 X Use Fraction Bars to illustrate 2/3 X 1/51/5 . .

2/152/15



A school’s new pump can fill the A school’s new pump can fill the swimming pool in 5 hours, the old swimming pool in 5 hours, the old pump takes 10 hours. How long will it pump takes 10 hours. How long will it take to fill the pool if both pumps are take to fill the pool if both pumps are used together?used together?

3 1/3 hours3 1/3 hours



Paula removed 4/5 of the disks from a Paula removed 4/5 of the disks from a new box of computer disks, and Sam new box of computer disks, and Sam removed 7/10 of the disks that removed 7/10 of the disks that remained in the box. If Sam removed remained in the box. If Sam removed 28 disks from the box, how many disks 28 disks from the box, how many disks did Paula remove?did Paula remove?

160 disks – not that anyone uses 160 disks – not that anyone uses computer disks anymore… computer disks anymore…


Final QuestionFinal QuestionFinal QuestionFinal Question

What are Polya’s 4 steps to problem What are Polya’s 4 steps to problem solving?solving?

1.1. Understand the problemUnderstand the problem

2.2. Devise a planDevise a plan

3.3. Carry out the planCarry out the plan

4.4. Look backLook back

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