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Number Games

444444444

444444444

444444444

444

444

444

444444444

444444444

444444444

444

444

444

444444444

444444444

444444444

5555

5555555

55555555

555 555

555

55555

5555555

5555555

555555

5555

555 555

555 555

555555555

55555555

55555

A Lesson in the Math + Fun! Series

11111

1111111

111111111

1111 1111

111 111

111

111

111 11111

111 11111

111 11111

111 111

1111 1111

1111111111

11111111

111111

222

2222

2222

22222

222 222

222 222

222 222

222 222

222 222

222222222

222222222

2222222222

222 222

222 222

222 222

3333 3333

3333 3333

33333 33333

33333 33333

33333 33333

333333333333

333333333333

333333333333

333 3333 333

333 3333 333

333 333 333

333 333 333

333 33 333

333 33 333

333 333

Math has many uses in geography. This lesson focuses on the relationship of math to making and using maps.

About This Presentation

This presentation is part of the Math + Fun! series devised by Behrooz Parhami, Professor of Computer Engineering at University of California, Santa Barbara. It was first prepared for special lessons in mathematics at Goleta Family School during the 2003-04 and 2004-05 school years. The slides can be used freely in teaching and in other educational settings. Unauthorized uses are strictly prohibited. Behrooz Parhami

EditionReleasedRevisedRevisedFirstApr. 2005

What Number Did You Choose?

1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 10

2. Multiply the number by 9. If the result has two digits, add the two digits;

otherwise leave the number alone.

3. Subtract 5 from the number that you got in step 2.

6. Use the last letter in your countrys name as the first letter of an animal.

7. Use the last letter of your animals name as the first letter of a color.

Orange kangaroo from Denmark

How Did the Game Work?

1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 10

2. Multiply the number by 9. 9 18 27 36 45 54 63 72 81 90

If the result has two digits, add the two digits You get 9 in all cases!

3. Subtract 5 from the number that you got in step 2. You get 4

Orange kangaroo from Denmark

More Mind-Reading Games

Think of a 2-digit number (10-99).Multiply your number by 5.Add 500 to the result of step 2.Add the number of your siblings.Double the result of step 4.

You got a 4-digit number that starts with 1, has your original 2-digit number in the middle, and double the number of your siblings at the end.

Think of a number between 1 and 30.Tell me in which of the five lists below the number appears.

List A: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

List B: 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30

List C: 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30

List D: 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30

List E: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

A

C

E

B

D

E

Activity 1: Mind-Reading Game

Think of a number between 1 and 20.Tell me in which of the five lists below the number appears.

List A: 1 4 6 8 9 11 14 16 19

List B: 2 6 7 8 12 17 20

List C: 3 4 6 9 13 14 18 19 20

List D: 5 7 8 9 15 16 17 18 19 20

List E: 10 11 12 13 14 15 16 17 18 19 20

Play the following mind-reading game with your friends and family

(First, discover how to tell the number if you know which lists it is in)

Challenge: Add a List F to the five lists given above, and complete the lists, so that you can play the game with numbers up to 40.

Activity 2: More Mind-Reading Games

Your final result is 36, isnt it?

Your final result shows the month and day of your birth

Explain how this game works.

Change the numbers to make your own game.

Explain how this game works.

Euclids Game for Two Players

A referee writes two numbers on the board

The two players take turns writing the difference of two numbers

already on the board, provided the difference is a new number

The player who cannot write a new number loses

The total number of values written on the board is

n = the larger number / greatest common divisor of the two numbers

If n is odd, player 1 wins

Activity 3: The Game of Nim

Write three numbers on three lines

The two players take turns reducing one of the numbers

The player who makes the last move loses

Challenge:

Discover a winning strategy with (5, 3, 1), if you are the first playerPlay the game with other numbers such as (7, 4, 2), (6, 5, 3), . . .

The Four 4s Puzzle

Use four 4s and any number of math symbols (such as +, -, , /, , . . .) to form as many different numbers as possible.

3 = (4 + 4 + 4) / 4

4 = (4 + 4) / 4 + 4

5 = (4 4 + 4) / 4

2 = 4 / 4 + 4 / 4 or 4 (4 + 4) / 4

6 = (4 + 4 + 4) / 4

8 = 4 (4 / 4) + 4

7 = 4 + 4 4 / 4 or 44 / 4 4

9 = 44 / 4 4 or 4 / 4 + 4 4

10 = (4 + 4 / 4) 4

11 = 44 / (4 + 4)

12 = 4 (4 4 / 4)

13 = 44 / 4 + 4

14 = 4 (4 + 4) 4

15 = 44 / 4 + 4

16 = 4 4 + 4 4 or 4 4 4 / 4

17 = 4 4 + 4 / 4

18 = 4 (4 + 4) + 4

20 = 4 (4 + 4 / 4)

22 = 4 4 + 4 + 4

25 = (4 + 4 / 4)4

24 = 4 (4 + 4 + 4)

Activity 4: The Five 5s Puzzle

Use five 5s and any number of math symbols (such as +, -, , /, , . . .) to form as many different numbers as possible.

3 =

4 =

5 =

2 =

6 =

8 =

7 =

9 =

10 =

11 =

12 =

13 =

14 =

15 =

16 =

17 =

18 =

20 =

22 =

25 =

1 = 55 / 5 5 5

0 = 5 (5 / 5 5 / 5)

Examples

24 =

19 =

21 =

23 =

Activity 5: Birth Year Puzzle

Use the digits in your year of birth, in order, plus any number of math symbols (+, , . . .) to form the numbers from 0 to 10.

This puzzle becomes more or less difficult, depending on your birth year. It is pretty simple for most years. However, for someone born in 2005, it is hard: 0 = 2x0 + 0x5, 1 = 2^0 + 0x5 = 2.0x0.5, 2 = 2 + 0 + 0x5, 3 = -2 + 0 + 0 + 5, 4 = -2^0 + 0 + 5, 5 = 2x0 + 0 + 5, 6 = 2^0 + 0 + 5, 7 = 2 + 0 + 0 + 5; I got stuck a this point!

Activity 6: Your Phone Number

Write down your phone number, with space between digits

Example: 5551253

Now, try to make as many different numbers as you can by

Putting + , - , , / signs between the digits.

0 =5 -5 +5 +1 + 2 -5 -3

1 =5 +5 +5 -1 + 2 -5 3

2 =5 +5 +5 +1 2 -5 3

3 =5 5 5 1 2 5 3

4 =5 5 5 1 2 5 3

5 =5 5 5 1 2 5 3

6 =5 5 5 1 2 5 3

7 =5 5 5 1 2 5 3

8 =5 5 5 1 2 5 3

Another Game for Two Players

Put some playing cards (or numbers) in a row

Players take turns removing a card from either end of the row

At the end, add up the numbers to see who wins

Game Tree

Player 1

Player 2

Player 1

Player 2

Player 1

Some Surprising Predictions

Answer these questions quickly.

If you pause, it wont work.

What is 1 + 1?

What is 2 + 2?

What is 3 + 3?

What is 4 + 4?

What is 5 + 5?

What is 6 + 6?

What is 7 + 7?

What is 8 + 8?

What is 9 + 9?

What is the first vegetable that comes to your mind?

What is 2 + 2?

What is 4 + 4?

What is 8 + 8?

What is 16 + 16?

Quickly, pick a number between 12 and 5

No one knows why these guesses work for most people.

Next Lesson

Thursday, May 19, 2005

What is special about 40? (Hint: Forty)

The only number with letters

appearing in alphabetical order

What is special about 6? (Hint: Divisible by 1, 2, 3)

The smallest

perfect number

What is special about 38? (Hint: XXXVIII)

The last Roman numeral

in alphabetical order

Math has many uses in geography. This lesson focuses on the relationship of math to making and using maps.

Orange kangaroo from Denmark

Orange kangaroo from Denmark

This puzzle becomes more or less difficult, depending on your birth year. It is pretty simple for most years. However, for someone born in 2005, it is hard: 0 = 2x0 + 0x5, 1 = 2^0 + 0x5 = 2.0x0.5, 2 = 2 + 0 + 0x5, 3 = -2 + 0 + 0 + 5, 4 = -2^0 + 0 + 5, 5 = 2x0 + 0 + 5, 6 = 2^0 + 0 + 5, 7 = 2 + 0 + 0 + 5; I got stuck a this point!