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Number Games444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444 5555 5555555 55555555555 55555555555 5555555 5555555 555555 5555555 555555 555555555555 55555555 55555A Lesson in the Math + Fun! Series 11111 1111111 111111111 1111 1111111 111111 111 111 11111111 11111111 11111111 1111111 1111 1111111111 11111111 1111112222222222222222222 222222 222222 222222 222222 2222222222222222222222222222222222 222222 222222 2223333 33333333 333333333 3333333333 3333333333 33333333333333333333333333333333333333333333 3333 333333 3333 333333 333 333333 333 333333 33 333333 33 333333 333Math has many uses in geography. This lesson focuses on the relationship of math to making and using maps.About This PresentationThis 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 ParhamiEditionReleasedRevisedRevisedFirstApr. 2005What Number Did You Choose?1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 102. 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 DenmarkHow Did the Game Work?1. Pick a number from this list: 1 2 3 4 5 6 7 8 9 102. 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 4Orange kangaroo from DenmarkMore Mind-Reading GamesThink 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 29List B: 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30List C: 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30List D: 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30List E: 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30ACEBDEActivity 1: Mind-Reading GameThink 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 19List B: 2 6 7 8 12 17 20List C: 3 4 6 9 13 14 18 19 20List D: 5 7 8 9 15 16 17 18 19 20List E: 10 11 12 13 14 15 16 17 18 19 20Play 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 GamesYour final result is 36, isnt it?Your final result shows the month and day of your birthExplain how this game works.Change the numbers to make your own game.Explain how this game works.Euclids Game for Two PlayersA referee writes two numbers on the boardThe two players take turns writing the difference of two numbers already on the board, provided the difference is a new numberThe player who cannot write a new number losesThe 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 winsActivity 3: The Game of NimWrite three numbers on three linesThe two players take turns reducing one of the numbers The player who makes the last move losesChallenge: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 PuzzleUse four 4s and any number of math symbols (such as +, -, , /, , . . .) to form as many different numbers as possible.3 = (4 + 4 + 4) / 44 = (4 + 4) / 4 + 45 = (4 4 + 4) / 42 = 4 / 4 + 4 / 4 or 4 (4 + 4) / 46 = (4 + 4 + 4) / 48 = 4 (4 / 4) + 47 = 4 + 4 4 / 4 or 44 / 4 49 = 44 / 4 4 or 4 / 4 + 4 410 = (4 + 4 / 4) 411 = 44 / (4 + 4)12 = 4 (4 4 / 4)13 = 44 / 4 + 414 = 4 (4 + 4) 415 = 44 / 4 + 416 = 4 4 + 4 4 or 4 4 4 / 417 = 4 4 + 4 / 418 = 4 (4 + 4) + 420 = 4 (4 + 4 / 4)22 = 4 4 + 4 + 425 = (4 + 4 / 4)424 = 4 (4 + 4 + 4)Activity 4: The Five 5s PuzzleUse 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)Examples24 = 19 = 21 = 23 = Activity 5: Birth Year PuzzleUse 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 NumberWrite down your phone number, with space between digits Example: 5551253Now, try to make as many different numbers as you can by Putting + , - , , / signs between the digits. 0 =5 -5 +5 +1 + 2 -5 -31 =5 +5 +5 -1 + 2 -5 32 =5 +5 +5 +1 2 -5 33 =5 5 5 1 2 5 34 =5 5 5 1 2 5 35 =5 5 5 1 2 5 36 =5 5 5 1 2 5 37 =5 5 5 1 2 5 38 =5 5 5 1 2 5 3Another Game for Two PlayersPut some playing cards (or numbers) in a rowPlayers take turns removing a card from either end of the rowAt the end, add up the numbers to see who winsGame TreePlayer 1Player 2Player 1Player 2Player 1Some Surprising PredictionsAnswer 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 5No one knows why these guesses work for most people.Next LessonThursday, May 19, 2005What is special about 40? (Hint: Forty)The only number with letters appearing in alphabetical orderWhat is special about 6? (Hint: Divisible by 1, 2, 3)The smallest perfect numberWhat is special about 38? (Hint: XXXVIII)The last Roman numeral in alphabetical orderMath has many uses in geography. This lesson focuses on the relationship of math to making and using maps.Orange kangaroo from DenmarkOrange kangaroo from DenmarkThis 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!