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NUMBER TRICKS

NUMBER TRICKS. Number Trick #1. Choose a number Add 3 Multiply by 2 Add 8 Divide by 2 Subtract the original number What is your result Show why this trick works using algebra. Number Trick #1. Choose a number—x Add 3—x + 3 Multiply by 2—2(x+3) = 2x + 6 Add 8—2x + 14

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NUMBER TRICKS

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  1. NUMBER TRICKS

  2. Number Trick #1 • Choose a number • Add 3 • Multiply by 2 • Add 8 • Divide by 2 • Subtract the original number • What is your result • Show why this trick works using algebra.

  3. Number Trick #1 • Choose a number—x • Add 3—x + 3 • Multiply by 2—2(x+3) = 2x + 6 • Add 8—2x + 14 • Divide by 2—x + 7 • Subtract the original number—x • What is your result—7

  4. Multiple Representations

  5. Multiple Representation • Can also be done by drawing pictures • A number = • Add 3 =

  6. Multiple Representation • Can also be done by drawing pictures • A number = • Add 3 = • Multiple by 2 • Add 8 • Divide by 2 • Subtract number

  7. Questions • Does the initial number selected have to be a single digit? • No, any number will work with this trick. • What happens at the last step if instead of subtracting the original number you subtract 7? • The answer will always be the original number selected instead of 7. • Does the order of the commands make a difference

  8. Students are problem solving. • Students enhance their fluency in mental calculations • Problems are personalized which provides motivation to find a solution. • Students formulate and reformulate generalized solution patterns from specific cases. • Students manipulate symbolic expressions.

  9. Considerations • Begin by doing the trick. • Calculations may be done mentally or with calculator. • Have students pick another number and try the trick. • Have the students do the trick with parents or someone in a different class. • Challenge the students to find out why the trick works.

  10. Notes • Once the trick is demonstrated have the students try to figure out why it works. • Introduce the visual and algebraic columns at an appropriate time. • Provide students visual or algebraic and have them create other columns • Multiplying 2n + 4 by 3 = 3(2n + 4) can be used to show distributive property. • Have students create their own number tricks • A blank table and other tricks is provided with the word document.

  11. Phone number • Enter the first 3 digits of your phone number, not the area code. • Multiply by 80 • Add 1 • Multiply by 250 • Add the last 4 digits of your phone number • Add the last 4 digits of your phone number again • Subtract 250 • Divide by 2 • What is the result?

  12. Why does this work? • Multiplying by 80 and 250 is the same as multiplying by 10,000. This creates a number which is the first three numbers of your phone followed by four zeros. Adding 1 and them multiplying by 250 is canceled by subtracting 250 in a latter step. The last 4 digits of the number is added twice so that it can be divided by 2.

  13. Birthday Trick • Start with the number of your birth month • Add 2 • Multiply by 200 • Subtract 400 • Add the number for the day of your birth • Add the day again • Multiply by 5000 • Add the 4 digit year of your birth • What is your result?

  14. Why does this work?

  15. Write down a two-digit number • Add 20 • Multiply by 4 • Add 200 • divide by 4 • subtract your number • What do you get?

  16. Why it works • N • N + 20 • 4(N + 20) • 4N +80 + 200 • (4N + 280)/4 • N + 70 – N • 70 • Pick a number • Add 20 • Multiply by 4 • Add 200 • divide by 4 • subtract your number • What do you get.

  17. Eating Chocolate • How many times a week do you want to eat chocolate? (Pick more than one but less than 10 times). • Multiply that number by 2. • Add 5. • Multiply that result by 50. • If your birthday has occurred this year, add 1760 to that result. If your birthday is still to come this year, add 1759. • Subtract the year (all four digits) in which you were born. • The result will be a three-digit number. The first digit will be the number of times a week that you want to eat chocolate, and the last two digits will be your age.

  18. Extension • Extension: Suppose you wanted chocolate 10 or more times a week, or no chocolate at all. Could you still make the puzzle work? • What if you are over 100 years old? • Will the puzzle need to be adjusted when the current year becomes 2012?

  19. Two Sums • Mathematics Teaching in the Middle School, September 2010, p 68-71. • Challenge: Place a 3X3 grid anywhere on a 100’s board (1-10 on first row, 11-20 on second, etc). • Find the sums of the two diagonals of thee 3X3 grid. • How to the two sums compare? Will this comparison always hold true? Why?

  20. Solution • The sum of the diagonals will always be equal. • The sum will always be 3 times the middle number. • Also the number in a cross (from the middle above and below, from the middle left and right) will also be equal and 3 times the middle number.

  21. The sum of the diagonals is (N-11) + N + (N+11) = 3N (N-9) + N + (N+9) = 3N The sum of the cross (the middle rows and middle column) (N-10) + N (N +10) = 3N (N-1) + N + (N +1) = 3N

  22. Challenges & Questions • Begin with N being the number in the top left corner and fill in the rest of the numbers) • Will this work with a 4X4 grid or a 5X5 grid? • What if the 100’s board is an 8X8 grid instead of a 10X10 grid?

  23. Number Card Trick • Take a deck of cards and take out the face cards leaving the numbers Ace (1) through 10. • Pick any card • Add the next number • Multiply by 5 • Add 6-clubs, 7 diamond, 8-heart, 9 spade

  24. To find the card: • Take the answer subtract 5, the first digit is the card and the second is the suit • Example • Card is 8 of diamonds, add 8+9 = 17, multiply by 5 = 85 add 7 for diamonds get 92 • Person subtracts 5 (92-5) = 87, card was 8 of (7)diamonds

  25. Why • n Pick any card • n + (n+1) Add the next number • (n + (n+1))*5 = 10n + 5 Multiply by 5 • Add 6-clubs, 7 diamond, 8-heart, 9 spade • Solution • Subtract 5

  26. Questions • Does it work for 10? • Would it work for higher numbers? • Why is the add 5 necessary? • Could the numbers for suits be different?

  27. Your Favorite Person • Pick your favorite number between 1-9 • Multiply by 3 then • Add 3 • Then again Multiply by 3 (I'll wait while you get the calculator....) • You'll get a 2 or 3 digit number.... • Add the digits together

  28. Use Your Number to Find Your Favorite Person • Albert Einstein • Oprah Winfrey • Snoopy • Bill Clinton • Bill Gates • George W. Bush • Barack Obama • Babe Ruth • Lenny VerMaas • 10. John Fitzgerald Kennedy

  29. Mathematical Private Eye • Think of your favorite number • Multiply it by 3 • Add your favorite number and 1 to it. • Add 11 to it • Divide by 4 • Add 2 to your answer • What is your answer? • To get the favorite number subtract 5

  30. Mathematical Private Eye • I know your Favorite Number! • (Alternate) I know your favorite number! • I Know What Month You Were Born! • I Know Your Mother’s Age! • I Know Your Favorite Day of the Week. • I Know What Numbers You Are Thinking Of! Three at a Time!

  31. Solving Simultaneous Equations • I know Your Birthdate

  32. Web Examples • Magic Goffer • http://www.learnenglish.org.uk/games/magic-gopher-central.swf

  33. Visa Number: 1234 5678 9012 3456 ADD 3 NUMBERS: a. 2 x Row 1 Sum b. Row 2 Sum c. # of numbers in Row 1 great than or equal to 5 Look at the Units Digit of this sum.

  34. Visa Number: 1234 5678 9012 3456 ADD 3 NUMBERS: a. 2 x Row 1 Sum b. Row 2 Sum c. # of numbers in Row 1 great than or equal to 5 Look at the Units Digit of this sum. Is it 0?

  35. Write down 4-digit number

  36. Write down 4-digit number • Scramble the digits to form a new 4-digit number

  37. Write down 4-digit number • Scramble the digits to form a new 4-digit number • Subtract smaller # from larger #

  38. Write down 4-digit number • Scramble the digits to form a new 4-digit number • Subtract smaller # from larger # • Draw circle around 1 digit of this difference (but not a 0)

  39. Write down 4-digit number • Scramble the digits to form a new 4-digit number • Subtract smaller # from larger # • Draw circle around 1 digit of this difference (but not a 0) • Jumble remaining digits to form new number.

  40. Write down 4-digit number • Scramble the digits to form a new 4-digit number • Subtract smaller # from larger # • Draw circle around 1 digit of this difference (but not a 0) • Jumble remaining digits to form new number. • Share this number.

  41. Write down 4-digit number • Scramble the digits to form a new 4-digit number • Subtract smaller # from larger # • Draw circle around 1 digit of this difference (but not a 0) • Jumble remaining digits to form new number. • Share this number. • I can tell you the digit you circled.

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