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NUMBER SENSE AT A FLIP

This is a new powerpoint. If you find any errors please let me know at kenneth.lee2@fortbendisd.com. NUMBER SENSE AT A FLIP. NUMBER SENSE AT A FLIP. Number Sense.

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NUMBER SENSE AT A FLIP

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  1. This is a new powerpoint. If you find any errors please let me know at kenneth.lee2@fortbendisd.com

  2. NUMBER SENSE AT A FLIP

  3. NUMBER SENSE AT A FLIP

  4. Number Sense Number Sense is memorization and practice. The secret to getting good at number sense is to learn how to recognize and then do the rules accurately . Then learn how to do them quickly. Every practice should be under a time limit.

  5. The First Step The first step in learning number sense should be to memorize the PERFECT SQUARES from 12 = 1 to 402 = 1600 and the PERFECT CUBES from 13 = 1 to 253 = 15625. These squares and cubes should be learned in both directions. ie. 172 = 289 and the 289 is 17.

  6. The Rainbow Method Work Backwards 2x2 Foil (LIOF)23 x 12 Used when you forget a rule about 2x2 multiplication The last number is the units digit of the product of the unit’s digits Multiply the outside, multiply the inside Add the outside and the inside together plus any carry and write down the units digit Multiply the first digits together and add and carry. Write down the number 2(1) 2(2)+3(1) 3(2) 2 7 6 276

  7. 2x2 Foil (LIOF)23 x 12 The Rainbow Method Work Backwards Used when you forget a rule about 2x2 multiplication • 45 x 31= • 31 x 62= • 64 x 73= • 62 x 87= • 96 x74=

  8. Squaring Numbers Ending In 5752 First two digits = the ten’s digit times one more than the ten’s digit. Last two digits are always 25 7(7+1)25 =5625

  9. Squaring Numbers Ending In 5752 • 45 x 45= • 952= • 652= • 352= • 15 x 15=

  10. Consecutive Decades35 x 45 First two digits = the small ten’s digit times one more than the large ten’s digit. Last two digits are always 75 3(4+1)75 =1575

  11. Consecutive Decades35 x 45 • 45 x 55= • 65 x 55= • 25 x 35= • 95 x 85= • 85 x75=

  12. Ending in 5…Ten’s Digits Both Even45 x 85 First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Last two digits are always 25 4(8) + ½ (4+8)25 =3825

  13. Ending in 5…Ten’s Digits Both Even45 x 85 • 45 x 65= • 65 x 25= • 85 x 65= • 85 x 25= • 65 x65=

  14. Ending in 5…Ten’s Digits Both Odd35 x 75 First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Last two digits are always 25 3(7) + ½ (3+7)25 =2625

  15. Ending in 5…Ten’s Digits Both Odd35 x 75 • 35 x 75= • 55 x 15= • 15 x 95= • 95 x 55= • 35 x 95=

  16. Ending in 5…Ten’s Digits Odd&Even35 x 85 First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Always drop the remainder. Last two digits are always 75 3(8) + ½ (3+8)75 =2975

  17. Ending in 5…Ten’s Digits Odd&Even35 x 85 • 45 x 75= • 35 x 65= • 65 x 15= • 15 x 85= • 55 x 85=

  18. (1/8 rule) Multiplying By 12 ½ 32 x 12 ½ 32 Divide the non-12 ½ number by 8. Add two zeroes. 4+00 = 8 =400

  19. (1/8 rule) Multiplying By 12 ½ 32 x 12 ½ • 12 ½ x 48= • 12 ½ x 88 = • 888 x 12 ½ = • 12 ½ x 24 = • 12 ½ x 16=

  20. (1/6 rule) Multiplying By 16 2/3 42 x 16 2/3 42 Divide the non-16 2/3 number by 6. Add two zeroes. 7+00 = 6 =700

  21. (1/6 rule) Multiplying By 16 2/3 42 x 16 2/3 • 16 2/3 x 42 = • 16 2/3 x 66 = • 78 x 16 2/3 = • 16 2/3 x 48= • 16 2/3 x 120=

  22. (1/3 rule) Multiplying By 33 1/3 24 x 33 1/3 • Divide the non-33 1/3 number by 3. • Add two zeroes. 24 8+00 = 3 =800

  23. (1/3 rule) Multiplying By 33 1/3 24 x 33 1/3 • 33 1/3 x 45= • 33 1/3 x 66= • 33 1/3 x 123= • 33 1/3 x 48= • 243 x 33 1/3=

  24. (1/4 rule) Multiplying By 2532 x 25 32 Divide the non-25 number by 4. Add two zeroes. 8 +00 = 4 =800

  25. (1/4 rule) Multiplying By 2532 x 25 • 25 x 44= • 444 x 25= • 25 x 88= • 25 x 36= • 25 x 12=

  26. (1/2 rule) Multiplying By 5032 x 50 32 Divide the non-50 number by 2. Add two zeroes. 16 = +00 2 =1600

  27. (1/2 rule) Multiplying By 5032 x 50 • 50 x 44= • 50 x 126= • 50 x 424= • 50 x 78= • 50 x 14=

  28. (3/4 rule) Multiplying By 7532 x 75 Divide the non-75 number by 4. Multiply by 3. Add two zeroes. 32 = 8x3=24+00 4 =2400

  29. (3/4 rule) Multiplying By 7532 x 75 • 75 x 44= • 75 x 120= • 75 x 24= • 48 x 75= • 84 x 75=

  30. (3/8 rule) Multiplying By 37 1/237 1/2 x 24 =900 00 (3/8)24

  31. (5/8 rule) Multiplying By 62 1/262 1/2 x 56 =3500 00 (5/8)56

  32. (7/8 rule) Multiplying By 87 1/287 1/2 x 48 =4200 00 (7/8)48

  33. (5/6 rule) Multiplying By 83 1/383 1/3 x 36 =3000 00 (5/6)36

  34. (2/3 rule) Multiplying By 66 2/366 2/3 x 66 =4400 00 (2/3)66

  35. (1/8 rule) Multiplying By 12532 x 125 Divide the non-125 number by 8. Add three zeroes. 32 4+000 = 8 =4000

  36. (1/8 rule) Multiplying By 12532 x 125 • 125 x 48= • 125 x 88= • 125 x 408= • 125 x 24= • 125 x 160=

  37. Multiplying When Tens Digits Are Equal And The Unit Digits Add To 1032 x 38 First two digits are the tens digit times one more than the tens digit Last two digits are the product of the units digits. 3(3+1) 2(8) =1216

  38. Multiplying When Tens Digits Are Equal And The Unit Digits Add To 1032 x 38 • 34 x 36= • 73 x 77= • 28 x 22= • 47 x 43= • 83 x 87=

  39. Multiplying When Tens Digits Add To 10 And The Units Digits Are Equal67 x 47 First two digits are the product of the tens digit plus the units digit Last two digits are the product of the units digits. 6(4)+7 7(7) =3149

  40. Multiplying When Tens Digits Add To 10 And The Units Digits Are Equal67 x 47 • 45 x 65= • 38 x 78= • 51 x 51= • 93 x 13= • 24 x 84=

  41. Multiplying Two Numbers in the 90’s97 x 94 Find out how far each number is from 100 The 1st two numbers equal the sum of the differences subtracted from 100 The last two numbers equal the product of the differences 100-(3+6) 3(6) =9118

  42. Multiplying Two Numbers in the 90’s97 x 94 • 98 x 93= • 92 x 94= • 91 x 96= • 96 x 99= • 98 x 98=

  43. Multiplying Two Numbers Near 100109 x 106 First Number is always 1 The middle two numbers = the sum on the units digits The last two digits = the product of the units digits 1 9+6 9(6) = 11554

  44. Multiplying Two Numbers Near 100109 x 106 • 106 x109= • 103 x 105= • 108 x 101= • 107 x 106= • 108 x 109=

  45. Multiplying Two Numbers With 1st Numbers = And A 0 In The Middle402 x 405 The 1st two numbers = the product of the hundreds digits The middle two numbers = the sum of the units x the hundreds digit The last two digits = the product of the units digits 4(4) 4(2+5) 2(5) = 162810

  46. Multiplying Two Numbers With 1st Numbers = And A “0” In The Middle402 x 405 • 405 x 405= • 205 x 206= • 703 x 706= • 603 x 607= • 801 x 805=

  47. 10101 Rule Multiplying By 336718 x 3367 Divide the non-3367 # by 3 Multiply by 10101 18/3 = 6 x 10101= = 60606

  48. Multiplying By 336718 x 3367 10101 Rule • 3367 x 33= • 3367 x123= • 3367 x 66= • 3367 x 93= • 3367 x 24=

  49. 121 Pattern Multiplying A 2-Digit # By 1192 x 11 (ALWAYS WORK FROM RIGHT TO LEFT) Last digit is the units digit The middle digit is the sum of the tens and the units digits The first digit is the tens digit + any carry 9+1 9+2 2 = 1012

  50. Multiplying A 2-Digit # By 1192 x 11 121 Pattern (ALWAYS WORK FROM RIGHT TO LEFT) • 11 x 34= • 11 x 98= • 65 x 11= • 11 x 69= • 27 x 11=

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