The 9 times table                        ...in a hurrydtcoulson@gmail.com
9    Begin with a space    shuttle countdown:
98    Begin with a space    shuttle countdown:
98    Begin with a space7   shuttle countdown:
98    Begin with a space7   shuttle countdown:6
98    Adding 9 is like7    adding 10 and     subtracting 1.65
98    Adding 9 is like7    adding 10 and     subtracting 1.654
98    Adding 9 is like7    adding 10 and     subtracting 1.6543
98    Adding 9 is like7    adding 10 and     subtracting 1.65432
98    Adding 9 is like7    adding 10 and     subtracting 1.654321
987   “Blast-Off!”6543210
9  8  7  6  5  4   Now do it again in          reverse.  3  2  19 0
9  8  7  6  5  4   Now do it again in          reverse.  3  28 19 0
9  8  7  6  5  4   Now do it again in          reverse.  37 28 19 0
9  8  7  6  5  4   Now do it again in          reverse.6 37 28 19 0
9  8  7  6  55 4   Now do it again in          reverse.6 37 28 19 0
9  8  7  64 55 4   Now do it again in          reverse.6 37 28 19 0
9  8  73 64 55 4   Now do it again in          reverse.6 37 28 19 0
9  82 73 64 55 4   Now do it again in          reverse.6 37 28 19 0
91 82 73 64 55 4   Now do it again in          reverse.6 37 28 19 0
91 82 73 64 55 46 37 28 1      Draw a line under a            zero.9 0
9   91 8   82 7   73 6   64 5   55 4   46 3   37 2   28 1   1   ... and start again.9 0   0
9   991 8    82 7    73 6    64 5    55 4    46 3    37 2    28 1    1   ... and start again.9 0    0
9    991 8   1 082 7      73 6      64 5      55 4      46 3      37 2      28 1      1   ... and start again.9 0      0
9    991 8   1 082 7   1 1 73 6      64 5      55 4      46 3      37 2      28 1       1   ... and start again.9 0      0
9    991 8   1 082 7   1 1 73 6   1 264 5      55 4      46 3      37 2      28 1       1   ... and start again.9 0      0
9    991 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4      46 3       37 2      28 1       1   ... and start again.9 0      0
9    991 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4   1 446 3       37 2      28 1       1   ... and start again.9 0      0
9    991 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4   1 446 3   1 5 37 2      28 1       1   ... and start again.9 0      0
9    991 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4   1 446 3   1 5 37 2   1 6 28 1       1   ... and start again.9 0    ...
9    991 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4   1 446 3   1 5 37 2   1 6 28 1   1 7 1   ... and start again.9 0    ...
9    991 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4   1 446 3   1 5 37 2   1 6 28 1   1 7 1   ... and start again.9 0   1...
9    991 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4   1 44    Draw another line.6 3   1 5 37 2   1 6 28 1   1 7 19 0   1 ...
9    99            1 891 8   1 082 7   1 1 73 6   1 264 5   1 3 55 4   1 44              You can go on like               ...
9    99            1 891 8   1 08           1 982 7   1 1 73 6   1 264 5   1 3 55 4   1 44              You can go on like...
9    99            1 891 8   1 08           1 982 7   1 1 7         2 0 73 6   1 264 5   1 3 55 4   1 44              You ...
9    99            1 891 8   1 08           1 982 7   1 1 7         2 0 73 6   1 26           2 164 5   1 3 55 4   1 44   ...
9    99     1 891 8   1 08    1 982 7   1 1 7   2 0 73 6   1 26    2 164 5   1 3 5   2 2 55 4   1 446 3   1 5 37 2   1 6 2...
9    99     1 891 8   1 08    1 982 7   1 1 7   2 0 73 6   1 26    2 164 5   1 3 5   2 2 55 4   1 44    2 346 3   1 5 37 2...
9    99     1 891 8   1 08    1 982 7   1 1 7   2 0 73 6   1 26    2 164 5   1 3 5   2 2 55 4   1 44    2 346 3   1 5 3   ...
9    99     1 891 8   1 08    1 982 7   1 1 7   2 0 73 6   1 26    2 164 5   1 3 5   2 2 55 4   1 44    2 346 3   1 5 3   ...
9    99     1 891 8   1 08    1 982 7   1 1 7   2 0 73 6   1 26    2 164 5   1 3 5   2 2 55 4   1 44    2 346 3   1 5 3   ...
9    99     1 891 8   1 08    1 982 7   1 1 7   2 0 73 6   1 26    2 164 5   1 3 5   2 2 55 4   1 44    2 346 3   1 5 3   ...
9    99     1 891 8   1 08    1 982 7   1 1 7   2 0 73 6   1 26    2 164 5   1 3 5   2 2 55 4   1 44    2 346 3   1 5 3   ...
9             99           1 891 8            1 08          1 98      Take a look at this:2 7            1 1 7         2 0...
9            99          1 891 8           1 08         1 98      The digits in each2 7   number 1add to 9.               ...
9               99            1 891 8             1 08            1 98      It‟s true for all these2 7          numbers.  ...
That can be used as              a shortcut.  4 5= 5 x 9
If you know the          first digit, then you            know the second            digit too because          they add t...
The first digit is            always one less          than the multiplier.  4 5                7 2= 5 x 9           = 8 x 9
Check it out: what‟s           the next number?  4 5               7 2= 5 x 9           = 8 x 9        7 x 9
Check it out: what‟s           the next number?  4 5               7 2          = 6 ?= 5 x 9           = 8 x 9        7 x 9
Check it out: what‟s           the next number?  4 5               7 2          = 6 3= 5 x 9           = 8 x 9        7 x 9
9 x 9
9 x 9= 8
9 x 9= 8 1
9 x 9   4 x 9= 8 1
9 x 9    4 x 9= 8 1   = 3
9 x 9    4 x 9= 8 1   = 3 6
9 x 9    4 x 9   7 x 9= 8 1   = 3 6
9 x 9    4 x 9   7 x 9= 8 1   = 3 6    = 6
9 x 9    4 x 9   7 x 9= 8 1   = 3 6    = 6 3
What about bigger   numbers?
19 x9        What about bigger           numbers?15 x917 x9
19 x9 = 171                 Number in the                teens start 2 less15 x9 = 135   than the multiplier.17 x9 = 153
19 x9 = 171            27 x9 = 243  Numbers in the„third decade‟ start   3 less than the     multiplier.17 x9 = 153
19 x9 = 171            27 x9 = 243   Numbers in the„third decade‟ start1 5 3x less than 5        9 = 1 3 the    26 x9 = 23...
19 x9 = 171            27 x9 = 243   Numbers in the„third decade‟ start1 5 3x less than 5        9 = 1 3 the    26 x9 = 23...
34 x9        What about number          in the „fourth            decade‟?
34 x9 = 30             Yup. Subtract 4...
34 x9 = 306              ...and balance with              a number that adds                      to 9.
34 x9 = 306 47 x9This number‟s inthe fifth decade
34 x9 = 306 47 x9 = 42This number‟s inthe fifth decade so subtract 5.
34 x9 = 30647 x9 = 423Then add to 9
34 x9 = 30647 x9 = 423              Try this one on68 x9           your own.
34 x9 = 30647 x9 = 42368 x9 = 61
34 x9 = 30647 x9 = 42368 x9 = 612
34 x9 = 306   32 x9                      Some numbers are47 x9 = 423                      easier than others.68 x9 = 612
34 x9 = 306   32 x9 = 28                    Some numbers are47 x9 = 423                    easier than others.68 x9 = 612
34 x9 = 306   32 x9 = 288                     ...and sometimes47 x9 = 423         adding to 9 means                    add...
34 x9 = 306   32 x9 = 28847 x9 = 423   31 x968 x9 = 612      Watch out for               numbers like this:
34 x9 = 306   32 x9 = 28847 x9 = 423   31 x9 = 2768 x9 = 612    The first 2 digits               already add to 9.
34 x9 = 306   32 x9 = 28847 x9 = 423   31 x9 = 27068 x9 = 612    ...so you might              want to add a zero.
34 x9 = 306   32 x9 = 28847 x9 = 423   31 x9 = 27968 x9 = 612    ...but you should              add a 9 to make 18.
34 x9 = 306        32 x9 = 288 47 x9 = 423        31 x9 = 279The process 6 1 2 6 8 x 9 = always   62 x9       works.
34 x9 = 306        32 x9 = 288 47 x9 = 423        31 x9 = 279The process 6 1 2 6 8 x 9 = always   62 x9 = 55       works.
34 x9 = 306        32 x9 = 288 47 x9 = 423        31 x9 = 279The process 6 1 2 6 8 x 9 = always   62 x9 = 558       works.
dtcoulson@gmail.com
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9 times table in a hurry (pdf)

  1. 1. The 9 times table ...in a hurrydtcoulson@gmail.com
  2. 2. 9 Begin with a space shuttle countdown:
  3. 3. 98 Begin with a space shuttle countdown:
  4. 4. 98 Begin with a space7 shuttle countdown:
  5. 5. 98 Begin with a space7 shuttle countdown:6
  6. 6. 98 Adding 9 is like7 adding 10 and subtracting 1.65
  7. 7. 98 Adding 9 is like7 adding 10 and subtracting 1.654
  8. 8. 98 Adding 9 is like7 adding 10 and subtracting 1.6543
  9. 9. 98 Adding 9 is like7 adding 10 and subtracting 1.65432
  10. 10. 98 Adding 9 is like7 adding 10 and subtracting 1.654321
  11. 11. 987 “Blast-Off!”6543210
  12. 12. 9 8 7 6 5 4 Now do it again in reverse. 3 2 19 0
  13. 13. 9 8 7 6 5 4 Now do it again in reverse. 3 28 19 0
  14. 14. 9 8 7 6 5 4 Now do it again in reverse. 37 28 19 0
  15. 15. 9 8 7 6 5 4 Now do it again in reverse.6 37 28 19 0
  16. 16. 9 8 7 6 55 4 Now do it again in reverse.6 37 28 19 0
  17. 17. 9 8 7 64 55 4 Now do it again in reverse.6 37 28 19 0
  18. 18. 9 8 73 64 55 4 Now do it again in reverse.6 37 28 19 0
  19. 19. 9 82 73 64 55 4 Now do it again in reverse.6 37 28 19 0
  20. 20. 91 82 73 64 55 4 Now do it again in reverse.6 37 28 19 0
  21. 21. 91 82 73 64 55 46 37 28 1 Draw a line under a zero.9 0
  22. 22. 9 91 8 82 7 73 6 64 5 55 4 46 3 37 2 28 1 1 ... and start again.9 0 0
  23. 23. 9 991 8 82 7 73 6 64 5 55 4 46 3 37 2 28 1 1 ... and start again.9 0 0
  24. 24. 9 991 8 1 082 7 73 6 64 5 55 4 46 3 37 2 28 1 1 ... and start again.9 0 0
  25. 25. 9 991 8 1 082 7 1 1 73 6 64 5 55 4 46 3 37 2 28 1 1 ... and start again.9 0 0
  26. 26. 9 991 8 1 082 7 1 1 73 6 1 264 5 55 4 46 3 37 2 28 1 1 ... and start again.9 0 0
  27. 27. 9 991 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 46 3 37 2 28 1 1 ... and start again.9 0 0
  28. 28. 9 991 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 1 446 3 37 2 28 1 1 ... and start again.9 0 0
  29. 29. 9 991 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 1 446 3 1 5 37 2 28 1 1 ... and start again.9 0 0
  30. 30. 9 991 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 1 446 3 1 5 37 2 1 6 28 1 1 ... and start again.9 0 0
  31. 31. 9 991 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 1 446 3 1 5 37 2 1 6 28 1 1 7 1 ... and start again.9 0 0
  32. 32. 9 991 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 1 446 3 1 5 37 2 1 6 28 1 1 7 1 ... and start again.9 0 1 8 0
  33. 33. 9 991 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 1 44 Draw another line.6 3 1 5 37 2 1 6 28 1 1 7 19 0 1 8 0
  34. 34. 9 99 1 891 8 1 082 7 1 1 73 6 1 264 5 1 3 55 4 1 44 You can go on like this forever.6 3 1 5 37 2 1 6 28 1 1 7 19 0 1 8 0
  35. 35. 9 99 1 891 8 1 08 1 982 7 1 1 73 6 1 264 5 1 3 55 4 1 44 You can go on like this forever.6 3 1 5 37 2 1 6 28 1 1 7 19 0 1 8 0
  36. 36. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 264 5 1 3 55 4 1 44 You can go on like this forever.6 3 1 5 37 2 1 6 28 1 1 7 19 0 1 8 0
  37. 37. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 55 4 1 44 You can go on like this forever.6 3 1 5 37 2 1 6 28 1 1 7 19 0 1 8 0
  38. 38. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 446 3 1 5 37 2 1 6 28 1 1 7 19 0 1 8 0
  39. 39. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 37 2 1 6 28 1 1 7 19 0 1 8 0
  40. 40. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 28 1 1 7 19 0 1 8 0
  41. 41. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 2 2 5 28 1 1 7 19 0 1 8 0
  42. 42. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 2 2 5 28 1 1 7 1 2 6 19 0 1 8 0
  43. 43. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 2 2 5 28 1 1 7 1 2 6 19 0 1 8 0 2 7 0
  44. 44. 9 99 1 891 8 1 08 1 982 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 2 2 5 28 1 1 7 1 2 6 19 0 1 8 0 2 7 0
  45. 45. 9 99 1 891 8 1 08 1 98 Take a look at this:2 7 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 2 2 5 28 1 1 7 1 2 6 19 0 1 8 0 2 7 0
  46. 46. 9 99 1 891 8 1 08 1 98 The digits in each2 7 number 1add to 9. 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 2 2 5 28 1 1 7 1 2 6 19 0 1 8 0 2 7 0
  47. 47. 9 99 1 891 8 1 08 1 98 It‟s true for all these2 7 numbers. 1 1 7 2 0 73 6 1 26 2 164 5 1 3 5 2 2 55 4 1 44 2 346 3 1 5 3 2 4 37 2 1 6 2 2 5 28 1 1 7 1 2 6 19 0 1 8 0 2 7 0
  48. 48. That can be used as a shortcut. 4 5= 5 x 9
  49. 49. If you know the first digit, then you know the second digit too because they add to make 9. 4 5= 5 x 9
  50. 50. The first digit is always one less than the multiplier. 4 5 7 2= 5 x 9 = 8 x 9
  51. 51. Check it out: what‟s the next number? 4 5 7 2= 5 x 9 = 8 x 9 7 x 9
  52. 52. Check it out: what‟s the next number? 4 5 7 2 = 6 ?= 5 x 9 = 8 x 9 7 x 9
  53. 53. Check it out: what‟s the next number? 4 5 7 2 = 6 3= 5 x 9 = 8 x 9 7 x 9
  54. 54. 9 x 9
  55. 55. 9 x 9= 8
  56. 56. 9 x 9= 8 1
  57. 57. 9 x 9 4 x 9= 8 1
  58. 58. 9 x 9 4 x 9= 8 1 = 3
  59. 59. 9 x 9 4 x 9= 8 1 = 3 6
  60. 60. 9 x 9 4 x 9 7 x 9= 8 1 = 3 6
  61. 61. 9 x 9 4 x 9 7 x 9= 8 1 = 3 6 = 6
  62. 62. 9 x 9 4 x 9 7 x 9= 8 1 = 3 6 = 6 3
  63. 63. What about bigger numbers?
  64. 64. 19 x9 What about bigger numbers?15 x917 x9
  65. 65. 19 x9 = 171 Number in the teens start 2 less15 x9 = 135 than the multiplier.17 x9 = 153
  66. 66. 19 x9 = 171 27 x9 = 243 Numbers in the„third decade‟ start 3 less than the multiplier.17 x9 = 153
  67. 67. 19 x9 = 171 27 x9 = 243 Numbers in the„third decade‟ start1 5 3x less than 5 9 = 1 3 the 26 x9 = 234 multiplier.17 x9 = 153
  68. 68. 19 x9 = 171 27 x9 = 243 Numbers in the„third decade‟ start1 5 3x less than 5 9 = 1 3 the 26 x9 = 234 multiplier.17 x9 = 153 25 x9 = 225
  69. 69. 34 x9 What about number in the „fourth decade‟?
  70. 70. 34 x9 = 30 Yup. Subtract 4...
  71. 71. 34 x9 = 306 ...and balance with a number that adds to 9.
  72. 72. 34 x9 = 306 47 x9This number‟s inthe fifth decade
  73. 73. 34 x9 = 306 47 x9 = 42This number‟s inthe fifth decade so subtract 5.
  74. 74. 34 x9 = 30647 x9 = 423Then add to 9
  75. 75. 34 x9 = 30647 x9 = 423 Try this one on68 x9 your own.
  76. 76. 34 x9 = 30647 x9 = 42368 x9 = 61
  77. 77. 34 x9 = 30647 x9 = 42368 x9 = 612
  78. 78. 34 x9 = 306 32 x9 Some numbers are47 x9 = 423 easier than others.68 x9 = 612
  79. 79. 34 x9 = 306 32 x9 = 28 Some numbers are47 x9 = 423 easier than others.68 x9 = 612
  80. 80. 34 x9 = 306 32 x9 = 288 ...and sometimes47 x9 = 423 adding to 9 means adding to 18 first.68 x9 = 612
  81. 81. 34 x9 = 306 32 x9 = 28847 x9 = 423 31 x968 x9 = 612 Watch out for numbers like this:
  82. 82. 34 x9 = 306 32 x9 = 28847 x9 = 423 31 x9 = 2768 x9 = 612 The first 2 digits already add to 9.
  83. 83. 34 x9 = 306 32 x9 = 28847 x9 = 423 31 x9 = 27068 x9 = 612 ...so you might want to add a zero.
  84. 84. 34 x9 = 306 32 x9 = 28847 x9 = 423 31 x9 = 27968 x9 = 612 ...but you should add a 9 to make 18.
  85. 85. 34 x9 = 306 32 x9 = 288 47 x9 = 423 31 x9 = 279The process 6 1 2 6 8 x 9 = always 62 x9 works.
  86. 86. 34 x9 = 306 32 x9 = 288 47 x9 = 423 31 x9 = 279The process 6 1 2 6 8 x 9 = always 62 x9 = 55 works.
  87. 87. 34 x9 = 306 32 x9 = 288 47 x9 = 423 31 x9 = 279The process 6 1 2 6 8 x 9 = always 62 x9 = 558 works.
  88. 88. dtcoulson@gmail.com

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