Exploration of function with a variable factor and constant factor
Use a electronic device to explore this function:
Row number |
Variable |
Constant factor |
Product |
Notes |
1 | 3 * | 27 = |
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2 | 6 * | 27 = |
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3 | 9 * | 27 = |
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4 | 12 * | 27 = |
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5 | 15 * | 27 = |
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6 | 18 * | 27 = |
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7 | 21 * | 27 = |
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8 | 24 * | 27 = |
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9 | 27 * | 27 = |
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10 | 30 * | 27 = |
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11 | 33 * | 27 = |
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12 | 36 * | 27 = |
- Find the products of the factors and enter them in the column.
- What patterns can be found?
- Write some notes about what was found.
- Did you include a pattern for the ones' place?
- Did you include a pattern for the ten's place?
- Did you include a pattern for all the places?
- Did you think to add the digits and see if that made a pattern?
- Did you think to add the digits and add the digits again until there was only one digit?
- Did you try to rearrange the digits for each product and see if that made a difference as to what it was divisible by?
- Research how this is related to casting out nines?
Hints
Row number |
Variable factor |
Constant
factor |
Product |
Notes |
1 | 3 * | 27 = |
81 |
|
2 | 6 * | 27 = |
162 |
|
3 | 9 * | 27 = |
243 |
|
4 | 12 * | 27 = |
324 |
|
5 | 15 * | 27 = |
405 |
|
6 | 18 * | 27 = |
486 |
|
7 | 21 * | 27 = |
567 |
|
8 | 24 * | 27 = |
648 |
|
9 | 27 * | 27 = |
729 |
|
10 | 30 * | 27 = |
810 |
|
11 | 33 * | 27 = |
891 |
|
12 | 36 * | 27 = |
972 |