# Exploration of function with a variable factor and constant factor

Use a electronic device to explore this function:

 Row number Variable factor Constant factor Product Notes 1 3 * 27 = 2 6 * 27 = 3 9 * 27 = 4 12 * 27 = 5 15 * 27 = 6 18 * 27 = 7 21 * 27 = 8 24 * 27 = 9 27 * 27 = 10 30 * 27 = 11 33 * 27 = 12 36 * 27 =

1. Find the products of the factors and enter them in the column.
2. What patterns can be found?
3. Write some notes about what was found.
4. Did you include a pattern for the ones' place?
5. Did you include a pattern for the ten's place?
6. Did you include a pattern for all the places?
7. Did you think to add the digits and see if that made a pattern?
8. Did you think to add the digits and add the digits again until there was only one digit?
9. Did you try to rearrange the digits for each product and see if that made a difference as to what it was divisible by?
10. 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