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 = 

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 = 
 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 