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
  

 

 

Dr. Robert Sweetland's notes
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