What is a spiral? Can you draw a spiral on a squared grid?
Start by finding some digit-sums:
24 > 2+4 = 6
47 > 4+7 = 11 > 1+1 = 2
149 > 1+4+9 = 14 > 1+4 = 5
So the digit sum of 149 is 5
Now create a digit-sum spiral for multiples of 3:
- Write out multiples of 3 in a column ( up to 15 x 3?)Write the digit-sum alongside each number. (3,6,9,3,6,9,3,6,9,3......)
- Discuss any patterns that can be seen in the sequence of digit sums.
- Start to draw the spiral (0.25 cm squared paper is recommended) :
- Starting point is at the top of the page, in the centre.
- First line : RIGHT 3 squares
- Turn clockwise 90 degrees, then DOWN 6 squares
- Turn clockwise 90 degrees, then LEFT 9 squares.....
- Turn clockwise 90 degrees, then UP 3 squares...
- Continue turning and using the digit sums until the starting point is reached: the 'spiral' is now complete!
It is perfectly OK to draw over part of a line that has already been drawn:
Digit-sum spiral for multiples of 3
Now try using multiples of other numbers:
1,2,6,7,8,9 are straightforward; 4 and 5 are slightly trickier.
You will need to experiment to find a good starting point so that the spiral doesn't go off the paper.
Do any numbers have similar digit-sum spirals?
What about multiples of 10? 11? 12?.....Can you make any generalized statements?
See some of the spirals here.