Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat this for a number of your choice from the second row. You
should now have just one number left on the bottom row, circle it.
Find the total for the three numbers circled. Compare this total
with the number in the centre of the square. What do you find? Can
you explain why this happens?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Can you explain how this card trick works?
Choose any 4 whole numbers, for example (100, 2, 37, 59). Now
take the difference between consecutive numbers, always subtracting
the smaller from the larger, and ending with the difference between
the first and the last numbers. What happens when you repeat this
process over and over again? For example, continue the sequence of
(100, 2, 37, 59), (98, 35, 22, 41), (63, 13, 19, 57),
(50, 6, 38, 6) , ...
Investigate starting with different sets of 4 numbers.
What happens when you use 3 numbers, or 5, or 6, or 7 or 8