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?
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
This problem offers students the opportunity to consider the underlying structure behind multiples and remainders, as well as leading to some very nice generalisations and justifications.
There are a few related problems that students could work on next:
Take Three from Five
Shifting Times Tables
Charlie's Delightful Machine
A Little Light Thinking
Where Can We Visit?
Begin by asking students to explore what happens when they add numbers chosen from a set of bags containing 2s, 4s, 6s and 8s.
They could then consider what happens when they add numbers chosen from a set of bags containing 1s, 11s, 21s and 31s.
Can they explain their findings?