### Calendar Capers

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!

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

# Top-heavy Pyramids

##### Stage: 3 Challenge Level:

Order the numbers in a variety of ways. Where a number is placed does make a difference.

Look at the first example given. How many times is the 4 used in an addition calculation in the pyramid? What about the 5? And the 7?
Try this with the second example too.
Would it help to make up some larger pyramids and then to repeat this process?
Do you notice a pattern? Could this help?