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?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
Choose any three by three square of dates on a calendar
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
Repeat this for a number of your choice from the second row.
Here is an example:
You should now have just one number left on the bottom row,
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?
Will the result be the same if you choose different numbers to
Do you think the results would be different if you used a four
by four square and end up with four circled numbers? Why?
Use your calendar to find a four by four square to test your
Choose another three by three square of numbers from the
Add the numbers in the four corners.
Add the numbers in each row, then each column and diagonal that
passes through the centre number. Can you discover why you get the
results that you do?
Find the total for all of the numbers that are in the right and
the left columns. Can you explain this answer?
What do you think will happen if you choose another set of nine
numbers? Try it and see if your prediction is correct.
Choose other sized squares of numbers to try these
Predict what the results might be.
What previous information will help you predict the results?
What would happen if you chose a rectangle on the calendar
rather than a square?