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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?

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Reverse to Order

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?

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Happy Numbers

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.

Card Trick 2

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here are the instructions to a second card trick. This is also mathematical. Try and explain how it works.

Volunteer selects any three cards and places them face down on the table.

Volunteer then shuffles the pack of cards and returns them to me.

You are going to find a card in this pack which depends on the three cards you have already chosen. I am going to try and predict what card that will be. I am not going to alter the order of the cards, I am just going to remove a card which points to the card you will find.


Check the fourth from bottom card and remove the card of the same numerical value and colour and place it face down on the table.

Volunteer turns over each of the three cards in turn and counts onto 15 for each one. Remove the counted out cards each time. (Jack =11 Queen =12 King =13)

The numbers of the three cards are added, and that number of cards is counted out, the last one being kept.

Turn over that card and the predicting card.