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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

The Number Crunching Machine

Age 7 to 11
Challenge Level

The Number Crunching Machine

Put a number at the top of the machine and collect a number at the bottom.

What do you get?

Which numbers get back to themselves?

perform operations as follows: add 5, multiply by 3, if even subtract 2 or if odd subtract 1, multiply by 5, divide by 10, if odd add 3 and halve result or if even halve then if that result is even halve again or add 2 if result is odd

Why do this problem?

This problem is an amusing and thought-provoking way of practising addition, subtraction, multiplication and division. The results are diverse enough to keep learners working for a considerable time and to encourage methodical working. This sheet might be helpful.

Key questions

What operation do you need to do next?
Would it be a good idea to jot down your calculations as you go?
What numbers have you put in so far?
Have you made a list of the numbers you have already done?
How many numbers have you found that come out unchanged?

Possible extension

Learners could make their own number-crunching machine and try it out on their friends.

Possible support

Suggest trying with different numbers below $50$. It may help to make a version going across the page with arrows or you could use this sheet.