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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?

Practice Run

Age 7 to 11
Challenge Level

Why do this problem?

This problem could be used when time, length and distance or doubling and halving are being introduced or discussed. It requires careful thinking to work out how the problem should be tackled so that doing it could lead to a useful classroom discussion.

Possible approach

This is a problem which is all too easily misread. It would therefore be a good idea for the whole group to read it together and then put it into their own words. These can then be compared and a discussion started on the best place to begin doing the problem itself.

After this learners could work on the problem in pairs so that they are able to talk through their ideas with a partner. It would be a good idea if squared paper were provided to encourage learners to make a table of their findings.

At the end of the lesson the group could be brought together again to discuss their findings and how they reached them.

Key questions

What exact measurement do we know from the question?
How far had Chandrika to go when she fell?
How might you use a table to organise the information?

Possible extension

Learners could change the problem to ask what the figures would be if the race was exactly $2$ kilometres long.

Possible support

For those who are struggling, you could suggest starting at the end of the problem and working backwards.