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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.

Magazines

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Investigating Pascal's Triangle

Age 7 to 11
Challenge Level

Exploring numbers in sequences and patterns can prove to be a very useful way of engaging pupils in mathematics for a valuable length of time. It can teach pupils about perseverance and enable them to reinforce some mathematical ideas, skills and concepts at the same time.

Because there is so much in the first big table [showing lines 1 to 30 as digital roots], it may be necessary to present just a small part of it to younger pupils. Perhaps take 5 or 6 of them and go to 27 numbers in length. There are so many opportunities for spotting addition and subtraction, as well as different kinds of patterning. Older pupils will be able to look at the table as a whole and as well as what the younger pupils do they may be interested in the overall arrays of numbers, particularly the number 9!

The "starting points for further extensions" section can be a good tool to help to bring some newer skills into play when doing a maths investigation. Using a spreadsheet will obviously make some aspects clearer and easier as well as opening up even more possibilities. These explorations are also a good tool to use when helping the pupils discover more about the use of a spreadsheet.

I feel I MUST emphasise the question for more experienced pupils as to WHY certain patterns occur. Sometimes when exploring digital roots with the older pupils some answers to "WHY?" come from realising thet they are working in mod 9 and working in other mods will make some things easier to explore.