### The Great Tiling Count

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

### Transformations Tables

These grids are filled according to some rules - can you complete them?

### Smaller and Smaller

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

# Investigating Pascal's Triangle

##### Age 7 to 11Challenge 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.