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Succeed with maths: part 2

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# 1 Exploring patterns and processes

Patterns occur in many different ways in everyday life. They include how petals are arranged on a flower and the repeating notes of bird song. These patterns give us a powerful tool in understanding the world and universe. Many centuries ago ancient civilisations recognised the yearly pattern of changing sunset and sunrise and used this to build places of worship, such as Stonehenge in the UK. Today, patterns in the progress of the sun and moon are used to work out accurate heights and times of tides. This course does not look at anything so complicated, but this example does show that patterns are important in many different ways.

The first section starts by looking at a do it yourself (DIY) problem using tiles. See how you get on with describing the pattern in this first activity.

## Activity 1 Tile pattern

Timing: Allow approximately 5 minutes

Suppose that somebody is tiling a bathroom, and the last row of square tiles is going to be a decorative border made up of blank tiles and patterned tiles, as shown in Figure 1 below:

Figure 1 Tiles

A friend has offered to help with the job. How would you describe the pattern so that they laid the tiles correctly? Click on ‘reveal comment’ if you would like a hint.

### Comment

There is no one correct answer to how to tackle this description, so just get stuck in! Think about what might be the best way to describe this to somebody who didn’t have the pattern in front of them.

There are lots of ways you could have tackled this. For example, you might say that you will need some blank tiles and some patterned tiles with the ‘bridges’ on. Start with a bridge tile, and then put a blank tile next to it. Take another bridge tile, but turn it around so that the bridge is upside down, like a smile, and put it next to the blank tile in the same line. Then put another blank tile next to the smile tile. This is the pattern: bridge, blank, smile, blank, bridge, blank, smile …

Or maybe you numbered the tiles, something like this:

1. bridge
2. blank
3. smile

The pattern would then be:

1,2,3,2,1,2,3,2 etc.

The decorative border is an example of a type of geometric pattern that has many applications in art, crafts and design. You may have something similar in your own home. If you have, see if you can describe this as some extra practice.

The next section looks at a number pattern that has fascinated people for many centuries.