We have seen how to continue shape patterns and continue number patterns by following rules. Now we are ready to work out the rule using patterns with numbers, shapes, and models. This video shows you how to find out the pattern that is being used.

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Examples

Example 1

Look at the shapes below:

A shape pattern that goes circle, square, triangle, circle, square, triangle.

Is there a repeated pattern?

Worked Solution

Create a strategy

Note if the sequence of the shapes repeated.

Apply the idea

We can see that the sequence of first three shapes are circle, square, and triangle, which is repeated after the triangle.

So, there is a repeated pattern.

What shape would come next in the pattern (the 7th shape)?

Worked Solution

Create a strategy

Look for what came after the triangle previously.

Apply the idea

The 6th shape is the last shape in the pattern which is a triangle. Previously the circle came after the triangle.

So the 7th shape will be a circle.

What would the 10th shape be?

Worked Solution

Create a strategy

Continue repeating the pattern.

Apply the idea

We knew from part (b) that the 7th shape is a circle, which means that the 8th will be a square, the 9th shape will be a triangle and the 10th shape will be a circle.

Example 2

Look at these numbers:

8, \,9, \,10, \,11, \,12

Choose the answer which best describes the pattern:

Adding 2 each time.

Adding 1 each time.

There is no pattern.

Adding 3 each time.

Worked Solution

Create a strategy

Count how much is added each time.

Apply the idea

From 8, we need to add 1 to get 9. From 9, we need to add 1 to get 10, and so on.

So the pattern is adding 1 each time, which is option B.

What number comes next in the pattern?

Worked Solution

Create a strategy

Apply the pattern found in part (a).

Apply the idea

Since the pattern is adding 1 each time, 12+1=13.

The next number is 13.

Example 3

These shapes made from blocks follow a pattern:

A pattern of 3 shapes made of blocks. They have 9, 7, and 5 blocks respectively. Ask your teacher for more information

Which shape comes next in the pattern (the 4th shape)?

A shape with 5 blocks. 3 in the top row and 2 in the bottom row.

A shape with 3 blocks. 2 in the top row and 1 in the bottom row.

A shape with 4 blocks that make a square.

Worked Solution

Create a strategy

Count how many blocks are being removed each time.

Apply the idea

We can see that the original shape have 9,\,5, and 7 blocks in them respectively. This means that the shapes are decreasing by 2 blocks each time.

So, the 4th shape has 5-2=3 blocks, which is in option B.

How many blocks would be needed to make the 5th shape in the pattern?

Worked Solution

Create a strategy

Subtract the number of blocks being removed each time from the blocks found in part (b).

Apply the idea

We knew from part (b) that the 4th shape has 3 blocks and the number of blocks in each shape are decreasing by 2.

So, the 5th shape needs 3-2=1 block.

Idea summary

We can see patterns in numbers or shapes. Once we have spotted the pattern we can continue it the pattern further.

12.01 Finding rules

Ideas

What's the rule?

Examples

Example 1

Example 2

Example 3

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