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12.01 Finding rules

Worksheet
Geometric patterns
1

These shapes made from blocks follow a pattern:

a

How many blocks are used to make the first shape in the pattern?

b

Draw the shape that comes next in the pattern.

c

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

2

These shapes made from blocks follow a pattern:

How many blocks are needed to make:

a

The first shape in the pattern?

b

The next shape in the pattern?

c

The 7th shape in the pattern?

3

These shapes made from blocks follow a pattern:

How many blocks are needed to make:

a

The first shape in the pattern?

b

The next shape in the pattern?

c

The 7th shape in the pattern?

4

These shapes made from blocks follow a pattern:

How many blocks are needed to make:

a

The first shape in the pattern?

b

The next shape in the pattern?

c

The 5th shape in the pattern?

5

These shapes made from blocks follow a pattern:

How many blocks are needed to make:

a

The first shape in the pattern?

b

The next shape in the pattern?

c

The 5th shape in the pattern?

6

Consider the pattern of shapes below:

a

How many shapes are there in total?

b

What shape would come next in the pattern?

c

What would the 10th shape be?

7

Consider the shapes below:

a

How many shapes are there in total?

b

Is there a repeating pattern?

8

Consider the pattern of shapes below:

The 5th shape is missing. If the pattern of shapes is repeating, what should the 5th shape be?

Number patterns
9

The following numbers form a pattern, but one number is missing:

82, \, 72, \, 62, \, ⬚, \, 42

a

Describe the pattern.

b

Write the missing number to complete the pattern.

10

For the following sets of numbers:

i

Describe the pattern.

ii

State the number that comes next in the pattern.

a

8, 9, 10, 11, 12

b

8, 7, 6, 5

c

8, 10, 12, 14, 16

d

15, 13, 11, 9

e

1, 11, 21, 31, 41

f

75, 65, 55, 45

11

Describe the pattern in the following set of numbers:

6, 8, 13, 16, 26

12

Consider the following sets of numbers:

i

Describe the pattern.

ii

State the number that completes the pattern.

a

9, 13, 17, ⬚, 25

b

11, 21, 31, ⬚, 51

c

15, 12, 9, ⬚, 3

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