NZ Level 4
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Finding Rules
Lesson

What's the rule?

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.

Remember

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

Worked Examples

Question 1

Look at the shapes below:

  1. How many shapes are there in total?

  2. What shape comes $1$1st?

    Triangle

    A

    Circle

    B

    Rectangle

    C

    Square

    D

    Triangle

    A

    Circle

    B

    Rectangle

    C

    Square

    D
  3. What is the $4$4th shape?

    Square

    A

    Rectangle

    B

    Triangle

    C

    Circle

    D

    Square

    A

    Rectangle

    B

    Triangle

    C

    Circle

    D
  4. Is there a repeated pattern?

    No

    A

    Yes

    B

    No

    A

    Yes

    B
  5. What shape would come next in the pattern (the $7$7th shape)?

    Triangle

    A

    Rectangle

    B

    Square

    C

    Circle

    D

    Triangle

    A

    Rectangle

    B

    Square

    C

    Circle

    D
  6. What would the $10$10th shape be?

    Circle

    A

    Triangle

    B

    Square

    C

    Rectangle

    D

    Circle

    A

    Triangle

    B

    Square

    C

    Rectangle

    D

Question 2

Look at these numbers:

$8,9,10,11,12$8,9,10,11,12

  1. Choose the answer which best describes the pattern:

    Adding $2$2 each time.

    A

    Adding $1$1 each time.

    B

    There is no pattern.

    C

    Adding $3$3 each time.

    D

    Adding $2$2 each time.

    A

    Adding $1$1 each time.

    B

    There is no pattern.

    C

    Adding $3$3 each time.

    D
  2. What number comes next in the pattern?

Question 3

These shapes made from blocks follow a pattern:

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

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

    A

    B

    C

    D

    A

    B

    C

    D
  3. How many blocks would be needed to make the $5$5th shape in the pattern?

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