Topics
12. Coding and algorithms
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AustraliaVIC
Level 4

12.01 Finding rules

Lesson
Practice
Lesson

Are you ready?

Can you continue a pattern?

Examples

Example 1

Create a pattern by adding 2 each time.

3, \,⬚, \, ⬚, \,⬚, \,⬚

Worked Solution
Create a strategy

Add 2 to the last given value to complete the pattern.

Apply the idea

Add 2 to the last number to complete the pattern.

\displaystyle 3 +2\displaystyle =\displaystyle 5Add 2 to 3
\displaystyle 5+2\displaystyle =\displaystyle 7Add 2 to 5
\displaystyle 7+2\displaystyle =\displaystyle 9Add 2 to 7
\displaystyle 9+2\displaystyle =\displaystyle 11Add 2 to 9

The complete pattern is 3,\, 5,\, 7,\, 9,\,11 .

Find the rule

You may not have realised but patterns have a rule that you follow to work out the next number, Let's look at how to write rules to describe patterns.

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Examples

Example 2

Complete the pattern:

a

5,\,7,\,9,\,⬚,\,⬚,\,⬚

Worked Solution
Create a strategy

Find how much the numbers are increasing by each time and add that to the last given value to complete the pattern.

Apply the idea

To work out how much the numbers are increasing by each time, you can count up or find the difference between two numbers.

\displaystyle 7-5\displaystyle =\displaystyle 2Subtract two numbers

Add 2 to each number to complete the pattern.

\displaystyle 9+2\displaystyle =\displaystyle 11Add 2 to 9
\displaystyle 11+2\displaystyle =\displaystyle 13Add 2 to 11
\displaystyle 13+2\displaystyle =\displaystyle 15Add 2 to 13

The complete pattern is 5,\,7,\,9,\,11,\,13,\,15.

b

What is the rule for filling in the pattern?

A
Add 2
B
Add 3
Worked Solution
Create a strategy

What number did we add by in part (a)?

Apply the idea

The numbers are increasing by 2\,, this means that the rule of filling in the pattern is add 2.

So, the correct option is A.

Idea summary

Think about how the numbers are changing to work out the rule. Are the numbers getting bigger or smaller, and by how many?

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