Topics
8. Patterns
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Australia
Year 3

8.02 Missing numbers

Lesson
Practice
Lesson

Are you ready?

Being able to find the number that we are skip counting by can help us find missing numbers. Let's give it a try.

Examples

Example 1

Write the next number in the pattern:

8,10,12,⬚,⬚,⬚

Worked Solution
Create a strategy

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

\displaystyle 10-8\displaystyle =\displaystyle 2Find the difference
\displaystyle 12+2\displaystyle =\displaystyle 14Add 2 to the last value

The complete pattern is 8,\,10,\,12,\,14,\,16,\,18.

Find missing numbers

Let's look now at how we can continue patterns to find missing numbers.

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Examples

Example 2

Complete the pattern below.

20,⬚, 44,⬚

Worked Solution
Create a strategy

Find the size of one jump and add that to the given values to complete the pattern.

Apply the idea

We are given two numbers in the pattern that are two jumps apart.

A table with arrows showing the jumps in a number pattern. Ask your teacher for more information.
\displaystyle 44 - 20\displaystyle =\displaystyle 24Subtract the given values

The difference between the two given numbers is 24. The size of one jump will be half of this which is 12.

A table with arrows showing the jumps in a number pattern. Ask your teacher for more information.
\displaystyle 20 + 12 \displaystyle =\displaystyle 32Add 12 to the first value
\displaystyle 44 + 12 \displaystyle =\displaystyle 56Add 12 to the third value

The complete pattern is 20,\,32,\,44,\,56.

Idea summary

To find the pattern, think about how the numbers are changing- are they getting bigger or smaller? Then you can work out the missing values.

Outcomes

AC9M3N07

follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

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