Introduction to Linear Patterns

Linear and non-Linear
Patterns

Checking the differences between the numbers in a list allows us to recognise the type of pattern...

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​Check 1st Differences

Adding or Subtracting the same thing each time means Linear

But if what happens changes each time then it's
non-Linear

And if it's not even Adding or Subtracting then it's also
non-Linear

Multiple Choice

What is are the differences between each of the values in this list?

• Add 2

• Add 1

• Times 2

• Subtract 3

Multiple Choice

Based on the difference you found,

in what pattern do you think this list of numbers is?

• non-Linear

• Linear

Remember, adding or subtracting the SAME thing each time makes a pattern

LINEAR

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​That's Right!

The differences were +1 each time...

Multiple Choice

What about the differences between each value in this list?

• • + 5

• - 5

• x 5

• / 5

Multiple Choice

Based on the difference you found,

what pattern do you think this list of numbers makes?

• non-Linear

• Linear

LINEAR

​

​Right Again!

The differences were -5 each time...

Multiple Choice

Is this pattern Linear or non-Linear?

• non-Linear

• Linear

LINEAR

​

​Right Again!

The differences were +2 each time...

Multiple Choice

What are the differences between each value in this list?

• +2 each time

• $$-3$$ each time

• $$\times2$$ each time

• $$+2,\ +3,\ +4,\ +5...$$

Multiple Choice

So what would you say about the pattern?

• Differences changing each time

  so

  non-Linear

• Differences the same each time

  so

  Linear

Non-LINEAR

​

​Right Again!

The differences kept changing...

Open Ended

Describe what's happening each time in this pattern?

Non-LINEAR

​

​Yes, Divide by 2!

The differences were the same but not addition or subtraction

The number of matchsticks at each stage here form a

Linear Pattern

​3 matches are added on each time to get to the next shape

​Real World Patterns

Draw

Draw Pattern 4 in the space provided?

You can use one colour...

Draw

Now Draw Pattern 5?

Multiple Choice

Did you notice?

1 difference added to the starting 4 gives the 2^nd Pattern

2 differences added to the starting 4 gives the 3^rd Pattern

3 differences added to the starting 4 gives the 4^th Pattern

How many differences would need to be added to the starting 4 to give the 10^th Pattern?

• 9 differences added

• 10 differences added

• 11 differences added

Multiple Choice

Therefore, can you work out the total number of matchsticks in the 10^th Pattern?

NB Each difference is 3 more matches...

• $$4+9\left(3\right)=31$$

• $$4+10\left(3\right)=34$$

• $$4+11\left(3\right)=37$$