Growing Patterns and Their Rules
Recognise and use rules that generate visually growing patterns and number patterns involving rational numbers.
Read this first
Find what changes each step. That change is the rule.
Each step adds 3. That is the rule.
Words you need
- Term
- One number in a pattern.
- Rule
- What you do to get the next term.
- Growing pattern
- A pattern that gets bigger each step.
Worked example
e.g. Find the rule for 4, 7, 10, 13 and give the next two terms.
- Find the gap between the first two. 7 - 4 = 3.
- Check the next gap. 10 - 7 = 3. The same.
- Check again. 13 - 10 = 3. The rule is add 3.
- The next two are 16 and 19.
Always check the gap more than once. One gap could be a coincidence.
Practice
The pictures fade as you go. By the last few you are on your own.
1Find the rule for 2, 6, 10, 14.with a picture
AnswerAdd 4.
2Find the next term of 20, 17, 14.with a picture
Answer11.
3Find the rule for 3, 6, 12, 24.with a hint
Need a hint?
Is it adding or multiplying?
AnswerDouble each time.
4Find the rule for 0.5 then 1.0 then 1.5.with a hint
Need a hint?
Look at the gap.
AnswerAdd 0.5.
5What is the 6th term of 5, 9, 13?on your own
Answer25.
6A pattern starts at 100 and halves. Give three terms.on your own
Answer100, 50, 25.
7Why check more than one gap?on your own
AnswerThe pattern might not be what the first gap suggests.
Think about it
1
How do you tell an adding rule from a times rule?
One good answerAdding gives equal gaps. Times makes the gaps grow.
2
Can a pattern go down?
One good answerYes. The rule can be take away or divide.
Common mistakes
Guessing from one gap.
Check at least two before deciding.
Assuming every pattern adds.
Some multiply or halve.