Finding the rule

Quick answer

Finding the rule means working out what pattern or rule is changing a number or set of numbers from one step to the next. It's like being a detective to figure out how things change in a sequence.

Learning outcome

By the end of this page, you will be able to look at a pattern of numbers and work out what rule is changing them from one number to the next.

• You can spot what happens to numbers in a sequence
• You can write down the rule that explains the pattern
• You can use the rule to predict what comes next
• You can check your rule by testing it with the numbers given

Why this matters

Understanding patterns and rules is a big part of algebra, which is like solving puzzles with numbers. When you can find the rule, you can:

• Predict what comes next in a pattern
• Figure out what number fits in a missing spot
• Help with maths problems in school
• Understand how numbers work together in games, cooking, and real life

It's like being a detective, and the detective skills you learn here will help you with more advanced maths later on!

How it works

Here's how to find the rule:

1. Look at the first few numbers in the pattern
2. Check how each number changes from the one before it
3. Figure out what operation (addition, subtraction, multiplication, or division) is happening
4. Test your rule with the other numbers to see if it works
5. Write down the rule clearly

Let's go through this step by step with some examples!

Examples you can see

Let's start with a simple pattern:

What is the rule?

1. Look at the numbers: 2, 4, 6, 8
2. How do they change? From 2 to 4, we add 2. From 4 to 6, we add 2. From 6 to 8, we add 2.
3. The rule is: Add 2
4. Test it: 2 + 2 = 4, 4 + 2 = 6, 6 + 2 = 8. It works!
5. So the rule is: Add 2

Here's another example with multiplication:

1. Look at the numbers: 3, 6, 12, 24
2. How do they change? From 3 to 6, we multiply by 2. From 6 to 12, we multiply by 2. From 12 to 24, we multiply by 2.
3. The rule is: Multiply by 2
4. Test it: 3 × 2 = 6, 6 × 2 = 12, 12 × 2 = 24. It works!
5. So the rule is: Multiply by 2

Here's a pattern that goes down:

1. Look at the numbers: 20, 15, 10, 5
2. How do they change? From 20 to 15, we subtract 5. From 15 to 10, we subtract 5. From 10 to 5, we subtract 5.
3. The rule is: Subtract 5
4. Test it: 20 - 5 = 15, 15 - 5 = 10, 10 - 5 = 5. It works!
5. So the rule is: Subtract 5

Try it as a mini adventure

Adventure: The Mystery Pattern Club

You are a detective in the Mystery Pattern Club. Each week, the club gets a new pattern to solve. This week, they have a pattern that looks like this:

Your job is to find the rule that explains how the number of members changes each week.

1. Look at the numbers: 10, 13, 16, 19
2. How do they change? From 10 to 13, we add 3. From 13 to 16, we add 3. From 16 to 19, we add 3.
3. The rule is: Add 3
4. Test it: 10 + 3 = 13, 13 + 3 = 16, 16 + 3 = 19. It works!
5. So the rule is: Add 3

Now, using the rule, predict how many members will be in the 5th week:

19 + 3 = 22 members

Great detective work! You've found the pattern and made a prediction.

Common mistakes

• Mistake: Thinking the rule is always addition or multiplication.

  Why it happens: Children often see a pattern and jump to the first operation they think of.

  Fix: Always check all operations. Look at the numbers and think if they go up or down. If they go down, it might be subtraction or division.

• Mistake: Not testing the rule with all numbers.

  Why it happens: It's easy to think you've found the rule and forget to double-check.

  Fix: Always test your rule with every number in the pattern. If it doesn't work for one, try another rule.

• Mistake: Confusing the rule with the actual numbers.

  Why it happens: The rule is about what happens to the numbers, not the numbers themselves.

  Fix: Remember: the rule is "what happens" not "what the numbers are".

Parent and carer guide

Helping your child find rules is about encouraging them to think and not rushing to an answer. Here's how you can help in 5-10 minutes:

• Ask questions: "What do you notice about the numbers?" "How do they change?"
• Use objects: Use counters, blocks, or toys to show patterns physically
• Be patient: Let them think and try different ideas
• Encourage testing: "Try this rule with the next number"
• Don't worry about mistakes: They're part of learning

Remember, this is about developing detective skills and pattern recognition. It's not about getting the right answer quickly. Keep it fun and exploratory!

Practice questions

1. Find the rule for this pattern: 5, 10, 15, 20
2. Find the rule for this pattern: 24, 18, 12, 6
3. Find the rule for this pattern: 1, 3, 9, 27
4. Find the rule for this pattern: 100, 50, 25, 12.5
5. Find the rule for this pattern: 7, 14, 21, 28

Answers:

1. Add 5
2. Subtract 6
3. Multiply by 3
4. Divide by 2
5. Add 7

FAQ

What is a rule in maths?

A rule in maths is a pattern or a way that numbers change from one to the next. It tells you what operation (add, subtract, multiply, divide) is happening to get from one number to the next.

Why do we need to find rules?

Finding rules helps us understand how numbers work together. It's like learning the secret code of numbers. This skill is important for algebra and helps us solve problems more easily.

How can I practice finding rules?

You can practice by looking at patterns in your daily life, like the number of steps you take, the number of cookies in each row, or the number of cars in a parking lot. Try to figure out what changes from one to the next.

Can rules be more than one operation?

Yes, some patterns use more than one operation. For example, a pattern might go: 2, 5, 10, 17. The rule might be "multiply by 2 and then add 1". This is more advanced, but it's good to know!

What if I can't find the rule?

That's okay! It's normal to take time to find the rule. Try different operations, look at the numbers carefully, and don't be afraid to ask for help. Sometimes, a small change in how you look at the numbers can make all the difference.