Input output tables

Quick answer

Input output tables help you see how a rule or pattern changes numbers. You put a number in, apply a rule, and get a new number out. These tables help you find the rule and predict what will happen next.

Learning outcome

By the end of this page, you will be able to fill in missing numbers in input output tables and find the rule that changes the input numbers to the output numbers.

Success signs:

• You can spot the pattern or rule in a table
• You can find missing numbers in the table
• You can explain how the rule works
• You can use the rule to predict new numbers

Why this matters

Input output tables are like little maths detectives. They help you understand how numbers change and what rules make that happen. This skill is important for:

• Learning algebra later on
• Understanding how games and apps work
• Working out how much money you'll have after saving
• Figuring out how long it takes to do things
• Building and designing things

Think of it like a magic box that changes your numbers – and you get to discover the secret rule!

How it works

Input output tables have two columns:

• Input – this is the number you start with
• Output – this is the number you get after applying a rule

Here’s how it works:

1. Look at the input numbers and the output numbers
2. See how the input number changes to the output number
3. Find the rule – is it adding, subtracting, multiplying, or dividing?
4. Use the rule to find missing numbers

Let’s look at an example:

What is the rule? If 2 becomes 6, and 4 becomes 12, what rule could this be?

Examples you can see

Let’s try a few examples together.

Example 1: Adding 3

What is the rule here? You add 3 to each input to get the output.

Let’s try one more:

Example 2: Multiplying by 2

Here, you multiply each input by 2 to get the output.

Example 3: Missing number

What is the rule? 2 becomes 8, 4 becomes 16. The rule is to multiply by 4.

So, 6 × 4 = 24. The missing number is 24.

Try it as a mini adventure

Adventure: The Magic Number Machine

You are a detective who finds a mysterious machine that changes numbers. The machine has a secret rule. You put numbers in and get new numbers out.

Here’s your mission:

1. Look at the numbers going in and out
2. Find the secret rule
3. Use the rule to find the missing number

Task:

What is the rule? What number should go in the box?

Answer: The rule is to multiply by 4. 9 × 4 = 36. The missing number is 36.

Common mistakes

• Mistake: Thinking the rule is adding when it’s multiplying.
• Why it happens: It’s easy to get confused when numbers get bigger quickly.
• Fix: Check by trying the rule with more than one pair of numbers.

• Mistake: Not looking at all the numbers in the table.
• Why it happens: Kids might focus on just one pair and miss the pattern.
• Fix: Look at all the input and output pairs to find the pattern.

• Mistake: Using the wrong operation.
• Why it happens: Confusing what happens when numbers get bigger or smaller.
• Fix: Try adding, subtracting, multiplying, and dividing to see which works.

Parent and carer guide

Helping your child with input output tables can be fun and easy!

• Ask your child to explain the rule they found
• Try to find the rule together – it’s a great team game
• Use everyday examples like “If you have 3 apples and get 2 more, how many do you have?”
• Don’t worry if they make a mistake – it’s part of learning
• Encourage them to check their rule with more than one pair of numbers

What to say:

• “Let’s look at the numbers together.”
• “What do you notice about the numbers?”
• “Does this rule work for all the numbers?”

What not to do:

• Don’t rush them or say “hurry up”
• Don’t correct them every time – let them think
• Don’t say “you’re wrong” – say “let’s try another way”

Practice questions

1. What is the rule if input 4 gives output 12?
2. Fill in the missing number: Input 5, Output 15. Input 7, Output ?
3. What rule makes input 3 give output 9?
4. Input 2 gives output 6. Input 8 gives output 24. What is the rule?
5. Input 10 gives output 30. What is the rule?

Answers:

1. Multiply by 3
2. 21
3. Multiply by 3
4. Multiply by 3
5. Multiply by 3

FAQ

What is an input output table?

An input output table shows how a rule changes numbers. You put a number in (input) and get a new number out (output).

Why do we need to learn input output tables?

They help us understand patterns and rules. This is a key skill for learning algebra and solving problems in real life.

How do I know which rule to use?

Look at how the numbers change. If they get bigger quickly, it might be multiplying. If they get bigger slowly, it might be adding.

Can I use input output tables for anything else?

Yes! You can use them to find out how much money you'll have after saving, how long a journey will take, or how many items you can make with a given number of materials.

What if I can’t find the rule?

That’s okay! Try different operations (add, subtract, multiply, divide) and check if your rule works for all the numbers in the table.