Number Patterns • Topic 3 of 3

Input-Output Tables and Rules

An input-output table shows pairs of numbers connected by a rule — like a machine that transforms the input into the output.

The rule can be:

  • Add or subtract: Input 3 → Output 8 (Rule: +5)
  • Multiply or divide: Input 4 → Output 12 (Rule: ×3)
  • Two-step rule: Input 2 → Output 5 (Rule: ×2+1)

How to find the rule:

  1. Look at the first input-output pair
  2. Try simple operations (+, -, ×, ÷)
  3. Test your rule on at least two more pairs
  4. If it works for all pairs, you have the rule

Once you know the rule, you can find any output for any input.

Input-Output Table (Rule: x3)InputOutputRule: x 3→→1, 2, 3, 4, 53, 6, 9, 12, 15Input x 3 = Output4 x 3 = 12 check, 5 x 3 = 15 check
Solved Examples
1
Worked Example
Find the rule: Input 5 → 15, Input 8 → 24, Input 10 → 30. What is the output when input = 6?
SolutionStep 1: Try ×3: 5×3=15 (yes!), 8×3=24 (yes!), 10×3=30 (yes!). Rule = ×3. Step 2: When input=6, output = 6×3 = 18. Answer: 18
2
Worked Example
Find the rule: Input 2 → 5, Input 3 → 7, Input 4 → 9. What is the output when input = 10?
SolutionStep 1: Try ×2+1: 2×2+1=5 (yes!), 3×2+1=7 (yes!), 4×2+1=9 (yes!). Rule = ×2+1. Step 2: When input=10, output = 10×2+1 = 21. Answer: 21
3
Worked Example
Input 1→1, 2→4, 3→9, 4→16. What is the rule and the next output?
SolutionStep 1: Notice 1=1×1, 4=2×2, 9=3×3, 16=4×4. Rule = input × itself (square the number). Step 2: Next input=5. Output = 5×5 = 25. Answer: 25

Key Points

  • An input-output table shows how inputs are transformed by a rule
  • Test your rule on ALL given pairs before finalising it
  • Rules can be one-step (x3) or two-step (x2+1)
  • Squaring means multiplying a number by itself: 4x4=16
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.An input-output table applies a ___ to each input.
Explanation: A rule.
Q2.If the rule is "$+5$" and the input is $3$, the output is:
Explanation: $3+5=8$.
Q3.If the rule is "$\times2$" and the input is $4$, the output is:
Explanation: $4\times2=8$.
Q4.To find the rule, compare the inputs and the:
Explanation: Outputs.
Practice more MCQs → 📝 Assignment · 35 marks