Number Machines (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Number Machines

What is a number machine?

• A number machine is a combination of one or more mathematical operations that takes a set of numbers and changes them into another set of numbers

  • For example, if the rule is “triple the number and subtract 2”, the two mathematical operations are "multiply by 3, (×3)" and "subtract 2, (-2)"  

    • Putting 2 in to the function would give (3 × 2) - 2 = 6 - 2 = 4

    • Putting -4 in would give (3 × (-4)) - 2 = -12 - 2 = -14

  • Putting in would give

• The number being put into the machine is called the input

• The number coming out of the machine is called the output

• The processes that happen in the middle are called operations

How will I be expected to use number machines?

• You will need to be able to use number machines to

  • Generate an output from a given input

    • Starting from the left hand side, apply the mathematical operation in the first box to the given input

    • Apply the mathematical operation in the next box to the result, and so on

    • Write down the output value after all operations have been completed

  • Find an input from a given output

    • Starting from the right hand side, apply the opposite mathematical operations to the given output

    • Apply the mathematical operation in the next box to the result, and so on

    • Write down the input value after all opposite operations have been completed

  • Find an unknown operation

    • You will be given a known input and output, and asked to find a missing operation in the number machine

• You may be asked to use number machines with numbers or algebra