Multiplication & Division Function Machines
Free printable multiplication and division function machine worksheets with answers. Feed a number into a × or ÷ machine and work out the result — or reverse it. Builds fact fluency. Play online or print the PDF.
Apply each machine's rule to fill the empty boxes — you'll see a ✓ when each is right.
Explore the Elementary Math & Number Sense Sequence
A structured progression following the Concrete-Pictorial-Abstract (CPA) framework — from part-whole number bonds to inverse operations, multi-digit arithmetic, and algebraic functions.
Function Machines
In, rule, out algebraic problem solving
Learn How to Play, Solve & Teach Multiplication & Division Function Machines
What Are Function Machines? A Simple Guide for Parents & Teachers
Function machines turn a number into another by applying a rule — a friendly first taste of functions and inverse operations. Learn how they work and make free printable function machine worksheets.
Frequently asked questions
What is a function machine?+
A function machine is a simple picture of a rule: a number goes IN, the machine applies a rule (like × 3 or + 5), and a new number comes OUT. It's an early, visual way to introduce functions and inverse operations.
How do you use a function machine?+
Read the rule, then apply it to each input to get the output. For example, with the rule × 3, an input of 4 gives an output of 12. Some rows work backwards — you're given the output and find the input by undoing the rule.
Why are function machines taught?+
They build fluency with the four operations and introduce the idea of a consistent rule and its inverse — the foundation of algebra. Working backwards through a machine is exactly the 'undo' thinking used to solve equations later.
What ages are function machines for?+
Addition and subtraction machines suit Grades 1–3; multiplication and division machines fit Grades 3–5 as times tables become fluent.
Are the function machine worksheets free?+
Yes. Generate unlimited worksheets and play online or download printable PDFs with an answer key for free — no signup.