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Maths History

Napier's bones story

Introduce John Napier's calculating rods and multiplication shortcuts.

Quick answer

Napier's bones are a clever way to multiply big numbers using simple rods and addition – invented by John Napier in the 1600s.

Learning outcome

By the end of this page, you will understand how Napier's bones work and be able to use them to multiply numbers up to 9 × 9. Success signs:
  • You can explain what Napier's bones are.
  • You can use the rods to multiply 3 × 7.
  • You can see how Napier's bones help make multiplication easier.
  • You can imagine how people used them before calculators.

Why this matters

Multiplication can be tricky, especially with big numbers. Before calculators, people needed clever tools to help them work quickly. Napier's bones were one of the first tools that made multiplication easier. They're like a magic trick for numbers! Understanding how they work helps you see that maths has a history and that people have always found ways to make hard things easier.

How it works

Napier's bones are a set of special rods or strips. Each rod has a multiplication table written on it. To multiply two numbers, you line up the rods and add up the numbers in a special way. It's like using a number helper to do the hard work for you. Let’s look at how to make and use Napier’s bones step by step:
  1. Make your bones: Draw or cut strips of paper or wood. On each strip, write a number from 1 to 9 down the side. Then, write the multiples of that number in rows underneath.
  2. Set up your problem: If you want to multiply 3 × 7, you line up the rod for 3.
  3. Read the answer: Look at the row for 7. The number in the box is your answer!

Examples you can see

Let’s imagine you're a shopkeeper and you need to count how many apples you have. You have 3 boxes, and each box has 7 apples. Using Napier's bones:
Rod for 3 Row for 7
3 21
So, 3 × 7 = 21 apples. You can also use it for bigger numbers. If you have 4 boxes with 6 apples each:
Rod for 4 Row for 6
4 24
So, 4 × 6 = 24 apples. Let’s draw a picture to show how this works:
  1. Draw 3 rows with 7 apples in each row.
  2. Count all the apples. That's 7 + 7 + 7 = 21 apples.
  3. Napier's bones gave us the same answer without counting each one!

Try it as a mini adventure

Adventure: The Treasure Hunt You are on a treasure hunt! You found a map that says “Multiply 5 by 8 to find the secret number.” You have a set of Napier's bones. What number do you find?
  1. Find the rod for 5.
  2. Look at the row for 8.
  3. What number do you see?
The answer is 40. That’s your secret number! You can now find the treasure chest. Try this again with 6 × 9. What number do you get?
  1. Find the rod for 6.
  2. Look at the row for 9.
  3. What number do you see?
The answer is 54.

Common mistakes

  • Mistake: Thinking you can read the answer from any row.
    Why it happens: Not paying attention to which row to look at.
    Fix: Always check which row matches your second number.
  • Mistake: Confusing which rod to use.
    Why it happens: Mixing up the first and second number.
    Fix: Remember the first number goes on the rod, the second number is the row.
  • Mistake: Not lining up the rods properly.
    Why it happens: Not knowing which rod to use.
    Fix: Place the rods side by side and make sure they are straight.

Parent and carer guide

As a parent or carer, you can help by:
  • Building a set of Napier's bones with paper or wood strips.
  • Practising multiplication with your child using the rods.
  • Encouraging your child to explain how the rods work.
  • Playing the treasure hunt game together to make it fun.
  • Letting your child make up their own problems to solve.
What to say:
  • “Let’s pretend we’re explorers and use Napier’s bones to find the treasure!”
  • “What number do you think will be in that row?”
  • “Can you show me how to use the rods?”
What not to worry about:
  • It’s okay if your child makes a mistake. They’re learning!
  • Don’t rush – let them explore and enjoy the process.
  • They don’t need to memorise all the tables yet – focus on understanding.

Practice questions

  1. What is 2 × 5 using Napier's bones?
  2. What is 4 × 8 using Napier's bones?
  3. What is 6 × 3 using Napier's bones?
  4. What is 7 × 9 using Napier's bones?
  5. What is 9 × 4 using Napier's bones?
Answers:
  1. 10
  2. 32
  3. 18
  4. 63
  5. 36

FAQ

Who was John Napier?

John Napier was a Scottish mathematician who lived in the 1500s and 1600s. He invented Napier's bones to help people multiply numbers more easily.

How were Napier's bones used?

People used Napier's bones to multiply large numbers by lining up the rods and reading off the answers. It was a faster way to do multiplication before calculators.

Can I make my own Napier's bones?

Yes! You can draw them on paper or cut them from wood. Just write the multiplication tables on strips of paper and line them up.

Are Napier's bones still used today?

Not really. Today we use calculators or computers, but Napier's bones are still fun to learn about and help understand how multiplication works.

Why are Napier's bones important?

Napier's bones show how people have always tried to find easier ways to do maths. They’re a great example of how creativity and problem-solving can help us learn.