DoingMaths - Free maths worksheets
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  • Number
    • Primary Addition and Subtraction
    • Addition and subtraction
    • Basic number work
    • BODMAS/PEMDAS/BIDMAS
    • Compound percentage change
    • Decimals
    • Factors and Multiples
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    • Fractions, decimals and percentages
    • Money
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    • Percentages
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    • Averages and the Range
    • Box plots
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  • More
    • Starters >
      • Puzzles and riddles
      • Maths Wordsearches
      • More Maths Lesson Starter Ideas
    • Christmas Maths Activities
    • Maths Articles >
      • Revision and How-To Guides >
        • How do Scale Factors Work for Area and Volume?
        • Edexcel GCSE Maths 2023 Paper 2: The Final Question
        • How to Find the Average From a Frequency Table
        • What Do the Angles in a Polygon Add Up To?
        • How to Integrate by Parts: Calculus Help
        • How to Use Pythagoras' Theorem
        • How to Calculate Compound Percentage Changes
        • How to Find Equivalent Fractions
        • How to Find the Averages and Range From Grouped Data
        • How to Factorise a Quadratic Algebraic Equation
        • How to Expand a Pair of Brackets
        • How to Complete the Square
        • How to Find the Average of a Group of Numbers
        • Hannah's Sweets - Tricky GCSE Question
        • Why Do We Rationalise the Denominator?
        • How to Add, Subtract, Multiply and Divide Fractions
        • How to Answer the 'Impossible' Question on the Edexcel GCSE Maths Paper 2022
        • How to Draw Pie Charts
        • How to Differentiate From First Principles
        • How to Solve Direct Proportion Questions
        • How to Calculate a Percentage of an Amount Using a Decimal Multiplier
        • How to Find the Lowest Common Multiple and Highest Common Factor of Two Numbers
        • How to Write a Number as a Product of Its Prime Factors
        • How to Solve a Quadratic Equation: 3 Methods
        • How To Solve the GCSE Maths Question That's Leaving Parents Stumped
        • How to Multiply Decimal Numbers Without a Calculator
        • Rationalizing the Denominator
      • How Many Gifts Do I Get Over the Twelve Days of Christmas?
      • How to Find the Sum of a Geometric Sequence
      • The Maths Behind A4 Paper
      • The Monty Hall Problem
      • How Do Binary Numbers Work?
      • Rice on a Chessboard
      • How to Prove Pi Equals 2
      • What is the Maximum Score in Ten-Pin Bowling?
      • The Prisoner's Dilemma
      • How Many Socks Make a Pair?
      • Four Interesting Types of Mathematical Numbers
      • How to Add the Numbers 1-100 Quickly
      • What Is the Sum of the Sequence 1, 1/2, 1/4, 1/8, 1/16, ...?
      • Find the Answer to 8×9×10×11×12 Without Using a Calculator
      • How to Prove that the Square root of 2 is Irrational
      • Three Interesting Fractals From Koch, Sierpinski and Cantor
      • How Many Squares Are on a Chessboard?
      • Different Kinds of Prime Numbers
      • How to Do Long Multiplication Using Napier's Method
      • The Handshake Problem
      • Why You Should Always Order the Large Pizza
      • Maximizing the Area of a Rectangle
      • Speed Arithmetic - How to Multiply by 11 Without a Calculator
      • Speed Arithmetic - How to Multiply and Divide by 5 Without a Calculator
      • Pythagoras' Theorem - A Proof
      • How Large Is Infinity?
      • Interesting Facts About Pascal's Triangle
      • Why Does Time Slow Down as You Approach the Speed of Light?
      • Five of History's Most Influential Women in STEM
      • Five More of History's Most Influential Women in STEM
      • How Likely Are You to Hit the Centre of the Archery Target?
      • Find Four Primes Smaller Than 100 Which Are Factors Of 3^32 − 2^32
      • Bertrand's Paradox: A Problem in Probability Theory
      • What Is an Erdős Number?
      • Three of Isaac Newton's Most Important Contributions to the World
      • Mathematical Numbers: What Is 'e'?
      • Hilbert's Paradox of the Grand Hotel: Another Look at Infinity
      • Decreasing the Circumference of Differently Sized Circles: A Counterintuitive Cricket Problem
      • Zeno's Paradox: Achilles and the Tortoise
      • What Are Hexadecimal Numbers?
      • Why Do We Split a Circle Into 360 Degrees?
      • N-bonacci Sequences - Taking Fibonacci Further
      • Being Careful When You Average an Average: A Basketball Problem
      • What Is a Dudeney Number?
      • Every Prime Number Larger Than 3 Is 1 Away From a Multiple of 6: A Proof
      • Why Do Buses Come in Threes?
      • A Quick Way to Solve 1000^2 − 999^2: The Difference of Two Squares
      • What Are Triangular Numbers?
      • What Is the Collatz Conjecture?
      • How to Make a Mathematical Paper Snowflake
      • What Is the Unexpected Hanging Paradox?
      • What Is Pi?
      • Is There a Biggest Prime Number or Do They Continue Infinitely?
    • A-Level Maths Paper Walkthroughs >
      • A-Level Maths, Edexcel, June 2018, Paper Walkthroughs >
        • A-Level Maths, June 2018, Pure Paper 1 Question Walkthroughs
        • A-Level Maths, June 2018, Pure Paper 2, Question Walkthroughs
        • A-Level Maths, June 2018, Statistics and Mechanics, Question Walkthroughs
      • A-Level Maths, Edexcel, June 2019, Paper Walkthroughs >
        • A-Level Maths, June 2019, Pure Paper 1, Question Walkthroughs
        • A-Level Maths, June 2019, Pure Paper 2, Question Walkthrough
        • A-Level Maths, June 2019, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, October 2020, Paper Walkthroughs >
        • A-Level Maths, October 2020, Pure Mathematics Paper 1, Question Walkthroughs
        • A-Level Maths, October 2020, Pure Mathematics Paper 2, Question Walkthroughs
        • A-Level Maths, October 2020, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, October 2021, Paper Walkthroughs >
        • A-Level Maths, October 2021, Pure Mathematics, Paper 1 Walkthroughs
        • A-Level Maths, October 2021, Pure Mathematics Paper 2 Walkthroughs
        • A-Level Maths, October 2021, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, June 2022, Paper 1 Walkthroughs
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Puzzles

These puzzles are ideal for a fun way to start a lesson and get everybody's brains warmed up.

Stationery dilemma

A man bought some pens, pencils and paperclips at the following prices:
Pens         10p each
Pencils      5p each
Paperclips  1p for two

If the man bought a total of 100 items for a total cost of £1. How many of each item did he buy?

Lightbulb problem

In your cellar there are three light switches in the OFF position. Each switch controls 1 of 3 light bulbs on the floor above.
You may move any of the switches but you may only go upstairs to inspect the bulbs one time. How can you determine the switch for each bulb with only one
inspection?

The lazy Gardener

It takes two gardeners 8 days to mow a lawn. 
One is lazy and one is energetic.
The energetic one would only take 12 days to
mow it on his own. 
How many days would the lazy gardener take to
mow the lawn on his own?


Spiders

Three spiders named Mr Eight, Mr. Nine and Mr. Ten are crawling on the jungle floor. One spider has 8 legs; one spider has 9 legs; one spider has 10 legs.
  “I think it is quite interesting,” says Mr. Ten, “that none of us have the same number of legs that our names would suggest.”
  “Who cares?” replies the spider with 9
legs.
 
How many legs does Mr. Nine have?

An old friend

A woman was walking down the street when she ran into an old friend whom she hadn’t seen since school.
 ‘Hello, I haven’t seen you for twenty years,’ she said. ‘How are you?’
 ‘Well I got married ten years ago, and this is our son,’ was the response.
 ‘Hello,’ said the woman to the boy,‘and what is your name?’
 ‘It’s the same as Daddy’s.’
 ‘Ah, then it’s Michael,’ said the woman.
How could she have known this when the boy’s name has not been mentioned?


Number magic

Pick a number (a whole number will be easier, but it doesn't have to be)
Add 5
Double your answer
Add 20
Halve you answer
Now minus the number you started with

What is your answer?
Try it again with another number

Notebook problem

If six boys can fill up six notebooks in six weeks and four girls can fill up four notebooks in four weeks, how many notebooks can a class of twelve boys and twelve girls fill up in twelve weeks?
 

Toasting problem

You want to make 3 slices of toast under the grill.
Your grill will only take 2 slices at the same time and only toasts one side at a time.
Assuming it takes 30 seconds to toast one side and moving a slice takes no time at all, how quickly can you toast all three slices on both sides?

Hint: It takes less than 120 seconds.
Check out this article on ideas for maths lesson starters.

The fastest man on Earth

In 2005, Asafa Powell of Jamaica was dubbed the fastest man on Earth after running the 100 metres in 9.77 seconds.

At the time, the record for the 200 metres was 19.32 seconds set by Michael Johnson.

Who had the fastest average speed?

(Work it out in metres per second)

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© Copyright DoingMaths free worksheets 2026 - All Rights Reserved
  • Home
  • Algebra
    • Algebraic expressions
    • Algebraic equations
    • Expanding brackets
    • Index notation
    • Inequalities
    • Quadratic equations
    • Sequences
    • Simultaneous equations
    • Straight line graphs
    • Substitution
  • Shapes, space and measures
    • Angles
    • Circles
    • Circle theorems
    • Compound measures
    • Construction
    • Distance/speed-time graphs
    • Length, area and volume
    • Metric and Imperial conversions
    • Metric units of measurement
    • Proof
    • Pythagoras' Theorem
    • Scale factors, similarity and congruence
    • Symmetry and reflection
    • Time
    • Trigonometry
  • Number
    • Primary Addition and Subtraction
    • Addition and subtraction
    • Basic number work
    • BODMAS/PEMDAS/BIDMAS
    • Compound percentage change
    • Decimals
    • Factors and Multiples
    • Fractions
    • Fractions, decimals and percentages
    • Money
    • Multiplication and division
    • Percentages
    • Ratio and Proportion
    • Rounding and estimating
    • Standard form
  • Statistics and Probability
    • Averages and the Range
    • Box plots
    • Collecting data
    • Pie charts
    • Probability
  • More
    • Starters >
      • Puzzles and riddles
      • Maths Wordsearches
      • More Maths Lesson Starter Ideas
    • Christmas Maths Activities
    • Maths Articles >
      • Revision and How-To Guides >
        • How do Scale Factors Work for Area and Volume?
        • Edexcel GCSE Maths 2023 Paper 2: The Final Question
        • How to Find the Average From a Frequency Table
        • What Do the Angles in a Polygon Add Up To?
        • How to Integrate by Parts: Calculus Help
        • How to Use Pythagoras' Theorem
        • How to Calculate Compound Percentage Changes
        • How to Find Equivalent Fractions
        • How to Find the Averages and Range From Grouped Data
        • How to Factorise a Quadratic Algebraic Equation
        • How to Expand a Pair of Brackets
        • How to Complete the Square
        • How to Find the Average of a Group of Numbers
        • Hannah's Sweets - Tricky GCSE Question
        • Why Do We Rationalise the Denominator?
        • How to Add, Subtract, Multiply and Divide Fractions
        • How to Answer the 'Impossible' Question on the Edexcel GCSE Maths Paper 2022
        • How to Draw Pie Charts
        • How to Differentiate From First Principles
        • How to Solve Direct Proportion Questions
        • How to Calculate a Percentage of an Amount Using a Decimal Multiplier
        • How to Find the Lowest Common Multiple and Highest Common Factor of Two Numbers
        • How to Write a Number as a Product of Its Prime Factors
        • How to Solve a Quadratic Equation: 3 Methods
        • How To Solve the GCSE Maths Question That's Leaving Parents Stumped
        • How to Multiply Decimal Numbers Without a Calculator
        • Rationalizing the Denominator
      • How Many Gifts Do I Get Over the Twelve Days of Christmas?
      • How to Find the Sum of a Geometric Sequence
      • The Maths Behind A4 Paper
      • The Monty Hall Problem
      • How Do Binary Numbers Work?
      • Rice on a Chessboard
      • How to Prove Pi Equals 2
      • What is the Maximum Score in Ten-Pin Bowling?
      • The Prisoner's Dilemma
      • How Many Socks Make a Pair?
      • Four Interesting Types of Mathematical Numbers
      • How to Add the Numbers 1-100 Quickly
      • What Is the Sum of the Sequence 1, 1/2, 1/4, 1/8, 1/16, ...?
      • Find the Answer to 8×9×10×11×12 Without Using a Calculator
      • How to Prove that the Square root of 2 is Irrational
      • Three Interesting Fractals From Koch, Sierpinski and Cantor
      • How Many Squares Are on a Chessboard?
      • Different Kinds of Prime Numbers
      • How to Do Long Multiplication Using Napier's Method
      • The Handshake Problem
      • Why You Should Always Order the Large Pizza
      • Maximizing the Area of a Rectangle
      • Speed Arithmetic - How to Multiply by 11 Without a Calculator
      • Speed Arithmetic - How to Multiply and Divide by 5 Without a Calculator
      • Pythagoras' Theorem - A Proof
      • How Large Is Infinity?
      • Interesting Facts About Pascal's Triangle
      • Why Does Time Slow Down as You Approach the Speed of Light?
      • Five of History's Most Influential Women in STEM
      • Five More of History's Most Influential Women in STEM
      • How Likely Are You to Hit the Centre of the Archery Target?
      • Find Four Primes Smaller Than 100 Which Are Factors Of 3^32 − 2^32
      • Bertrand's Paradox: A Problem in Probability Theory
      • What Is an Erdős Number?
      • Three of Isaac Newton's Most Important Contributions to the World
      • Mathematical Numbers: What Is 'e'?
      • Hilbert's Paradox of the Grand Hotel: Another Look at Infinity
      • Decreasing the Circumference of Differently Sized Circles: A Counterintuitive Cricket Problem
      • Zeno's Paradox: Achilles and the Tortoise
      • What Are Hexadecimal Numbers?
      • Why Do We Split a Circle Into 360 Degrees?
      • N-bonacci Sequences - Taking Fibonacci Further
      • Being Careful When You Average an Average: A Basketball Problem
      • What Is a Dudeney Number?
      • Every Prime Number Larger Than 3 Is 1 Away From a Multiple of 6: A Proof
      • Why Do Buses Come in Threes?
      • A Quick Way to Solve 1000^2 − 999^2: The Difference of Two Squares
      • What Are Triangular Numbers?
      • What Is the Collatz Conjecture?
      • How to Make a Mathematical Paper Snowflake
      • What Is the Unexpected Hanging Paradox?
      • What Is Pi?
      • Is There a Biggest Prime Number or Do They Continue Infinitely?
    • A-Level Maths Paper Walkthroughs >
      • A-Level Maths, Edexcel, June 2018, Paper Walkthroughs >
        • A-Level Maths, June 2018, Pure Paper 1 Question Walkthroughs
        • A-Level Maths, June 2018, Pure Paper 2, Question Walkthroughs
        • A-Level Maths, June 2018, Statistics and Mechanics, Question Walkthroughs
      • A-Level Maths, Edexcel, June 2019, Paper Walkthroughs >
        • A-Level Maths, June 2019, Pure Paper 1, Question Walkthroughs
        • A-Level Maths, June 2019, Pure Paper 2, Question Walkthrough
        • A-Level Maths, June 2019, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, October 2020, Paper Walkthroughs >
        • A-Level Maths, October 2020, Pure Mathematics Paper 1, Question Walkthroughs
        • A-Level Maths, October 2020, Pure Mathematics Paper 2, Question Walkthroughs
        • A-Level Maths, October 2020, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, October 2021, Paper Walkthroughs >
        • A-Level Maths, October 2021, Pure Mathematics, Paper 1 Walkthroughs
        • A-Level Maths, October 2021, Pure Mathematics Paper 2 Walkthroughs
        • A-Level Maths, October 2021, Statistics and Mechanics, Walkthrough answers
      • A-Level Maths, Edexcel, June 2022, Paper 1 Walkthroughs
    • Mathematician of the Month
    • Tricky Geometry Problems
    • DoingMaths video channel
    • DoingMaths Shop
    • Contact us
    • Privacy policy