Arithmetic

Activities

23 or Bust
Activity
A game involving mental arithmetic and strategy for two players or one player against the computer.

Addle
Activity
Arrange the numbers from 1 to 14 in the spaces to make the sums correct.

Arithmagons
Activity
Find the missing numbers in these partly completed arithmagon puzzles.

Basic Addition
Activity
A self marking exercise on addition with increasing levels of difficulty.

Basic Division
Activity
A self marking exercise on division with increasing levels of difficulty.

Basic Multiplication
Activity
A self marking exercise on multiplication with increasing levels of difficulty.

Basic Subtraction
Activity
A self marking exercise on subtraction with increasing levels of difficulty.

Beat The Clock
Activity
It is a race against the clock to answer 30 mental arithmetic questions. There are nine levels to choose from.

BIDMAS
Activity
A self marking exercise testing the application of BIDMAS, an acronym describing the order of operations used when evaluating expressions.

BIDMAS Game
Activity
An online interactive game celebrating the order of mathematical operations.

Bidmaze
Activity
Find your way through the maze encountering mathematical operations in the correct order to achieve the given total.

Brainbox
Activity
A puzzle requiring the arrangement of numbers on the function machines to link the given input numbers to the correct output.

Broken Calculator
Activity
Some of the buttons are missing from this calculator. Can you make the totals from 1 to 20?

Centexpression
Activity
Arrange the numbers from 1 to 9 to make an expression with a value of 100.

Chain Challenge
Activity
How fast can you perform all of the given operations without using a calculator?

Clouds
Activity
Can you work out which numbers are hidden behind the clouds in these calculations?

Decimal Plus
Activity
Practise mental and written methods for adding and subtracting decimal numbers.

Decimal Times
Activity
Practise mental and written methods for multiplying and dividing decimal numbers.

Digital Darts
Activity
An online darts game for one or two players requiring skill, strategy and mental arithmetic.

Digivide
Activity
Arrange the numbers from 1 to 6 in the spaces to make the division calculation correct.

Discombobulated
Activity
A fun game requiring you to find numbers which add up to the target number as quickly as possible.

Doubling Quiz
Activity
Drag the number cards onto their doubles. No calculators or writing allowed.

Fast Factors
Activity
How quickly can you arrange the cards to match the times tables?

Fifteen
Activity
A strategy game. Play against the computer to select three numbers that add up to 15.

Heptaphobia Research
Activity
Use written methods to answer ten arithmetic questions. When you have finished you will find the results of this amazing research.

How Many of Each?
Activity
Work out how many items were bought from the information given.

Know Your Place
Activity
Without a calculator perform some calculations requiring a knowledge of place value.

Largest Product
Activity
A drag and drop activity challenging you to arrange the digits to produce the largest possible product.

Letter Sums
Activity
Add up the values of the letters in these mathematical words.

Ludicross
Activity
Arrange the given numbers on the cross so that the sum of the numbers in both diagonals is the same.

Magic Square
Activity
Each row, column and diagonal should produce the same sum.

Magic Square Puzzle
Activity
Find all of the possible ways of making the magic total from the numbers in this four by four magic square.

Make 1000
Activity
Use the numbers on the strange calculator to make a total of 1000

Make an expression
Activity
Use the digits given to form an expression equivalent to the given total.

Masad
Activity
For each pair of numbers subtract the sum from the product then divide the result by 20 without a calculator.

Mixpressions
Activity
Arrange the cards to create a valid mathematical statement.

Multi-step Problems
Activity
Solve multi-step problems in contexts, deciding which operations and methods to use and why.

Nine Nine Nine
Activity
Use the digits 1 to 9 to make three 3 digit numbers which add up to 999.

No Partner
Activity
Find which numbers in a given list do not combine with other numbers on the list to make a given sum.

Number Crunch Saga
Activity
A lively numeracy game requiring you to align three numbers to create the given target sum or product.

Number Skills Inventory
Activity
A checklist of basic numeracy techniques that every pupil should know.

Numerate
Activity
Earn points by creating equations on the grid in this game of equations.

Numskull
Activity
Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.

One Digit Only
Activity
Find expressions using only one digit which equal the given targets.

Pentadd Quiz
Activity
Find the five numbers which when added or multiplied together in pairs to produce the given sums or products.

Pentransum
Activity
Mathematical questions with five possible answers. If you get 20 correct you can add your own question to the database.

Plane Numbers
Activity
Arrange numbers on the plane shaped grid to produce the given totals

Plus
Activity
A number arranging puzzle with seven levels of challenge.

Powten
Activity
Practise multiplying and dividing by powers of ten without using a calculator.

Pyramid Puzzle
Activity
Numbers in the bricks are found by adding the two bricks immediately below together. Can you achieve the given target?

Quick
Activity
Can you multiply a number by 1001 in your head? This exercise provides practice in this and other similar challenges.

Roman Numerals Quiz
Activity
This online, self marking quiz tests your ability to convert Roman numerals.

Six Discrimination
Activity
The six button has dropped off! How could these calculations be done using this calculator?

Six Keys
Activity
Use just six keys on your calculator to make a given total. How many different ways can it be done?

Spinsum
Activity
Arrange the numbers on the squares so that the totals along each line of three squares are equal.

Stamp Sticking
Activity
Drag stamps onto the envelopes to make the exact postage as shown at the top left of each envelope.

Standard Form
Activity
A self marking exercise on standard form.

Suko Sujiko
Activity
Interactive number-based logic puzzles similar to those featuring in daily newspapers.

Sum Game
Activity
A game against the clock to find the numbers which add up to the target number.

TablesMaster
Activity
How fast can you answer times table questions? This activity provides feedback to help you improve.

The Miller's Puzzle
Activity
This is an interactive version of the puzzle described by Henry Ernest Dudeney in The Canterbury Puzzles

Think of a Number
Activity
Ten students think of a number then perform various operations on that number. You have to find what the original numbers were.

Times Tables
Activity
A collection of activities to help you learn your times tables in only 5 days.

Tools
Activity
In how many different ways can the numbers be arranged to give the same totals?

Triplets
Activity
Find as many sets of three of the available numbers as possible which add up to the given total.

Tug of War
Activity
A game for two players or teams testing their speedy reactions to mental arithmetic questions.

Unmagic Square
Activity
Like the magic square but all of the totals should be different.

Zygo
Activity
Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.

Investigations

Aunt Sophie's Post Office
Activity
Investigate the ways of making up various postage amounts using 3p and 8p stamps. An online stamp calculator is provided for you to check your working.

Decimal Products
Activity
Find two decimal numbers that add up to exactly one. What is the product of these two decimals?

The Four Rules
Activity
See if you can make all of the numbers from 0 to 10 using four threes

Videos

BIDMAS Misconception
Activity
This Maths problem went viral on Twitter and there has been debate about the answer. Presh explains why one interpretation is considered correct.

Multiplication
Activity
A different way to multiply together numbers. Can you see how it works?

Multiplication Song
Activity
Wako shows how to multiply 47 by 83 in his crazy cartoon singing way!

Visual Aids

Countdown
Activity
How close can you get to the target by making a calculation out of the five numbers given?

Formal Written Methods
Activity
Examples of formal written methods for addition, subtraction, multiplication and division.

Just In Time
Activity
Every 10 seconds a new calculation appears on the screen: A dynamic visual aid.

Maths Bingo
Activity
This application will pick the bingo numbers for you and present each of the numbers as a mathematical expression.

Quickulations
Activity
A mental arithmetic visual aid that displays random calculations then after a few seconds displays the answers.

Word Sums Guide
Activity
A step by step guide showing how to solve a Word Sum where each letter stands for a different digit.

Starters

Starter
5.5 Times Table
Write out the 5.5 times table as far as possible.

Starter
Abundant Buses
A game based around the concept of abundant numbers.

Starter
Add Quickulations
Calculations appear on the screen every few seconds. This mental arithmetic starter provides pace to the start of the Maths lesson.

Starter
Addle
Arrange the numbers 1 to 14 in the circles so that the sums are correct.

Starter
All for 100
Can you write an expression for 100 which uses all the digits 1 to 9?

Starter
All The Nines
Add up all the numbers in the nine times table.

Starter
Arithmagons
This lesson starter requires pupils to find the missing numbers in this partly completed arithmagon puzzle.

Starter
Aunt Sophie's Post Office
Work out the number of stamps needed to post a parcel.

Starter
Big Order
Estimate or calculate then put the large numbers in order of size.

Starter
Blots
The calculations are obscured by ink blots. What do you think the calculations would look like if there were no blots?

Starter
Broken Calculator
Use only the 1, 5 and 0 keys on a calculator to make given totals.

Starter
Broken Calculator (2 and 3)
Make the numbers 1 to 10 using only the keys on the broken calculator.

Starter
Broken Calculator (3 and 4)
Some keys are missing from this calculator. Just how useful is it?

Starter
Broken Calculator (4 and 5)
Which numbers can be made with the buttons which have not yet dropped off this calculator?

Starter
Calc-A-Hundred
A game for two players requiring a calculator and thinking skills.

Starter
Calculator Nim
A game in which players take turns to add a single-digit number to what is already in the calculator. The winner is the player who makes the display show 30.

Starter
ClockEquate
Can you use the digits on the left of this clock along with any mathematical operations to equal the digits on the right?

Starter
Clouds
Some calculations are partly obscured. Work out what those calculations might be.

Starter
Consecutive
Three consecutive numbers multiplied together give a given product. Students are asked to figure out what the numbers are.

Starter
Consecy Brothers
Which three consecutive numbers multiplied together give the given answer.

Starter
Countdown
How close can you get to the target by making a calculation from the five numbers given?

Starter
Cracked Clock
How did the clock break if the numbers on each of the pieces added up to the same total?

Starter
Cracker Joke
Answer the mental arithmetic questions then convert the answers to letters to find the joke.

Starter
Digivide
Arrange the digits 1 to 6 to make a three digit number divided by a two digit number giving a one digit answer.

Starter
Dimidiate
Arrange the digits from 1 to 9 in alphabetical order. How many times can this number be halved?

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Division Quickulations
Random division calculations appear on screen every few seconds.

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Double Trouble
Begin with one, double it, double it again and so on. How many numbers in this sequence can you write down before the register has been called?

Starter
Eleventh of the Eleventh
Practise multiplying and dividing by eleven in your head.

Starter
Faulty Button
Find out which of the calculator keys is faulty from the given information. A mathematical puzzle requiring good problem solving strategies.

Starter
Firewords
Find words which cost 100p if A costs 1p, B costs 2p etc

Starter
Flabbergasted
If each number in a sequence must be a factor or multiple of the previous number what is the longest sequence that can be made from the given numbers?

Starter
Flowchart
Use the flowchart to generate a sequence of numbers. Which number will reach 1 the fastest?

Starter
Fly Catching
Find which whole number divided by another whole number gives the answer: 1.090909091

Starter
For Starters
Four calculations. Add up the answers.

Starter
For Thought
Add up the answers to the four real life questions.

Starter
Four Gone
An activity involving a broken calculator which is missing the four button. Can you evaluate the given expressions without using the four?

Starter
Four Make 999
Find four numbers from those given that add up to 999. How many different sets of four numbers can be found?

Starter
Four problems
For mathematical questions to get everyone thinking at the beginning of the lesson..

Starter
Four to Seven
Which of the numbers from one to twenty can you make with the digits 4, 5, 6 and 7?

Starter
Four's Independence
A clock face containing only the number 4. Can you make a clock face containing any other single number?

Starter
Half a Dozen
Six calculations to complete without a calculator.

Starter
Half a Pound
If A costs 1p, B costs 2p, etc can you find a word which costs exactly 50p?

Starter
Half and Half
Start with 100. Halve it to get 50. Halve that to get 25. Continue as far as possible.

Starter
Halve it
Start with 512. Halve it to get 256. Halve it to get 128. Continue as far as possible.

Starter
Happy Numbers
To find out whether a number is happy or not, square each of its digits, add the answers and repeat. If you end up with 1 the number is happy! How many other happy numbers can you find?

Starter
Hole in One
If six girls can plant 90 trees in a day. How many trees can ten girls plant in a day? The unitary method.

Starter
How Do You Do?
A little lateral thinking will help you solve this number puzzle.

Starter
How many of Each?
Pens cost 12p each, Pencils cost 9p each, Richard spent 72p altogether. How many pens and pencils did he buy?

Starter
Inbetween Table
Write down as many multiples of 3.5 as possible in 3.5 minutes.

Starter
Jeopardy
Loosely based on the famous television show, how many questions cn you come up with for a given answer?

Starter
Justundera Quid
Find a word whose letters would cost exactly ninety nine pence.

Starter
Khmer's Homework
Check a student's homework. If you find any of the answers are wrong write down a sentence or two explaining what he did wrong.

Starter
Know Weigh
Find the weight of one cuboid (by division) of each colour then add your answers together.

Starter
Letter Clue Calculations
Work out what the calculations might be from the letter clues.

Starter
Lucky Numbers
Arrange the numbers so that the totals of the three numbers along any line are the same.

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Maggots
Do as many of the calculations as possible before the maggots infest!

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Magic Square
Arrange the numbers 1 to 9 in a 3 by 3 grid to form a magic square.

Starter
May Day
Add together the dates of all the Thursdays in May this year. Which day sum is largest?

Starter
Mental Maths Quiz
A traditional twenty question mental arithmetic test presented as a PowerPoint presentation.

Starter
Mental Maths Test
The starter is a PowerPoint file containing a twenty question mental arithmetic test. It will advance from one question to the next automatically.

Starter
Meta Products
Which numbers when multiplied by the number of letters in the word(s) of the number give square numbers?

Starter
Mirror Maths
The bottom half of some symmetrical calculations are shown above. Can you work out the answers?

Starter
Missing digits
Work out what the missing digits in the calculations are.

Starter
Missing Operations
Each red box represents a missing operation (+, -, x or ÷). Can you work out what they are?

Starter
Missing Pound
A puzzle about a restaurant bill. Exactly where did the missing pound go?

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Ms Tayke
How many times can you take one number from another?

Starter
Multiplication Grid
Copy and complete the multiplication grid. The higher levels include negative numbers.

Starter
Multiply Quickulations
Random multiplications appear on screen every few seconds.

Starter
Nine Digit Sum
Arrange the digits one to nine to make a correct addition calculation.

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Nine Nine Nine
Arrange the numbers 1-9 to make three 3 digit numbers that add up to 999.

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No Partner
Find which numbers in a given list do not combine with other numbers on the list to make a given sum.

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Noodlewhack
Divide one whole number by another on your calculator. If the answer has one digit repeated but no other digits you have a Noodlewhack.

Starter
On The Double
Double the numbers given in the table.

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One Digit 100
How many ways can you write an expression for 100 which only uses the same digit repeated and any operations?

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Only One Number
Find other numbers that can be changed to 1 on a calculator using only the 4 key and any operation.

Starter
Outnumbered
Which group of four numbers, arranged in a square, has the largest total?

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Pears Make Squares
Find three numbers such that each pair of numbers adds up to a square number.

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Pentadd
Five numbers are added together in pairs and the sums shown. What might the five numbers be?

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PercenTable
Complete the table by calculating common percentages without using a calculator.

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Plane Numbers
Arrange numbers on the plane shaped grid to produce the given totals

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Planet Numpair
The sum and product are given, can you find the two numbers?

Starter
Plus
A number puzzle suitable for children with a wide range of abilities.

Starter
Plus Four
Work out the answers to the four given sums then add the answers together.

Starter
Positions Please
Stand at the point between the classroom walls to represent a given number.

Starter
Product Practice
Work out the answers to the given calculations then add the answers together. There are three different levels of difficulty.

Starter
Puddings
Complete the calculations with the weights of the puddings

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Pyramid Puzzle
Arrange numbers at the bottom of the pyramid which will give the largest total at the top.

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Quick
Develop a quick way of multiplying by 1001.

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Quotients
Work out the answers to the given division calculations then add the answers together.

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Recurring Decimal
Use your calculator to find which whole number divided by another whole number gives the answer 1.36363636

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Refreshing Revision
It is called Refreshing Revision because every time you refresh the page you get different revision questions.

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Render Digitful
Find a calculation for the current year which uses all of the digits 1 to 9.

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Roman Numerals
Learn a very different method for writing numbers using Roman numerals.

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Roundabout
Go around the roundabout performing each of the operations. Which starting point gives the largest answer?

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Rounding 1dp
Round off the given numbers to 1 decimal place then add the answers together.

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Rounding 2dp
Round off the given numbers to 2 decimal places then add the answers together.

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Rounding Whole
Round off the given numbers to the nearest whole number then add the answers together.

Starter
Route to Las Vegas
Work out the cheapest way from Los Angeles to Las Vegas by choosing the best route and adding up the given numbers.

Starter
Scaramouche
Can you work out from the five clues given what the mystery number is?

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Second Holiday
Estimate then work out the period of time equal to the given number of seconds.

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Shadow Sums
Make sums from the three digit numbers given.

Starter
Sid's Schemes
Work out which is the best scheme for Sid to choose for his summer bonus. One scheme involves a common misconception about percentages.

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Sign Sequences
Continue the sequences if you can work out the rule.

Starter
Six Discrimination
An activity involving a calculator which is missing the six button. Can you evaluate the given expressions without using the six?

Starter
Six of the Best
Six calculations to perform without a calculator.

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Spinsum
Arrange the numbers on the grid of squares so that the totals along each line of three squares are equal.

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Square Pairs
Arrange the numbered trees so that adjacent sums are square numbers.

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Square Thinkers
Can you find three square numbers where the third is the sum of the first two?

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Stacks of Sums
Write down many different types of calculations which give a particular answer.

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Stencils
Which of the coloured stencils will fit over the numbered card to produce correct calculations?

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Strange Tables
A challenge to learn an unfamiliar times table involving decimals.

Starter
Student Loans
Six students borrow £5000 to help pay for their university course. Calculate how much each student will have to pay back to the lender.

Starter
Subtract Quickulations
Calculations appear on the screen every 10 seconds.

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Subtract Quickulations
Calculations appear on the screen every few seconds.

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Sudoku Sum
What is the sum of the numbers missing from the given Sudoku puzzle?

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Sum Square
Arrange the numbers one to eight into the calculations to make the totals correct..

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Sum Story
Make up real life stories for the given calculations.

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Table Legs
Learn an unusual times table from the strategic finger moving up and down the 'Table Leg'!

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Targets
Use the given numbers to produce a calculation to get as close as possible to the given target.

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Tasty Take-Aways
Four subtractions to be done without a calculator. The answers are then to be added together.

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Team Age
Work out who is in which team from the information given.

Starter
Three Make 1000
Find three numbers from those given that add up to 1000. How many different sets of three numbers can be found?

Starter
Three Wise Gifts
Find as many sets of three of the available numbers as possible which add up to the given total.

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Ticker News
A Think Of A Number problem presented as a news ticker.

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Time Trials
You have 10 seconds to answer each of the mental arithmetic questions.

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Timed Tables
How fast can you answer 24 mixed times tables questions?

Starter
Tools
Place the numbers on the triangle so that the totals along each of the sides are equal.

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Triple Totals
Complete the sums using only the given numbers then check your calculations are correct.

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Triplets
Find as many sets of three of the available numbers as possible which add up to the given total.

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Twin Totals
Find the two calculations that give the same total.

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Two Numbers
Find the two numbers whose sum and product are given.

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Two Thirds
Make a poster showing a variety of calculations that give the answer two thirds.

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Unmagic Square
Arrange the numbers 1 to 9 in a 3 by 3 grid so that none of the line totals are the same.

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Use the digits
Create a calculation with the given digits to equal a given target.

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Verruca Value
The Verruca Value of a word is the number of vowels multiplied by the number of consonants. How many words can you find with Verruca Value of 24?

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Warm Up
Four quick Maths questions to warm up the brain.

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What are they?
A starter about sums, products, differences, ratios, square and prime numbers.

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Word Difference
Can you find substitutions which will make the word sum correct?

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Word Sum
Each letter stands for a different digit. Can you make sense of word sum?

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Wrong Way Round
Find calculations which written back to front give the same answer.

214 items are currently in this category.

Teachers might find the complete Arithmetic Topic List useful.

The ability to perform mathematical calculations is still very important despite our hi-tech environment. Good numeracy skills support the understanding of more advanced mathematical concepts at all levels. Mathematicians still consider mastery of the manual algorithms to be a necessary foundation for the study of algebra and computer science.

Pupils should have a good grasp of the meaning of numbers and use their understanding of place value to multiply and divide whole numbers and fractions. They should be able to order, add and subtract negative numbers in context. They should use all four operations with decimals rounding answers where required. They should be able to solve simple problems involving ratio and direct proportion and calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate.

See also the Mental Methods topic and our Number Skills Inventory.


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