# Arithmetic

## Activities

Think of a Number

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

A self-marking exercise on addition with increasing levels of difficulty.

Fifteen

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

Basic Subtraction

A self-marking exercise on subtraction with increasing levels of difficulty.

Times Tables

Fast Factors

Match the numbers with the answer to the times table. A timed activity to improve instant recall of key table facts.

BIDMAS

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

Basic Multiplication

A self-marking exercise on multiplication with increasing levels of difficulty.

BIDMAS Game

An online interactive game celebrating the order of mathematical operations.

Basic Division

A self-marking exercise on dividing numbers of up to four digits by one or two-digit whole numbers using the formal written methods of short and long division

23 or Bust

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

Arrange the numbers from 1 to 14 in the spaces to make the sums correct. How fast can you do it?

Four Sum

Arrange the given number tiles to make two 2 digit numbers that add up to the given total.

Clouds

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

Brainbox

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

Broken Calculator

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

Stepwise Sums

Arrange the numbers one to nine on the stairs to obtain the given sums.

Chain Challenge

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

Column Method for Multiplication

Practise your multiplication skills with this exercise that already has the calculation set out for you.

Multitude

Arrange the given digits to make three numbers such that the third is the product of the first and the second.

Palindrome Products

Use long multiplication and pattern spotting to fill in the table with palindromic products.

Nine Digits

Arrange the given digits to make three numbers such that two of them add up to the third.

Long Division

Practise long division with this exercise that already has the calculation set out for you.

Beat The Clock

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

Discombobulated

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

Divides Exactly

Find which divisions result in whole number quotients. A mental arithmetic speed challenge.

Doubling Quiz

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

Equatero

Find the expression from a series of guesses and clues.

Arithmagons

Find the missing numbers in these triangular, self-checking puzzles and discover the wonders of these fascinating structures.

Decimal Plus

Practise mental and written methods for adding and subtracting decimal numbers.

Decimal Times

Practise mental and written methods for multiplying and dividing decimal numbers.

Furthermore

A self-marking exercise on counting forwards or backwards in tens, hundreds, thousands etc.

How Many of Each?

Work out how many items were bought from the information given.

Yohaku Puzzles

Fill in the blank spaces so that the cells give the sum or the product shown in each row and column.

Without a calculator perform some calculations requiring a knowledge of place value.

Largest Product

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

Letter Sums

Use your mental arithmetic skills to add up the values of the letters in these mathematical words.

Ludicross

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

Magic Square

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

Make 1000

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

Make an expression

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

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

Missing Operations Exercise

Each box represents a missing operation (add, subtract, multiply or divide). What are they?

Mixpressions

Arrange the cards to create a valid mathematical statement.

Multi-step Problems

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

Nine Nine Nine

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

No Partner

Find which numbers in a given list do not combine with other numbers on the list to make a given sum.

Numbasics

A daily workout strengthening your ability to do the basic mathematical operations efficiently.

Centexpression

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

Number Skills Inventory

A checklist of basic numeracy techniques that every pupil should know.

Standard Form

Test your understanding of standard form (scientific notation) with this self-marking quiz.

Sum of Three Palindromes

Every whole number can be expressed as the sum of three palindromic numbers like this...

Numerate

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

Numskull

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

One Digit Only

Find expressions using only one digit which equal the given targets.

Partial Pyramids

Calculate the missing numbers in these partly completed pyramid puzzles.

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

Pentransum

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

Pick Up Sticks

If you were to pick up the sticks from this pile so that you were always removing the top stick what calculation would you create?

Plane Numbers

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

Plus

A number arranging puzzle with seven levels of challenge.

Powten

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

Pyramid Puzzle

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

Quick

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

Remainder Race

A game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number.

Roman Numerals Quiz

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

Six Keys

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

Short Division

Practise short division with this exercise that already has the calculation set out for you.

Six Discrimination

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

Spinsum

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

Stamp Sticking

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

Suko Sujiko

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

Bidmaze

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

Sum Game

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

Partition Clues

Partition numbers in different ways according to the clues given. The higher levels are quite hard!

TablesMaster

Digital Darts

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

The Miller's Puzzle

This is an interactive version of the puzzle described by Henry Ernest Dudeney in The Canterbury Puzzles

Tools

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

Triplets

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

Tug of War

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

Perfect Magic Square

Arrange the sixteen numbers on the four by four grid so that groups of four numbers in a pattern add up to the same total.

Unmagic Square

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

Which Operation?

Decide which mathematical operation is required then use it to find the answers.

Zygo

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

Magic Square Puzzle

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

Digivide

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

Heptaphobia Research

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

## Investigations

Aunt Sophie's Post Office

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.

The Four Rules

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

Cosmic Redshift

Investigate the number found by performing an algorithm on a three digit number.

Decimal Products

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

## Videos

This is the main Transum help video on Arithmetic.

A reminder of how to add two or more numbers using the column method.

BIDMAS Video

A reminder of the order of operations often referred to as BIDMAS, BODMAS or PEMDAS.

Division Video

A reminder of how to divide one number into another using short or long division.

Misconceptions

Some people have some strange ideas about multiplication and division.

Multiplication

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

Multiplication Methods

Can you understand the explanation of these multiplication methods even though you may not speak the teacher's language?

Multiplication Song

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

Multiplication Video

A reminder of how to multiply two numbers using the column method or long multiplication.

BIDMAS Misconception

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

Subtraction Video

A reminder of how to subtract one number from another using the column method.

## Visual Aids

Formal Written Methods

Examples of formal written methods for addition, subtraction, multiplication and division.

Column Method for Multiplication

Practise your multiplication skills with this exercise that already has the calculation set out for you.

Countdown

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

Long Division

Practise long division with this exercise that already has the calculation set out for you.

Just In Time

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

Maths Bingo

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

Divisibility Tests 2-12

A visual aid designed to be projected in the classroom. Here you can find the quick ways of telling whether a number is exactly divisible by the numbers two to twelve.

Quickulations

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

Short Division

Practise short division with this exercise that already has the calculation set out for you.

Word Sums Guide

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

## Starters

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

A Thousand and One
Develop a quick way of mentally multiplying any number by 1001.

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

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

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

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

All The Nines
Add up all the multiples of nine in an elegant way.

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

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

Balloon Bursting Buttons
Use only the 1, 5 and 0 keys on a calculator to make given totals.

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

Cunning Code
Decode the message by doing the calculations given for each letter.

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

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

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

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?

Eleventh of the Eleventh

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

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

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?

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

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

For Starters
Four problems involving addition, subtraction, multiplication and division

For Thought

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

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

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

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

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

Half a Dozen
Six calculations to complete without a calculator.

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

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

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

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?

How Do You Do?

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

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

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

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

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.

Know Weigh

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

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

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

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

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

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.

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

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

Missing digits
Find which digits are missing from the randomly generated calculations.

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

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

Multi-Toil Panic
Copy and complete the multiplication grid. The higher levels include negative numbers.

Multiply Quickulations
Random multiplications appear on screen every few seconds.

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

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

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

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.

On The Double
Double the numbers given in the table.

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

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

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

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

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

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

Pipeline Puzzle
Arrange the numbers so that the totals of the three numbers along any pipe are the same.

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

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

Plant More Trees
If six girls can plant 90 trees in a day. How many trees can ten girls plant in a day? The unitary method.

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

Plus Four

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

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

Puddings
Complete the calculations with the weights of the puddings

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

Quotients

Recurring Decimal
Use your calculator to find which whole number divided by another whole number gives a recurring decimal.

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

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

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

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

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

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

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

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.

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

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

Make sums from the three digit numbers given.

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.

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

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

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

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

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

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

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

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

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

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.

Subtract Quickulations
Calculations appear on the screen every few seconds.

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

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

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

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

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

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

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

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

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

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

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

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

Tool Triangle
Place the numbers on the triangle so that the totals along each of the sides are equal.

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

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

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

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

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

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

Weather Report
Find five different integers that multiply together to give a product of twelve.

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

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

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

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

240 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.