Transum Maths Software


There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Arithmetic. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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Arithmetic 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.

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

Addle: 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 numbers in the nine times table.

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.

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

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. Students 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.

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: Practise multiplying and dividing by eleven in your head.

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 calculations. Add up the answers.

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

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?

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.

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

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

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

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

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: Work out what the missing digits in the calculations are.

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

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?

Multiplication Grid: 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.

Pentadd: 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.

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?

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

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

Positions Please: 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: Work out the answers to the given division calculations then add the answers together.

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.

Roundabout: 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.

Shadow Sums: 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?

Three Wise Gifts: 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.

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

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

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?

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

Weather Report: Find five 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 word sum?

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


Small images of these Starters | | |  Complete Index of Starters

Featured Activity

Car Park Puzzle

Car Park Puzzle

Can you get your car out of the very crowded car park by moving other cars forwards or backwards? There are five levels of increasing difficulty and the interactive interface makes this a fun problem solving exercise.



Comment recorded on the 10 April 'Starter of the Day' page by Transum, :

"Sorry Mike, because some of the starters link to live data on the Internet there is no CD version. Thanks for your comments."


The ability to perform mathematical calculations is still very important and supports the understanding of Mathematics. Mathematicians still consider mastery of the manual algorithms to be a necessary foundation for the study of algebra and computer science.

See also the "Mental Methods" Starters.

The English National Curriculum states that at Level 5 "Pupils use their understanding of place value to multiply and divide whole numbers and decimals. They order, add and subtract negative numbers in context. They use all four operations with decimals to two places. They solve simple problems involving ratio and direct proportion. They calculate fractional or percentage parts of quantities and measurements, using a calculator where appropriate."

Arithmetic Teacher Resources:

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

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

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.

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

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

Arithmetic Activities:

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

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

Arithmagons: An extensive collection of Arithmagons arranged in levels according to their features. Find the missing numbers in these online, self-checking exercises and discover the wonders of Arithmagons.

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

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

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

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

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

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

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

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

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?

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

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

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

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.

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

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

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

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

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

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

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

Heptaphobia Research: 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?: Work out how many items were bought from the information given.

Know Your Place: 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.

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

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.

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

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.

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

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.

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

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

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.

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

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

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.

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

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

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

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

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

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

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.

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

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

Finally there is Topic Test, a set of 10 randomly chosen, multiple choice questions suggested by people from around the world.

Arithmetic 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.

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?

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

Arithmetic Videos:

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.

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!

Arithmetic Worksheets/Printables:

Game Board for 23 or Bust: A printable game board for 23 or Bust. Choose your own object to serve as the lifesaver such as a pencil sharpener, a rubber or a coin.

Maggots Template: A blank Maggots screen designed for pupils to record their answers on for the Maggots Starter activity.

Missing Operations Worksheet: Each red box represents a missing operation (plus, minus, times or divide). Can you work out what they are?

Pyramid Worksheet: Put the numbers 1 to 5 in the bottom row of the pyramid then each other brick is the sum of the two below.

Strategy for 23 or Bust: A printable worksheet containing a table to be filled in with the best moves for the game 23 or Bust.

Take Sides Questions: Thirty pairs of numbers or calculations. Which one of the pair is the largest?

Arithmetic External Links:

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Circle Equations

Circle Equations

Recognise and use the equation of a circle with centre at the origin and the equation of a tangent to a circle. So far this activity has been accessed 89 times and it is ready for you to enjoy!



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