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S = Starter of the Day A = Advanced Starter R = Riddle

Title | Description | |
---|---|---|

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

S | 9:50 Puzzle | A little lateral thinking might help you solve this puzzle. |

S | A Number | When written as a word or words what is the smallest positive whole number containing the letter 'a'? |

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

S | A Very Strange Game | Four different actions depending on the number which appears. |

S | Absolutely Everyone | A choice of questions about the current world population which is constantly changing. |

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

S | Add 'em | Add up a sequence of consecutive numbers. Can you find a quick way to do it? |

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

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

S | Air Traffic Control | Work out which aircraft are in danger of colliding from their positions and direction of travel. An exercise in understanding bearings. |

A | Algebraic Product | Finding the value of the expression is easier than you think! |

S | All for 100 | Can you write an ex |

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

S | Alphanumbetical | A challenge to find the number which when written as a word has all the letters in alphabetical order. |

S | Anagrams | Can you un-jumble these mathematical words? |

S | Analogies | Make more of analogies to help remember mathematical concepts. |

S | Ancient Mysteries | This activity requires students to memorise fifteen numbers in a three by five grid. |

S | Angle Estimates | Estimate the sizes of each of the angles then add your estimates together. |

A | Angle Thinking | Find the range of possible angles, x, for which tan x > cos x > sin x |

R | Animals at the Oasis | Calculate the number of animals gathered at the oasis according to the clues. |

S | Area Two | How many different shapes with an area of 2 square units can you make by joining dots on this grid with straight lines? |

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

R | Audible Riddles | Listen to these audible mathematical riddles and use your ingenuity to figure out the answers. |

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

S | Aunty Dotty | A real life situation requiring the division an amount of money according to a given ratio. |

A | Average Cycling Speed | Work out the average speed of two journeys. The obvious answer is not the correct answer. |

S | Average Smile | Calculate the mean, median and range of the given scores. |

A | Back To The Factory | Find all the numbers below 1000 which have exactly 20 factors |

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

A | Barmy BIDMAS | A misleading way of stating the answer to a simple calculation. |

A | Bertrand's Box Paradox | Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in 1889 |

A | Best Dice | Which of the unusual dice would you choose to give you the best chance of winning the prize? |

A | Biased Coin | Use a biased coin to obtain a fair result |

S | Big Bieber | If the dimensions of an object double, its volume increases by a factor of eight. |

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

S | Birthday Clues | Work out the date Will was born by answering some number questions. |

S | Bizarre Triangle | By how much would the area of this triangle increase if its base was enlarged to 8cm? |

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

S | Book Worm | Work out the distance the book worm needs to eat through to get to the back cover of the last book. |

S | Boxing Day | Work out the contents and the cost of the Christmas boxes from the given clues. |

S | Breathe Easily | How many breaths have you taken in your lifetime? |

S | Bridge Crossing | The classic puzzle of finding a route which crosses each bridge once. |

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

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

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

S | BTS | You have four minutes to write down as many equations as you can involving B, T and S. |

R | Bus Driver | A riddle about a bus driver on quite a busy route. |

S | Bus Stop | How many different ways can four people stand in line? |

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

S | 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. |

R | Calendar Clue | Find the murderer from the clue written on the calendar |

R | Calendar Riddle | Work out the date of my birthday from the clues in rhyme. |

S | Can You Decide? | Recognise odd, even, square, prime and triangular numbers. |

A | Car Inequalities | Solve three simultaneous inequalities to find how many cars I own. |

S | Cars | Calculate the total cost of four cars from the information given. |

A | Charging Rhinos | Find the easy way to solve this kinematics problem involving a fly and two rhinos. |

A | Cheryl's Birthday | Use a process of elimination to work out the correct date from the clues given. |

S | Chin-Ups | Work out the number of chin ups the characters do on the last day of the week give information about averages. |

S | Christmas Bells | If all the bells ring together at noon, at what time will they next all ring together? This problem requires the use of LCM. |

S | Christmas Eve | Is there a pattern in the number of palindromic numbers to be found less than powers of 10? |

S | Christmas Eve Snow | Each different letter stands for a different digit. Can you make sense of this word sum? |

S | Christmas Ornaments | A Maths Starter activity requiring students to arrange Christmas ornaments in a square box. |

S | Christmas Presents | Work out the total cost of five Christmas presents from the information given. |

S | Christmas Tables | Which of the two shapes has the largest area? You will be surprised! |

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

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

S | Coins in Envelopes | Fifteen pennies are placed in four envelopes and the envelopes are sealed. It is possible to pay someone any amount from 1p to 15p by giving them one or more envelopes. |

S | Coins On The Table | A puzzle about the number of coins on a table given information about fractions of them. |

S | Coloured Sheep | What is the probability of picking a red sheep from the sheep in the field? |

R | Company or Crowd? | If two's company and three's a crowd, what's four and five? |

S | Connecting Rules | Give 20 rules connecting x and y given their values. |

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

S | Consecutive Squares | What do you notice about the difference between the squares of consecutive numbers? |

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

A | Coordinate Distance | Find k given that(-2,k) is 13 units away from (10,9) |

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

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

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

S | Cross Perimeter | Calculate the distance around the given shape |

R | Cube Ages | Calculate the mean age of the two fathers and two sons with the given clues. |

S | Cube Calendar | What numbers should be on each face of the two cubes to make this perpetual calendar? |

A | Cuboid | Find the dimensions of a cuboid matching the description given |

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

A | Curved Angles | How many right angles are there in a semicircle? |

S | Dancing | Work out how many people were at the dance from the clues given. |

S | Dice Nets | Determine whether the given nets would fold to produce a dice. |

S | Dice Reflections | A dice is reflected in two mirrors. What numbers can be seen? |

A | Difference Cipher | Find the mathematical word from the cipher |

S | Digital Lights | Questions about the Small LEDs used to make up the digits on a calculator display. |

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

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

S | Divided Age | How old is a person if when her age is divided by certain numbers, the calculator display ending are as shown. |

A | Divisible by 11 | Can you prove that a three digit number whose first and third digits add up to the value of the second digit must be divisible by eleven? |

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

R | Doctor's Son | The doctor's son's age does not add up! |

R | Does not add up! | Why would eight and five add up to one? |

S | Don't Touch! | A number placing puzzle which, when solved, raises the notion of proof. |

A | Double or Half? | At ten percent change per day is doubling achieved faster than halving? |

S | 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? |

S | Eleven Plus Two | Rearrange the letters in the ex |

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

S | Estimating | Estimate the lengths of four lines then add your answers together. |

S | Estimating Percentages | Estimate the percentages of full circles and rectangles the sectors represent. |

A | Exceeds by 99 | Find the number whose double exceeds its half by exactly 99. |

S | Exponential Error | This lesson starter presents a number of statements about indices and pupils are asked if they can spot the mistake. |

S | Faces and Edges | Find the number of faces, edges and vertices on some familiar objects. |

S | Factuples | Spot the factors and the multiples amongst the numbers in the grid. |

S | Family Buses | Fit families onto eleven seater buses without splitting up the families. |

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

A | Fence Optimisation | Find the length of a rectangle enclosing the largest possible area. |

A | Fermi Problem | The classic Fermi problem using standard estimation techniques |

S | Figuratively Speaking | Write the numbers written as words using digits. |

A | Find The Radius | Find the radius of the circle from the small amount of information provided. |

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

S | Five Digits | Five digits have the same mean, median, mode and range. |

S | 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? |

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

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

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

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

S | Four Factors | Find four single digit numbers that multiply together to give 120. How many different ways are there of answering this question? |

A | Four Fraction Division | Explain why the answer to a series of fraction divisions is a whole number. |

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

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

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

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

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

S | Fractangle | Can you see what fractions of the shapes have been shaded? It is not as difficult as it first appears. |

S | Fraction Order | Arrange the fractions and decimals in order from smallest to largest. |

S | Fractions Decimals Percentages | Convert fractions to decimals, decimals to percentages and percentages to fractions. |

R | Fractions of Animals | What is three sevenths of a chicken, two thirds of a cat and 50% of a goat? |

S | Freemason's Cipher | Find symmetric words in this ancient cipher. |

R | Fried Eggs | How many eggs remain after the events that took place in the kitchen? |

R | Fruit Snacks | Work out the numbers of each type of fruit bought for snacks |

A | GDC Challenge | Produce the given graph on a graphic display calculator |

A | Geometry Snack | Find the value of the marked angle in this diagram from the book Geometry Snacks |

S | Get A Wiggle On | A mixture of calculations to get your brain working at the start of a mathematics lesson. |

S | Giraffe | The height of this giraffe is three and a half metres plus half of its height. How tall is the giraffe? |

S | Goat Grazing | Find the loci of the goat's position as it eats the grass while tethered to the rope. |

A | Grandmother | How far would grandma have travelled after a suitably large number of days given her walking regime? |

S | Graph Picture | Plot the given coordinates then join them up to form a picture. |

R | Growing Fast | How can it be that Percy will be 16 next year when he was only 13 the day before yesterday? |

S | Guitar For Sale | A question about the profit made when buying and selling a guitar. |

S | Half a Dozen | Six calculations to complete without a calculator. |

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

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

S | Half Hearted | Find the number which when added to the top (numerator) and bottom (denominator) of each fraction make it equivalent to one half. |

S | Halloween | Five problems with a Halloween theme. |

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

A | Hands Together | The hands of a clock are together at midnight. At what time are they next together? |

S | Handshakes | If all the students in this room shook hands with each other, how many handshakes would there be altogether? |

S | Happy New Year | Work out the date for various given amounts of time after the beginning of the year. |

S | 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? |

A | HCF and LCM given | If given the HCF, LCM and the smaller of two numbers can you find the other? |

S | Hexagon | On a full page in the back of your exercise book draw a perfectly regular hexagon. |

S | High Interest | Finding a good personal loan requires an ability to calculate percentage and this page provides some practice. |

S | Hold 'Em Up! | Everyone in the class holds up an item to show which is the correct answer to the multiple choice question. |

S | Hot Estimates | Estimate the number of chillies in the photograph. |

S | Hot Numbers | Move the numbered cards to form five 2 digit numbers which are all multiples of three. |

S | Hot Summer Test | Write out a large times table. Get as far as possible in 5 minutes. |

S | Hotel Digital | A puzzle about the lifts in a hotel which serve floors based on the day of the week. |

S | Hotel Sumview | Can you work out what rooms at the hotel the family booked to produce the given bill? |

S | Hours To Go | How many full hours are left till the end of the year? |

S | House Numbers | The numbers on five houses next to each other add up to 70. What are those five numbers? |

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

A | How Many Left Handers? | Work out the number of members if the probability of left-handed members being randomly selected is given. |

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

S | How Many Rectangles? | How many rectangles can you find in this pattern? Can you come up with a systematic method for counting them all? |

S | How Many Squares? 1 | Work out how many squares are there altogether in the given pattern then tackle the chess board. |

S | How Many Squares? 2 | How many squares can be found by joining four dots on the grid? |

S | How Many Triangles? 1 | How many Triangles can you find in the diagram? |

S | How Many Triangles? 2 | How many triangles are hidden in the pattern? What strategy might you use to count them all to ensure you don't miss any out? |

S | How Many Triangles? 3 | Find a systematic way of counting the number of triangles in the given diagram. |

A | Hundred and Fifty Percent | Divide 110 into two parts so that the larger part is 150% of the smaller part. |

S | Ice Cream | How many different ice cream cones can be made by choosing two scoops from six flavours? |

S | Icosahedron | How many triangles are there on the surface of a regular icosahedron. |

S | In Your Head | Here are the simple percentage calculations everyone should be able to do in their heads. |

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

S | Inbetweens | Find fractions between two given values. |

S | Intents Excitement | Work out the mathematical words missing from the story about buying a tent. |

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

S | Just Four Questions | Four mathematical questions to think about at the beginning of the lesson. |

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

A | Key Eleven | Prove that a four digit number constructed in a certain way will be a multiple of eleven. |

S | 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. |

S | Kim's Game 1 | This is the Maths version of the traditional memory game. Memorise 10 mathematical facts then recall them as they disappear from view. |

S | Kim's Game 2 | This is the Maths version of the traditional memory game. Memorise 10 mathematical facts then recall them as they disappear from view. |

S | Kim's Game 3 | This is the Maths version of the traditional memory game. Memorise 10 mathematical facts then recall them as they disappear from view. |

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

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

S | Last Day | The 31st of December is the last day of the year. What mathematical lasts do you know? |

S | Leap Year | A question about the birthdays of a child born on the 29th February. |

S | Lemon Law | Change the numbers on the apples so that the number on the lemon is the given total. |

S | Less Than | This mathematics lesson starter invites pupils to interpret a three part algebraic inequality. |

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

S | Letters in a Number | Questions about the number of letters in numbers. |

S | Light Shopping | A lamp and a bulb together cost 32 pounds. The lamp costs 30 pounds more than the bulb. How much does the bulb cost? |

A | Log Perfection | Determine whether the given statements containing logarithms are true or false |

A | Logarithm Equation | Solve an equation containing logarithms with different bases |

S | Loopy Lake | Match the fractions to their decimal equivalents and join them with lines that do not cross. |

S | Lost Sheep | Which algebraic expression is the odd one out? |

S | Love Maths | Find the nine mathematical words hidden in the love story. The last letters of the hidden words form an anagram of the name of a famous mathematician. |

S | Lyric Lacking Limerick | Find the words missing from the mathematical limerick. |

S | M for Mathematics | Write down as many mathematical words as possible that begin with the letter M. |

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

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

S | Match Fish | A classic matchstick puzzle designed to challenge your spacial awareness. |

S | Maths Crossword | A small crossword puzzle containing mathematical words. |

S | Maths In School | Find mathematical words which can be made by using the letters in the name of your school? |

S | Mathster Mind | Guess the four digit number with help from the clues. |

S | Mathterpiece | Memorise a picture made up of geometrical shapes |

A | Maximum Product | Two numbers add up to 10. What's the largest possible product they could have? |

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

S | Memor Sea | Twelve numbers in a seascape need to be memorised in order to answer the five questions. |

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

S | 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. |

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

S | Middle of Centres | The blue point is exactly in the middle of two red points. What are their coordinates? |

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

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

S | Missing Lengths | Introduce linear equations by solving these problems about lengths. |

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

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

S | Missing Square Puzzle | The missing square puzzle is an optical illusion used to help students reason about geometrical figures. |

S | Missing Terms | Find the missing terms from these linear sequences. |

S | Mix and Match | Work out which team played which from the information given. |

S | Moon Lengths | Estimate the distances shown on this photograph of the moon's surface. |

R | Moses' Roses | How can ten roses be planted in five rows of four? |

S | Movie Minutes | Calculations involving hours and minutes based on the runing times of popular DVDs. |

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

S | Mult Sum Diff Div | For each pair of numbers multiply the sum by the difference then divide the answer by 5. |

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

A | Multiple of sum of digits | What number is six times the sum of its digits? |

S | Multiply Quickulations | Random multiplications appear on screen every few seconds. |

S | Multiply, Add, Subtract and Divide | For each pair of numbers subtract the sum from the product then divide the result by 20 without a calculator. |

S | Mystery Numbers | Can you recognise the mystery numbers from the clues? |

S | Mystic Maths | Work out why subtracting a two digit number from its reverse gives a multiple of nine. |

S | Name Again | Work out what the nth letter will be in a recurring pattern of letters in a person's name |

S | Negative Numbers | Perform calculations involving negative numbers |

S | Negative Vibes | Practise techniques for answering questions involving negative numbers. |

S | News Common | Follow the compass directions given in the squares to find where the route starts? |

A | Nine Digit Numbers | How many different nine digit numbers are their that contain each of the digits from one to nine? |

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

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

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

S | 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. |

S | North Pole Test | This starter requires you to write out a difficult times table. |

S | Not Multiples | Write down the numbers from a list which are not multiples of a given number. |

S | Not Too Close | This activity requires eight students to sit non consecutively on a grid of chairs. |

S | Noughts and Crosses | In how many different ways can the first X and O by placed on the grid? |

S | Number Recall | Can you improve your ability to remember telephone numbers? |

S | Number Riddles | Can you work out the numbers from the given clues. |

S | Numbers in words | Write out in words some numbers writen as digits (optional pirate theme) |

S | Oblongs | Find the dimensions of a rectangle given the perimeter and area. |

S | Odd One Out | From the numbers given, find the one that is the odd one out. |

S | Odd Percent Out | A number of simple percentage calculations are given. The answers are in pairs. Which is the odd one out? |

S | On The Double | Double the numbers given in the table. |

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

S | One Fifth | Investigate three fractions which add together to give one fifth. |

S | One Ninth | Investigate three fractions which add together to give one ninth. |

S | One one | Continue the given number pattern with the help of a little lateral thinking. |

S | One out of Ten | This Mathematics lesson starter has been designed for April Fool's Day. Don't be caught out! |

S | One Torch Tunnel | Work out the least amount of time for four people to walk through a tunnel? |

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

A | Other Child's Gender | What is the probability that the other child is also a boy? |

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

S | Overlapping Squares | If two squares overlap, what shapes can the overlapping region make? |

A | Paper Ratio | Calculate the ratio of the sides of an A4 sheet of paper without any measuring. |

A | Paper Surprising Perimeter | Find the perimeter of a folded sheet of A4 paper as described in this short video. |

S | Paradox | Can you solve this paradox by agreeing whether the statements are right or wrong? |

A | Parallel Graphs | Determine from their equations which of the straight line graphs are parallel and perpendicular. |

S | Peanuts and Buttons | Two questions involving estimating a quantity. |

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

A | Penny Bags | Can you place 63 pennies in bags in such a way that you can give away any amount of money (from 1p to 63p) by giving a selection of these prepacked bags? |

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

S | Pentagon | On a full page in the back of your exercise book draw a perfectly regular pentagon. |

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

A | Perennial Rivals | Which football team will be first to win four games? |

S | Perfect Numbers | Six is a perfect number as it is the sum of its factors. Can you find any other perfect numbers? |

A | Permutable Functions | Find pairs of functions that are commutative under composition. |

S | Pi Day | March 14th is Pi Day. The third month and the 14th day relates to 3.14 which is pi to three significant figures. How many figures of pi can you memorise? |

S | Pick From The Pot | The pot contains 10 counters which are being randomly removed and replaced. How many of each colour do you think are in the pot? |

S | Pie Chart | An exercise in estimating what the sectors of a pie chart represent. |

A | Piece of String | Find where a piece of string should be cut to form a circle and a square of equal areas. |

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

A | Pizza Slice | A problem which can be solved by considering the areas of a triangle and a sector of a circle. |

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

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

S | 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. |

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

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

S | Polygon Riddle 1 | Solve the riddle to find the name of the polygon then sum the interior angles. |

S | Polygon Riddle 2 | A "My first is in..." type riddle leading to a polygon interior angle calculation. |

S | Polygon Riddle 3 | A 'My first is in...' riddle that describes a geometrical shape. Can you construct it? |

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

A | Product of Indices | Find the product of the unknown indices that feature in two equations |

S | Product Placement | Arrange the numbers to produce the largest product. |

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

S | Puddings | Complete the calculations with the weights of the puddings |

S | PYA | You have four minutes to write down as many equations as you can involving the given letters. |

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

S | Quad Areas | Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid. |

A | Quad Midpoints | What shape is created when the midpoints of the sides of a quadrilateral are joined together? |

S | Quick Percentages | Simple percentage questions appear on screen then fade every 8 seconds. This Starter is customisable. |

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

S | Rabbits and Chickens | There are some rabbits and chickens in a field. Calculate how many of each given the number of heads and feet. |

S | Rail Weigh | Record the weights of the trains to work out the weight of a locomotive and a coach. A real situation which produces simultaneous equations. |

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

S | Red Lines | Either estimate the lengths of the red lines or, if you know how, calculate how long they are. |

S | Reflective Cat | On squared paper copy the drawing of the face then reflect it in three different lines. |

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

S | Register | When the register is called answer with a multiple of 7. |

R | Rejuvenate | A girl was 16 years old in 2010 but just 8 years old in 2018 |

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

A | Restrained Flea | How many different places could the flea find itself after 8 foot-long jumps either north, south, east or west? |

A | Reverse Connection | Find a general rule for the difference between a two digit number and that same number with the digits reversed. |

A | Rice on a Chess Board | How many grains of rice are on a chess board if each square has twice the number of grains as the previous square. |

A | Rich or Poor? | An interesting outcome of percentage increase and decrease |

A | Road Connections | Design roads to connect four houses that are on the corners of a square, side of length one mile, to minimise the total length of the roads. |

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

R | Rope Ladder | How many rungs of a rope ladder remain above the water line after the tide has risen two metres? |

S | Ropey Snowballs | Arrange the numbers on the snowballs so that no two consecutive numbers are directly connected by rope. |

R | Rosie's Cube | How many of the small cubes does Rosie need to complete the big cube? |

S | Rotational Symmetry | Draw a pattern with rotational symmetry of order 6 but no line symmetry. |

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

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

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

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

S | 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. |

S | Rows of Roses | Can you draw 4 straight lines, without taking your pencil off the paper, which pass through all 9 roses? |

S | Same Same | A problem involving two people's ages which can be solved using algebra. |

A | Same Series Sum | Find an arithmetic series and a geometric series that have the same sum of the first five terms. |

A | Same Three Digits | Find ex |

S | Santa's Sleigh | Work out the number of clowns and horses given the number of heads and feet. |

S | Satisfaction | Rearrange the numbers, row and column headings so that this table is mathematically correct. |

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

S | Sea Shells | A question which can be best answered by using algebra. |

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

S | Secret Symbol | Place a symbol between the four and the five to get a number greater than four and less than five. |

S | Sectors | Work out which sectors fit together to make complete circles. Knowledge of the sum of the angles at a point will help find more than one correct solution to this puzzle. |

S | Seedy CDs | Interpret data given in the form of a bar chart then create a new bar chart showing the given statistics. |

S | Seeing Squares | How many square numbers can be found in the grid of digits. |

S | Separated Twins | Can you find a 14 digit number containing two each of the digits one to seven which obeys the rules given? |

S | Sequence Dancing | Find the next term of the number sequences. |

A | Seventeen Camels | Explain the mathematics of the classic ninteenth century fraction sharing story. |

S | Shadow Sums | Make sums from the three digit numbers given. |

R | Sharing Apples | Share five apples between five children while leaving one in the basket. |

S | Shopping List | A quick quiz about five items on a shopping list written 40 years ago. |

S | Shunting Problem | Allow two trains to pass by using the limited amount of siding space. |

S | Siam Symbols | Can you work out what each of the strange symbols represents in these calculations? |

R | Sibling Count | How many boys and how many girls are there in the family? |

S | 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. |

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

S | Simple Nim | The classic game of Nim played with a group of pens and pencils. The game can be extended to the multi-pile version. |

A | Simplify | Simplify an algebraic fraction |

S | Simultaneous Occasions | A problem which can best be solved as a pair of simultaneous equations. |

A | Single Fraction | Simplify an expression involving fractions, exponents and a quare root. |

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

S | Six Keys | Use just six calculator keys to make a total of 20. In how many different ways can it be done? |

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

S | Small Satisfaction | Arrange the digits one to nine in the grid so that they obey the row and column headings. |

R | Smart Animals | Who is most likely to be able to work out the square root of 121? |

S | Snowman and Woman | How many different ways can you spell out the word snowman by moving from snowflake to snowflake. |

A | Speed Circles | Find the diameters of the circles in the corners of the square. |

A | Sphere Hole | Find the volume of the remaining part of a sphere after a 10cm cylindrical hole has been drilled through it. |

S | Spider Sequences | Find the next term of the given number sequences. Can you also find a general rule for predicting the nth term of the sequence? |

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

S | Square and Even | Arrange the numbers on the cards so that each of the three digit numbers formed horizontally are square numbers and each of the three digit numbers formed vertically are even. |

S | Square Angles | Find a trapezium, a triangle and a quadrilateral where all of the angles are square numbers. |

S | Square Christmas Tree | Draw a picture of a Christmas tree using only square numbers. |

S | Square Circle Kite | Write down the names of all the mathematical shapes you know. |

A | Square in Rectangle | Find the area of a square drawn under the diagonal of a rectangle |

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

A | Square Root of 1% | What is the square root of one percent? |

S | Square Sequence | Write out as many square numbers as possible in 4 minutes. |

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

S | Squared Animals | Separate three rows of three animals using three squares. |

S | Squigits | A challenge to find numbers which have each of their digits as square numbers. |

S | St Ives | The traditional "As I was going to St Ives" riddle. |

S | Stable Scales | Solve these balance puzzles by taking the same away from both sides. An introduction to linear equations. |

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

S | Stair Perimeter | Use the information implied in the diagram to calculate the perimeter of this shape. |

S | Star Wars Day | Estimate the size of an alien given the size of their hand. This could be an introduction to scale factors. |

S | Starting With | Write down as many mathematical words as possible that begin with a particular letter. |

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

S | Step Perimeter | Is it possible to work out the perimeter of this shape if not all the side lengths are given? |

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

S | Structured Settlement | Without a calculator match a a pie slice to a calculation to an answer. |

S | 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. |

S | Subtract Quickulations | Calculations appear on the screen every few seconds. |

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

S | Suko | Interactive number-based logic puzzle similar to those featuring in The Times and Telegraph newspapers. |

S | Sum Equals Product | What are the numbers if their sum equals their product? |

S | Sum of the Signs | Each traffic sign stands for a number. Some of the sums of rows and columns are shown. What numbers might the signs stand for? |

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

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

S | Summer Holidays | How many children and how many donkeys are on the beach? You can work it out from the number of heads and the number of feet! |

R | Sums With Hundreds | When is eighteen hundred minus fifty the same as seventeen hundred plus ten? |

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

S | Table Spiders | Multiply the number on the spider's back by the numbers next to its legs. |

S | Take Sides | Put up your right hand or left hand depending on the expressions that appears. |

A | Tan 22.5 | Find an exact value for tan 22.50 without using a calculator. |

A | Tansum | Find the sum of the tangents of angles on a straight line. |

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

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

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

A | Temperature Sum | Can you explain why 0^{o}C + 0^{o}C does not equal 64^{o}F |

A | Test Scores | Explore the misconception that when adding fractions you add both the numerators and the denominators |

S | Thai Baht | How many different ways can you make a given total with Thai coins? |

R | The Blue Arrows | What is the smallest number of jets that could have been in the formation according to the sighting information? |

S | The Power of Christmas | Find a power of 2 and a power of 3 that are consecutive numbers. |

S | The story of ... | Be creative and come up with as many facts about a number as you can think of. |

S | Think Back | A problem which can be answered by forming an algebraic equation then solving it. |

S | THOAN | THOAN stands for 'Think of a number' and there are four randomly generated THOAN puzzles to solve. |

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

A | Three Right Triangles | Calculate the lengths of the unlabelled sides of these right-angled triangles. |

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

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

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

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

S | Tindice | How can you put the dice into the tins so that there is an odd number of dice in each tin? |

S | To Be Continued | Work out the next term in the given sequences. |

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

S | Top Transfer | Beginning with 100 on your calculator, what is the largest and smallest totals you can end up with after travelling through each of the possible routes. |

S | Tran's Hats | In how many different ways might Tran decide to wear his hats in one week? |

A | Transum Tonic | What is the largest number of bottles that it is not possible to buy if they come in packs of 6, 9, and 20? |

A | Tri-Junction | A real life situation that can be analysed with the use of a tree diagram. |

A | Triangle or Quadrilateral | Can a quadrilateral have a straight angle? |

R | Tricky Takeaway | Take away some of the letters in a word to get a surprising result. |

A | Trig Blot | Find all the measurements of the given triangle. |

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

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

S | True or False? | An activity designed to address common misconceptions. |

S | Twelve Days | A Maths puzzle based on the 12 Days of Christmas song. |

R | Two Coins | What two coins add up to 70p (one of them is not a 50p coin) |

A | Two Equals One | What is wrong with the algebraic reasoning that shows that 2 = 1 ? |

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

S | Two Pots Make Four | Make four litres given a seven and a five litre jug. |

A | Two real numbers | The sum of the reciprocals of two real numbers is -1, and the sum of their cubes is 4. What are they? |

S | Two Squares | Using six pencils can you make two equal sized squares? |

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

S | Two Twins and Tim | A tricky problem set on a coordinate grid. |

A | Unfinished Game | Share the prize in a fair ratio according to the probability of each player willing. |

A | Unlucky Seven Eleven | Follow the instructions to multiply a chosen number then explain the result you get. |

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

S | Upside Number | Work out the phone number from the clues given. |

S | Valentine's Puzzle | Work out which boy sent a Valentine's Day Card to which girl. |

S | Venn Diagram | Arrange numbers on the Venn Diagram according to their properties. |

S | 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? |

A | Vowel Code | How many ways can you create a code for the vowels by assigning to each vowel a different vowel? |

S | Vowelless | Vowels have been taken out of mathematical words. Can you recognise them? |

R | Wandering Bear | A bear walks south, east then north and finds it is back where it started. What colour is the bear? |

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

S | Weather Maths | Eight mathematical questions about the current weather and times in four cities around the world. |

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

A | Weather Reports | Which five different integers multiply together to give 12? |

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

A | What Question? | Write down all the possible questions that could have been asked if this was the diagram provided in a mathematics textbook. |

S | Windmill Sequence | Find the value of the missing term of the sequence. It is easier than you may think! |

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

S | Word Search | Create your own mathematical word search for the whole class to enjoy. |

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

S | Wordles | Turn mathematical words into designs which will help you remember the meanings of the words. |

S | Wrapping Paper | Find the order of rotational symmetry of the repeating pattern. |

S | Writing Cheques | Complete some imaginary cheques, the amount needs to be written in words. |

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

A | X Divided by 2Y | Why do different calculators not agree on the order of operations? |

A | Zero Even | Prove that zero is an even number. |

Wow, that's a long list! There are 469 Starters to choose from. You are spoiled for choice!

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