Investigations Starters:Aunt Sophie's Post Office: Work out the number of stamps needed to post a parcel. Bus Stop: How many different ways can four people stand in line? Digital Lights: Questions about the Small LEDs used to make up the digits on a calculator display. Flowchart: Use the flowchart to generate a sequence of numbers. Which number will reach 1 the fastest? Four's Independence: A clock face containing only the number 4. Can you make a clock face containing any other single number? Handshakes: If all the students in this room shook hands with each other, how many handshakes would there be altogether? 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? Hotel Digital: A puzzle about the lifts in a hotel which serve floors based on the day of the week. May Day: Add together the dates of all the Thursdays in May this year. Which day sum is largest? Meta Products: Which numbers when multiplied by the number of letters in the word(s) of the number give square numbers? Nine Nine Nine: Arrange the numbers 19 to make three 3 digit numbers that add up to 999. One Fifth: Investigate three fractions which add together to give one fifth. One Ninth: Investigate three fractions which add together to give one ninth. Only One Number: Find other numbers that can be changed to 1 on a calculator using only the 4 key and any operation. Plus: A number puzzle suitable for children with a wide range of abilities. Quads: Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid. Spinsum: Arrange the numbers on the grid of squares so that the totals along each line of three squares are equal. Tool Triangle: Place the numbers on the triangle so that the totals along each of the sides are equal. Wrong Way Round: Find calculations which written back to front give the same answer.
Small images of these Starters    Complete Index of Starters
Feedback:Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich: "My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource  thanks a million." Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access the whole month so I can use favourites with classes I see at different times of the week. Thanks." Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School: "What a brilliant website. We have just started to use the 'starteroftheday' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources online we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun." Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull: "Dear Transum, Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.: "A really useful set of resources  thanks. Is the collection available on CD? Are solutions available?" Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College: "Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work" Comment recorded on the 1 February 'Starter of the Day' page by Terry Shaw, Beaulieu Convent School: "Really good site. Lots of good ideas for starters. Use it most of the time in KS3." Comment recorded on the 6 May 'Starter of the Day' page by Natalie, London: "I am thankful for providing such wonderful starters. They are of immence help and the students enjoy them very much. These starters have saved my time and have made my lessons enjoyable." Comment recorded on the 8 May 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. 
Notes:An investigation, as defined by a dictionary, is a searching enquiry for ascertaining facts. In mathematics this enquiry is a journey into the unknown without a map. Pupils should enjoy choosing the direction they will take in exploring a situation which has been described in an openended way. They will also develop pride in describing their findings to their classmates and may even stumble across findings that will suprise their teacher. Investigations Teacher Resources:Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds. Maths Mind Reader: Investigate this amazing mind reading performance based on simple mathematical principles. Mystic Rose: Investigate the properties of the Mystic Rose by using this interactive diagram. Pin Board: Rows and columns of dots that can be joined using straight lines to create shapes. Prison Cell Problem: A number patterns investigation involving prisoners and prison guards. Investigations Activities:Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters. 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? Frustration: A logical challenge requiring a strategy to update each of the numbers in a grid. Function Builder: An interactive function machine for patterns, numbers and equations. Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds. Green Fingers: Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible. Happy Numbers: To find out whether a number is happy square each of its digits, add the answers and repeat. End in one and the number is happy. Jugs: Can you make 4 litres if you only have 7 and 5 litre jugs? Largest Product: A drag and drop activity challenging you to arrange the digits to produce the largest possible product. Prison Cell Problem: A number patterns investigation involving prisoners and prison guards. River Crossing: The traditional River Crossing challenge. Can you do it in the smallest number of moves? Six Keys: Use just six keys on your calculator to make a given total. How many different ways can it be done? Take Baht: How many different ways can you make a given total with Thai coins? Tantrum: A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid. Classic Investigations:Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters. Area shapes: Investigate polygons with an area of 4 square units. This is your starting point, you can decide how to proceed. Aunt Lucy's Legacy: Decide which of the four schemes Aunt Lucy proposes will provide the most money. This investigation involves the sum of sequences as well as considering life expectancy. 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. Beginning with One: Is it true that most numbers begin with 1? Think of numbers you see everyday and it is a surprising fact that so many of them begin with a one. Can you think why this is true? Braille: Investigate the possibility of redesigning the Braille alphabet to make it easier to learn. You will first need to examine the current version and learn how it is used. Calendar Maths Investigation: Investigate the connection between the numbers in a T shape drawn on this month's calendar. Crossing the River: Two men and two boys want to cross a river and they only have one canoe which will only hold one man or two boys. Decimal Products: Find two decimal numbers that add up to exactly one. What is the product of these two decimals? Design a badge: How many different badges can you make using three different coloured squares put together to make a rectangle? Dice Investigation: Throw two dice and multiply the scores. Investigate the different products you can obtain. What about adding? What about using three dice? Digit Sums and Multiples: Investigate numbers which are multiples of the sum of their digits. Digital Lights: Investigate the way small LEDs were used to make up the digits on a calculator display. Egg boxes: In how many different ways can two eggs be arranged in an egg box? First Impressions: This activity will collect data about your first impressions of some optical illusions. You can then analyse the data to come to your own conclusions. Football Scores: If you know the final score of a football match, what might the half time score have been? Four Ever: Generate a number sequence based on the number of letters needed to spell the previous number. Frustration: A logical challenge requiring a strategy to update each of the numbers in a grid. Function Builder: An interactive function machine for patterns, numbers and equations. Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds. Green Fingers: Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible. Halving: How many different ways can you cut this shape in half! Handshakes: If everyone in this room shook hands with each other, how many handshakes would there be? Happy Numbers: To find out whether a number is happy square each of its digits, add the answers and repeat. End in one and the number is happy. Have you got change?: An investigation about making change for different amounts. House Painting: The houses in Mathsland are all three storeys tall. Each storey is painted using one colour. How many ways can the houses be painted. How Many Sides?: How many different polygons can you make on a 3 by 3 pin board? What about larger pin boards? Hula Hoops: If a number of Hula Hoops are dropped on the floor, what is the maximum number of regions they might form? Jugs: Can you make 4 litres if you only have 7 and 5 litre jugs? Lampposts: What is the greatest number of lampposts that could be needed for a given village? Leapfrog: An investigation of the fewest number of moves required to make the blue and green frogs swap places. lnvestigating stamps: How many different letters can you send with the given stamps. Maths Mind Reader: Investigate this amazing mind reading performance based on simple mathematical principles. Maxvoltray: Find the maximum volume of a tray made from an A4 sheet of paper. A practical mathematical investigation. Mystic Rose: Investigate the properties of the Mystic Rose by using this interactive diagram. Number Stairs: Find the relationships between the numbers on different size grids. Odd Dice: Take three dice. How many ways can they be turned so that they show only odd numbers on top? Palandromic numbers: How many steps does each number take to become palandromic? Pin Board: Rows and columns of dots that can be joined using straight lines to create shapes. Polygon Areas: Investigate polygons with an area of 4 sq. units. Investigate polygons with other areas. Reaction Time: When the numbers appear hit the correct button depending on whether the numbers are even or odd Rectangle Perimeters: The perimeter of a rectangle is 28cm. What could its area be? Rod Triangles: Using 12 rods of varying lengths how many different triangles can you make? Search for Infinity: Manipulate the Lissajou curve to produce a perfectly symmetrical (vertically and horizontally) infinity symbol. Snooker Investigation: Investigate a special snooker table with only four pockets. Which hole will the snooker ball fall into for various sized snooker tables? Songkran Game: Where should you stand in the circle to win the Songkran game? Steps: Investigate this growing sequence of steps. Tantrum: A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid. Tessellations: Drag the shapes onto the canvas to create tessellating patterns and investigate the laws of tessellations. Tetrominoes: A tetrominoe is a shape made of four squares joined edge to edge. How many different tetrominoes are there? The Four Rules: See if you can make all of the numbers from 0 to 10 using four threes Traffic Jams: How many ways can three cars be lined up in a traffic jam? Transum Club: How many different colour schemes can you devise for the Transum Club Badge. Trapezia: Which numbers can be represented by groups of circles in the shape of a trapezium? Trilett: A strategy game requiring you to select three words with a common letter before the computer does. Investigations Videos:Investigation with Grid Mazes: This video explores different mazes composed of consecutive numbers and their greatest sum. The magic of Fibonacci numbers: Arthur Benjamin gives a TED talk on Fibonacci numbers. Investigations Worksheets/Printables:How Many Squares? 1: A printable grid containing many copies of the design used in the shape counting Starter. How Many Squares? 2: A printable grid containing many copies of the design used in the second shape counting Starter. Mystic Roses: Eighteen mystic roses to print out to help with the investigation. 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. Two Twins Printable: This worksheet extends the puzzle in the July 21st Starter of the Day. Investigations External Links:Links to other websites containing resources for Investigations are provided for those logged into 'Transum Mathematics'. 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Wednesday, October 18, 2017