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? 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. Tools: 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.
Feedback: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 10 September 'Starter of the Day' page by Carol, Sheffield PArk Academy: "3 NQTs in the department, I'm new subject leader in this new academy  Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!" 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 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk: "Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!" Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, : "We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much 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 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon: "Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated." Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School: "My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions." 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 5 April 'Starter of the Day' page by Mr Stoner, St George's College of Technology: "This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative." Comment recorded on the 3 October 'Starter of the Day' page by Fiona Bray, Cams Hill School: "This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register." Comment recorded on the 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy: "I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson." Comment recorded on the 7 December 'Starter of the Day' page by Cathryn Aldridge, Pells Primary: "I use Starter of the Day as a registration and warmup activity for my Year 6 class. The range of questioning provided is excellent as are some of the images. 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 11 January 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast: "My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please." Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." 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 2007. 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 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School: "This is a great memory aid which could be used for formulae or key facts etc  in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is  my pupils love it! Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School: "Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work." Comment recorded on the 2 May 'Starter of the Day' page by Angela Lowry, : "I think these are great! So useful and handy, the children love them. Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." Comment recorded on the 26 March 'Starter of the Day' page by Julie Reakes, The English College, Dubai: "It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages." Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales: "I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!" Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry: "Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils. Comment recorded on the 23 September 'Starter of the Day' page by Judy, Chatsmore CHS: "This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles." Comment recorded on the 2 April 'Starter of the Day' page by Mrs Wilshaw, Dunsten Collage,Essex: "This website was brilliant. My class and I really enjoy doing the activites." Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset: "A set of real life savers!! 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." 
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. Students 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: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 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. Happy Numbers: How many happy numbers can you find? Jugs: Can you make 4 litres if you only have 7 and 5 litre jugs? Largest Product: Arranging digits to produce the largest 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. 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 shapes: Investigate polygons with an area of 4 square units. This is your starting point, you can decide how to proceed. Perhaps squared paper or an online pinboard may help. 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. 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 squares put together to make a rectangle. You can use three different colours but the finished design must be symmetrical. 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 small LEDs 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? 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. 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: How many happy numbers can you find? 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? Lamp posts: What is the greatest number of lampposts that could be needed for a given village? Leapfrog: Can you make the blue and green frogs swap places in the smallest number of moves? lnvestigating stamps: How many different letters can you send with the given stamps. Maxvoltray: Find the maximum volume of a tray made from an A4 sheet of paper. A practical mathematical investigation. Number Stairs: Find the relationships between the numbers on the grid. 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. Rectangles 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? Snooker: 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: Which polygons tessellate? Which pentominoes tessellate? 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 Calendar: Investigate the connection between the numbers in a T shape drawn on this month's calendar. Transum Club: How many different colour schemes can you devise for the Transum Club Badge. Trilett: A strategy game requiring you to select three words with a common letter before the computer does. Investigations External Links:Links to other websites containing resources for Investigations are provided for teachers logged into 'Class Admin'. Subscribing to this service also opens up the opportunity for you to add your own links to this panel. 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