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 Investigations. 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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### 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 1-9 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.

Quad Areas: 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.

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

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.

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

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

Zero Even: Prove that zero is an even number.

#### Area Builder

An interactive workspace in which to make shapes using square tiles with given areas and perimeters.

Transum.org/go/?to=areabuilder

### Feedback:

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 s /Indice 'Starter of the Day' page by Busolla, Australia:

"Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students - all trying to reach their highest level and competing with their peers while also learning. Thank you very much!"

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 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.
To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)."

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 9 May 'Starter of the Day' page by Liz, Kuwait:

"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

Comment recorded on the s /Coordinate 'Starter of the Day' page by Greg, Wales:

"Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!"

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 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 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 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!
Thanks"

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 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 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 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 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 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 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 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 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.
Thanks again"

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 'starter-of-the-day' 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 on-line 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 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 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 Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."

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 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 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 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Comment recorded on the 28 September 'Starter of the Day' page by Malcolm P, Dorset:

"A set of real life savers!!
Keep it up and thank you!"

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
Best wishes from Inger Kisby"

Comment recorded on the i asp?ID_Top 'Starter of the Day' page by Ros, Belize:

"A really awesome website! Teachers and students are learning in such a fun way! Keep it up..."

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 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 9 April 'Starter of the Day' page by Jan, South Canterbury:

"Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you."

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 warm-up activity for my Year 6 class. The range of questioning provided is excellent as are some of the images.
I rate this site as a 5!"

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.
Could we have some on angles too please?"

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 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 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."

### 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 open-ended way. They will also develop pride in describing their findings to their classmates and may even stumble across findings that will suprise their teacher.

Take a look at our main page of investigation starting points which can be the seed of creative and exciting course work.

### Investigations Teacher Resources:

Maths Mind Reader: Investigate this amazing mind reading performance based on simple mathematical principles.

Prison Cell Problem: A number patterns investigation involving prisoners and prison guards.

Mystic Rose: Investigate the properties of the Mystic Rose by using this interactive diagram.

Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds.

### Investigations Activities:

Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters.

Function Builder: An interactive function machine for patterns, numbers and equations.

Green Fingers: Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible.

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

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?

Leapfrog: An investigation of the minimum number of moves required to make the blue and green frogs swap places.

Frustration: A logic challenge requiring a strategy to update each of the numbers in a grid.

Jugs: Can you make four litres if you only have seven and five litre jugs?

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?

Prison Cell Problem: A number patterns investigation involving prisoners and prison guards.

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.

Take Baht: How many different ways can you make a given total with Thai coins?

Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds.

### Classic Investigations:

Area Builder: An interactive workspace in which to make shapes using square tiles with given areas and perimeters.

Function Builder: An interactive function machine for patterns, numbers and equations.

Steps: Investigate the numbers associated with this growing sequence of steps made from Multilink cubes.

Lamp Posts: What is the greatest number of lamp posts that would be needed for a strange village with only straight roads?

Green Fingers: Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible.

Egg Box Investigation: In how many different ways can two eggs be arranged in an egg box?

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.

Design a badge: How many different badges can you make using three different coloured squares put together to make a rectangle?

Four Ever: Generate a number sequence based on the number of letters needed to spell the previous number.

Maths Mind Reader: Investigate this amazing mind reading performance based on simple mathematical principles.

How Many Sides?: How many different polygons can you make on a 3 by 3 pin board? What about larger pin boards?

Reaction Time: When the numbers appear hit the correct button depending on whether the numbers are even or odd

lnvestigating stamps: How many different postage amounts can you make with the given stamps?

Leapfrog: An investigation of the minimum number of moves required to make the blue and green frogs swap places.

Trilett: A strategy game requiring you to select three words with a common letter before the computer does.

Tridots: Find all the triangles that can be drawn by joining dots on a 3 by 3 grid of dots.

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.

Have you got change?: An investigation about making change for different amounts.

Frustration: A logic challenge requiring a strategy to update each of the numbers in a grid.

Calendar Maths Investigation: Investigate the connection between the numbers in a T shape drawn on this month's calendar.

Football Scores: If you know the final score of a football match, what might the half time score have been?

Polygon Areas: Investigate which polygons have an area of 4 square units on this interactive dotty grid.

Transum Club: How many different colour schemes can you devise for the Transum Club Badge.

Halving: An open-ended investigation challenging pupils to find many different ways to you cut the shape in half.

Area shapes: Investigate polygons with an area of 4 square units. This is your starting point, you can decide how to proceed.

Jugs: Can you make four litres if you only have seven and five litre jugs?

Tetrominoes Investigation: A tetromino is a shape made of four squares joined edge to edge. How many different tetrominoes are there?

Palindromic numbers: How many steps does each number take to become palandromic?

Dice Investigation: Throw two dice and multiply the scores. Investigate the different products you can obtain. What about adding? What about using three dice?

Traffic Jams: How many ways can three cars be lined up in a traffic jam?

Number Stairs: Find the relationships between the numbers in the stairs on different size grids.

Tessellations: Drag the shapes onto the canvas to create tessellating patterns then try the tessellations quiz.

Trapezia: Which numbers can be represented by groups of circles arranged in the shape of a trapezium?

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?

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?

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.

Mystic Rose: Investigate the properties of the Mystic Rose by using this interactive diagram.

Digit Sums and Multiples: Investigate numbers which are multiples of the sum of their digits.

Hula Hoops: If a number of Hula Hoops are dropped on the floor, what is the maximum number of regions they might form?

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.

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

Snooker Investigation: Investigate a special snooker table with only four pockets. Which pocket will the ball fall into for various sized snooker tables?

Braille: Investigate the possibility of redesigning the Braille alphabet to make it easier to learn.

Digital Lights: Investigate the way small LEDs were used to make up the digits on a calculator display.

Handshakes: If everyone in this room shook hands with each other, how many handshakes would there be?

Polygon Hunting: Find all the polygons that can be drawn by joining dots on this seven dot grid.

Songkran Game: Where should you stand in the circle to win the Songkran game?

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

Graph Plotter: An online tool to draw, display and investigate graphs of many different kinds.

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

Beginning with One: Is it true that most numbers begin with the digit one? 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?

Search for Infinity: Manipulate the Lissajou curve to produce a perfectly symmetrical (vertically and horizontally) infinity symbol.

Maxvoltray: Find the maximum volume of a tray made from an A4 sheet of paper. A practical mathematical investigation.

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.

Odd Dice: Take three dice. How many ways can they be turned so that they show only odd numbers on top?

Featured Investigations

Anti-Calculator: A puzzle about a two digit number divided by the sum of its digits.

Diagonal Through Squares: How many squares does the diagonal of a rectangle drawn on squared paper pass through?

Painted Cube: The classic Painted Cube investigation. How many faces of the smaller cubes are painted blue?

### Investigations Videos:

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 Worksheet: A printable grid containing many copies of the design used in the second shape counting Starter.

Two Twins Printable: This worksheet extends the puzzle in the July 21st Starter of the Day.

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.

Links to other websites containing resources for Investigations are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

### Search

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### Other

Is there anything you would have a regular use for that we don't feature here? Please let us know.

#### Graph Plotter

An online tool to draw, display and investigate graphs of many different kinds.

Transum.org/go/?to=graphplotter

### Teaching Notes:

Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

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