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.
Knights of the Circular Table
A royal seating investigation for brave pattern spotters, careful counters, and anyone willing to seat a few knights at the round table.
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.
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.
Knights of the Circular Table
A royal seating investigation for brave pattern spotters, careful counters, and anyone willing to seat a few knights at the round table.
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.
Octagon Loops
Investigate the features of loops created from octagons.
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?
Consecutive Squares
Investigate the difference between two consecutive square numbers.
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?
Maths Investigations
A video leading you to loads of exciting, engaging and challenging mathematical investigations.
The magic of Fibonacci numbers
Arthur Benjamin gives a TED talk on Fibonacci numbers.
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.
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.
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Teachers might find the complete Investigations Topic List useful.
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.
