Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Here is a chance to play a version of the classic Countdown Game.
If you have only four weights, where could you place them in order
to balance this equaliser?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Can you complete this jigsaw of the multiplication square?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
A card pairing game involving knowledge of simple ratio.
Meg and Mo still need to hang their marbles so that they balance,
but this time the constraints are different. Use the interactivity
to experiment and find out what they need to do.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Work out how to light up the single light. What's the rule?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Choose a symbol to put into the number sentence.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
A train building game for 2 players.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Meg and Mo need to hang their marbles so that they balance. Use the
interactivity to experiment and find out what they need to do.
Can you find all the different ways of lining up these Cuisenaire
An animation that helps you understand the game of Nim.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Use the interactivities to complete these Venn diagrams.
An interactive activity for one to experiment with a tricky tessellation
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .