Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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
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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Here is a chance to play a version of the classic Countdown Game.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Can you complete this jigsaw of the multiplication square?
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!
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?
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....?
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
An environment which simulates working with Cuisenaire rods.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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?
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Work out how to light up the single light. What's the rule?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.