Work out how to light up the single light. What's the rule?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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. . . .
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
Here is a chance to play a version of the classic Countdown Game.
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.
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.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
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!
An environment which simulates working with Cuisenaire rods.
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?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Can you complete this jigsaw of the multiplication square?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
If you have only four weights, where could you place them in order
to balance this equaliser?
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Identical discs are flipped in the air. You win if all of the faces
show the same colour. Can you calculate the probability of winning
with n discs?
Can you set the logic gates so that the number of bulbs which are
on is the same as the number of switches which are on?
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 coach your rowing eight to win?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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?
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
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....?
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
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
Find out what a "fault-free" rectangle is and try to make some of
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
A train building game for 2 players.
Can you find all the different ways of lining up these Cuisenaire
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Can you work out what is wrong with the cogs on a UK 2 pound coin?
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?