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
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
If you have only four weights, where could you place them in order
to balance this equaliser?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
Use the interactivities to complete these Venn diagrams.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 complete this jigsaw of the multiplication square?
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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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.
A collection of resources to support work on Factors and Multiples at Secondary level.
An environment which simulates working with Cuisenaire rods.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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?
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 aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Here is a chance to play a version of the classic Countdown Game.
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?
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. . . .
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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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!
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
An interactive activity for one to experiment with a tricky tessellation
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
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. . . .
Can you beat the computer in the challenging strategy game?
Can you discover whether this is a fair game?
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?
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
A card pairing game involving knowledge of simple ratio.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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?
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?
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?
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.
A generic circular pegboard resource.
Match pairs of cards so that they have equivalent ratios.
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.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.