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
Can you explain the strategy for winning this game with any target?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
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?
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.
Can you complete this jigsaw of the multiplication square?
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?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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!
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?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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. . . .
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
A card pairing game involving knowledge of simple ratio.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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
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.
A collection of resources to support work on Factors and Multiples at Secondary level.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Mo has left, but Meg is still experimenting. Use the interactivity
to help you find out how she can alter her pouch of marbles and
still keep the two pouches balanced.
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
A generic circular pegboard resource.
An animation that helps you understand the game of Nim.
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.