Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Can you be the first to complete a row of three?
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
A group of interactive resources to support work on percentages Key
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?
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?
in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Match the cards of the same value.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you find all the 4-ball shuffles?
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
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
Have you seen this way of doing multiplication ?
Here is a chance to play a fractions version of the classic
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.
Here is a chance to play a version of the classic Countdown Game.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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.
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.
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
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...
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
A counter is placed in the bottom right hand corner of a grid. You
toss a coin and move the star according to the following rules: ...
What is the probability that you end up in the top left-hand. . . .
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .
This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
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
To avoid losing think of another very well known game where the
patterns of play are similar.
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?