Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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 hit?
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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 coach your rowing eight to win?
If you have only four weights, where could you place them in order to balance this equaliser?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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.
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?
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
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?
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
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...
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.
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.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
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!
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Can you beat the computer in the challenging strategy game?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
An animation that helps you understand the game of Nim.
Choose a symbol to put into the number sentence.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Can you explain the strategy for winning this game with any target?
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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.
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?