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.
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.
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
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?
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!
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
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?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
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 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?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Choose a symbol to put into the number sentence.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
If you have only four weights, where could you place them in order
to balance this equaliser?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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 areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you beat the computer in the challenging strategy game?
Can you coach your rowing eight to win?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of Little Fung at the table?
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?
Use the interactivity to make this Islamic star and cross design.
Can you produce a tessellation of regular octagons with two
different types of triangle?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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...
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
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.