A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
See if you can anticipate successive 'generations' of the two animals shown here.
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
Can you maximise the area available to a grazing goat?
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
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?
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Join pentagons together edge to edge. Will they form a ring?
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Which hexagons tessellate?
Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
If you move the tiles around, can you make squares with different coloured edges?
Find all the ways to cut out a 'net' of six squares that can be folded into a cube.
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
What is the shape of wrapping paper that you would need to completely wrap this model?
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.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
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?
For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
What can you see? What do you notice? What questions can you ask?
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.
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
A huge wheel is rolling past your window. What do you see?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
What is the minimum number of squares a 13 by 13 square can be dissected into?
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?