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A metal puzzle which led to some mathematical questions.
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?
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?
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
Use Excel to explore multiplication of fractions.
Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?
Use Excel to investigate the effect of translations around a number grid.
Use an interactive Excel spreadsheet to explore number in this exciting game!
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.
This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.
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.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.
Match pairs of cards so that they have equivalent ratios.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Use an interactive Excel spreadsheet to investigate factors and multiples.
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
A tool for generating random integers.
Here is a chance to play a fractions version of the classic Countdown Game.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
A collection of our favourite pictorial problems, one for each day of Advent.
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
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 moves.
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
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. . . .
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
An environment that enables you to investigate tessellations of regular polygons
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?
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.
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?
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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. . . .
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
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.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!