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?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
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
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
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. . . .
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.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Match pairs of cards so that they have equivalent ratios.
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. . . .
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
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.
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?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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...
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
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.
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
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.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Use Excel to explore multiplication of fractions.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a version of the classic Countdown Game.
Use an interactive Excel spreadsheet to investigate factors and
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an Excel spreadsheet to explore long multiplication.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.