What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Match pairs of cards so that they have equivalent ratios.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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?
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 ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
Prove Pythagoras Theorem using enlargements and scale factors.
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
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
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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?
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
An environment that enables you to investigate tessellations of
The classic vector racing game brought to a screen near you.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
How good are you at finding the formula for a number pattern ?
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. . . .
To avoid losing think of another very well known game where the
patterns of play are similar.
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. . . .
A metal puzzle which led to some mathematical questions.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Find the vertices of a pentagon given the midpoints of its sides.
Discover a handy way to describe reorderings and solve our anagram
in the process.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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. . . .
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
Use Excel to explore multiplication of fractions.
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.
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.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Can you beat the computer in the challenging strategy game?
A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
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?
Match the cards of the same value.
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.
Square It game for an adult and child. Can you come up with a way of always winning this game?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
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. . . .
Use an interactive Excel spreadsheet to investigate factors and
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?
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to explore number in this
Use Excel to practise adding and subtracting fractions.