What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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
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.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you discover whether this is a fair game?
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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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
How good are you at finding the formula for a number pattern ?
To avoid losing think of another very well known game where the
patterns of play are similar.
This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you find all the 4-ball shuffles?
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. . . .
This set of resources for teachers offers interactive environments
to support work on loci 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. . . .
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
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.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Find the vertices of a pentagon given the midpoints of its sides.
An environment that enables you to investigate tessellations of
Match pairs of cards so that they have equivalent ratios.
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?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Use an interactive Excel spreadsheet to investigate factors and
A java applet that takes you through the steps needed to solve a
Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
An Excel spreadsheet with an investigation.
Use Excel to practise adding and subtracting fractions.
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 Excel to explore multiplication of fractions.
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
Use Excel to investigate the effect of translations around a number
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Use an interactive Excel spreadsheet to explore number in this
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Use an Excel spreadsheet to explore long multiplication.
Prove Pythagoras' Theorem using enlargements and scale factors.
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?
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?
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.