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Napoleon's Theorem

Stage: 4 and 5 Challenge Level:

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?

A Resource to Support Work on Transformations

Stage: 4 Challenge Level:

This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.

Cushion Ball

Stage: 4 Challenge Level:

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Tracking Points

Stage: 4 Challenge Level:

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

Excel Interactive Resource: Multiples Chain

Stage: 3 and 4 Challenge Level:

Use an interactive Excel spreadsheet to investigate factors and multiples.

Excel Interactive Resource: Fraction Addition & Fraction Subtraction

Stage: 3 and 4 Challenge Level:

Use Excel to practise adding and subtracting fractions.

Excel Interactive Resource: Haitch

Stage: 3 and 4 Challenge Level:

An Excel spreadsheet with an investigation.

Zodiac

Stage: 4 Challenge Level:

Garfield's Proof

Stage: 4 Challenge Level:

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.

Excel Interactive Resource: Fraction Multiplication

Stage: 3 and 4 Challenge Level:

Use Excel to explore multiplication of fractions.

Excel Interactive Resource: the up and Down Game

Stage: 3 and 4 Challenge Level:

Use an interactive Excel spreadsheet to explore number in this exciting game!

A Resource to Support Work on Coordinates

Stage: 4 Challenge Level:

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

Overlaid

Stage: 2, 3 and 4 Challenge Level:

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Cushion Ball Interactivity

Stage: 4 Challenge Level:

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

Excel Interactive Resource: Number Grid Functions

Stage: 3 and 4 Challenge Level:

Use Excel to investigate the effect of translations around a number grid.

Excel Interactive Resource: Equivalent Fraction Bars

Stage: 3 and 4 Challenge Level:

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

Tablecloth

Stage: 4 Challenge Level:

Colour the squares of the square tablecloth so that each square is the same colour as all the symmetrically placed squares and a different colour from the rest of the squares.

Excel Interactive Resource: Long Multiplication

Stage: 3 and 4 Challenge Level:

Use an Excel spreadsheet to explore long multiplication.

Matter of Scale

Stage: 4 Challenge Level:

Prove Pythagoras Theorem using enlargements and scale factors.

Rollin' Rollin' Rollin'

Stage: 3 Challenge Level:

Two circles of equal radius kiss 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?

Triangles and Petals

Stage: 4 Challenge Level:

An equilateral triangle rotates polygons with equal length sides and produces an outline like a flower. What is its perimeter?

Loci Resources

Stage: 4 Challenge Level:

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

A Number Sequences Resource

Stage: 4 Challenge Level:

This resource contains interactive problems to support work on number sequences at Key Stage 4.

Excel Interactive Resource: Interactive Division

Stage: 3 and 4 Challenge Level:

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

Bow Tie

Stage: 3 Challenge Level:

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.

Cubic Rotations

Stage: 4 Challenge Level:

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?

Ratio Pairs 3

Stage: 3 and 4 Challenge Level:

Match pairs of cards so that they have equivalent ratios.

Circuit Maker

Stage: 2, 3, 4 and 5 Challenge Level:

Investigate how logic gates work in circuits.

100 Percent

Stage: 3 Challenge Level:

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100 percent.

Countdown Fractions

Stage: 3 and 4 Challenge Level:

Here is a chance to play a fractions version of the classic Countdown Game.

Disappearing Square

Stage: 3 Challenge Level:

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. . . .

Khun Phaen Escapes to Freedom

Stage: 3 Challenge Level:

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Tessellation Interactivity

Stage: 2, 3 and 4 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons

Multiplication Tables - Matching Cards

Stage: 1, 2, 3 and 4 Challenge Level:

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Fifteen

Stage: 3 Challenge Level:

Fifteen is a game for two players that you can play anywhere, anytime. Players take it in turns to select a number from 1 to 9. The aim is to choose 3 numbers that total 15.

An Unhappy End

Stage: 3 Challenge Level:

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...

Slippage

Stage: 4 Challenge Level:

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. . . .

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of 9 cm squared and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Overlap

Stage: 3 Challenge Level:

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. . . .

Poly-puzzle

Stage: 3 Challenge Level:

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.

Percentages for Key Stage 4

Stage: 4 Challenge Level:

A group of interactive resources to support work on percentages Key Stage 4.

Just Rolling Round

Stage: 4 Challenge Level:

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?

Pentagon

Stage: 4 Challenge Level:

Find the vertices of a pentagon given the midpoints of its sides.

Solving with Euclid's Algorithm

Stage: 4 and 5 Challenge Level:

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.

Conway's Chequerboard Army

Stage: 3 Challenge Level:

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Flip Flop - Matching Cards

Stage: 1, 2 and 3 Challenge Level:

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Polycircles

Stage: 4 Challenge Level:

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?

Proof Sorter - Quadratic Equation

Stage: 4 and 5 Challenge Level:

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.

More Number Pyramids

Stage: 3 Challenge Level:

Are there any patterns within the pyramid? Can you explain why you only get multiples of 4 at the top when you start with an integer in the bottom left hand corner?

Number Pyramids

Stage: 3 Challenge Level:

Using the same starter numbers 2, 1, 4 and 6 can you get a larger total at the top of the pyramid? What is the largest total you can get?