Number Stairs

This Subtangent investigation looks at the total of the squares inside a stair shape.

Initially students investigate the relationship of the totals of a three step stair and its position on a 10 by 10 grid.

Using algebra, students may discover a general rule which applies to any stair on the grid....

Colouring Maps

This activity from Subtangent is based on the four colour theory, which is used by mapmakers. There is an interactive task which challenges students to colour a map using no more than four colours and ensuring that no two regions which share a border have the same colour. Further resources include examples of...

Diagonal Differences

This Subtangent investigation looks at what happens if the numbers in opposite corners of a three by three square, placed on an eight by eight grid, are multiplied then their difference found. Using algebra, students may discover a general rule which applies to any three by three square placed on the grid. Students...

Galton's Quincunx

This Subtangent investigation is based on the probability of balls, which are dropped through a triangular array of pins (a quincunx), into slots beneath. Every time a ball hits a nail it has a probability of fifty percent to fall to the left of the nail and a probability of fifty percent to fall to the right of...

Loopy Snooker

A special snooker table is the basis for this investigation from Subtangent. There are only four pockets on the table and you can only play the ball at 45⁰ to the sides of the table. The ball begins from a given corner of the table and keeps moving until it hits a pocket. The number of bounces is...

Leapfrog

The frogs in this Subtangent investigation have to be moved from one set of lily pads to another, following specific rules. This classic investigation is suitable for a wide age range of students. The number of frogs on each side can be varied, allowing further investigation and generalisations for the number of...

The mathematics of aircraft navigation

This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the aeronautical industry. Students are given a scenario which involves the recovery of stranded mountaineers by a rescue helicopter and the considerations required for a successful outcome. Trigonometry, formula...

Steam Pipe Insulation

This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics within the field of mechanical engineering. Here students learn that lack of proper insulation results in large energy losses which, over time, cost a lot of money. Models are used to calculate the value of the critical...

Underground Storage Tank

This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics when building an underground storage tank, with an elliptical cross section. Health and safety requirements apply and the depth to which the tank must be buried is established using the 2D geometry of an ellipse,...

The Mathematics of Escalators on the London Underground

This resource, from Mathematics for Engineering Exemplars, shows the application of mathematics for the operation of escalators on the London underground. Students consider a variety of issues which include passenger numbers and flow, as well as carbon emissions, escalator speed and energy efficiency. Detailed...