These interactive investigations from Subtangent help to develop a systematic approach but require students to use their own recording methods. They can be used as a whole class introduction to an investigation or as individual tasks. There are additional resources with some of the investigations so that pupils can either work at the computer or on paper. As these investigations are open ended and students can make their own decisions as to the direction of the task, no answers are given.


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....

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...


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...

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