Resources by Something in Common

Survey Plot

There are a series of 8 sided polygons for which the areas are to be calculated. The area of each one turns out to be the same. This provides a lead in to asking how the...

Target Range

A cannon ball is fired and passes through two given points. The task is to discover the range of the cannon ball, the angle of projection, and the initial velocity. Solving the problem involves...

The Shortest Race

The introduction to this problem involves modelling a race from one tree to another, and the requirement to touch a fence on the way. The challenge is to determine the...

Think of a number

After thinking of a number, a series of steps is given that result in an answer that is independent of the initial number. There is scope to use fractions and directed numbers in the problem....

Three Circles and a Tangent

Three circles are shown touching and sharing a common tangent. The radii of the two larger circles are given. The challenge is to calculate the value of the radius of the smallest circle....

Three triangles and a square

In this presentation and collection of student worksheets a diagram shows a square and three right angled triangles, with each shape sharing a common side. Some of the lengths are given in surd form, from which students have to find the area of the square.

The solution involves the use of Pythagoras’ theorem...

Train length

In this resource the time is given for a train to pass a signal. The time is also given for a train to completely pass through a tunnel. It is assumed that the train is travelling at constant speed. The task is to calculate the length of the train.

Solving the problem requires the use of the formula for...

Trapezium and Diagonals

The opposite corners of a trapezium are joined, creating four triangles within the trapezium. The areas of the triangles formed using the parallel sides as is given. The task is to calculate the...

Triangle multiple

A triangle is split into two parts by drawing a line from one side to the base of the triangle. The ratio in which the sides are split is shown for each of the sides connected by the line. The task is to find what multiple of the smaller triangle is the larger triangle.

The ‘something in common’ between each...

Triangle tan product and sum

In this resource the side lengths of a triangle are given. The challenge is to find the ratio of the product of each of the tangents, divided by the sum of each of the tangents.

Each student worksheet contains a different triangle, but the answers all have something in common.

The solution involves...