Resources by Something in Common

Straight Line

A straight line is shown with the x and y axis intercepts shown. A point P is marked on the line but the coordinates are not given. P is then joined back to the origin, splitting the triangle into two parts. The challenge is to find the area of...

Straight line and circle

In this resource students are challenged to determine the equation of the line that goes through a given coordinate point and is also tangential to a circle centred on the origin. The final step is to determine the radius of the circle.

The solution involves determining the gradient of the tangent and also...

Strange Guys

Two verticals masts on a horizontal base have ropes tethered to each other’s base. The challenge is to find the height at which the ropes cross. When working on numerical examples, it becomes...

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...