Resources by Something in Common

Heads will roll

In this resource the head of a circular snowman rolls around its circular body to make one trip back to where it started. The ratio of the diameters of the circles is given. The challenge is to find how many times the head will revolve throughout the journey, and find a general rule.

The resource contains a...

How Close

The coordinates of two points on a line are given. The task is to find the shortest distance from the line of a third given point. The task involves finding the equation of...

How Many Sides

A section of a regular polygon is shown with diagonals drawn from a hidden vertex. The angle between two diagonals their corresponding sides are given. The challenge is to work out how many...

Hyper-parabola

A hyperbola is given with a parabola ax²  touching each branch of the hyperbola at single points. The task is to determine the value of a.

A formal proof of the general situation involves substituting the equation of the parabola into the equation of the hyperbola. The...

Integration Stretch

The initial problem looks at an area given between two curves. The first curve is a parabola with the x and y axis intercepts given. The second curve is a stretch parallel...

L Centre

An ‘L’ shape is shown and the task is to find the centre of mass using only a straight edge and pencil. The solution makes use of the fact that the centre of mass of two objects will lie on a...

Leonardo of Pisa

This is an investigation into how the Fibonacci sequence gives rise to the Golden Ratio. The supporting spreadsheet allows the initial values of the sequence to be changed and an interactive...

Letter Wheel

A series of wheels are shown that are in perfect ‘non-slip’ contact with their neighbours and driven by a first wheel. The diameter of each wheel is given. The final wheel has letters evenly...

Magic Bag

A magic bag contains some black balls and some white balls. Two balls are removed simultaneously and they are both the same colour. The magic bag says ‘the probability of this happening is 0.5...

Magic Fractions

Three distinct non-zero integers are chosen such that their sum is equal to zero. From the three numbers all six possible ordered pairs are formed. Each ordered pair is then turned into a...