Investigations 1 

Investigate the number of concrete flags that are required to surround a pond.


Investigate the number of rebounds on a frictionless pool table. Change the length and width of the pool table. Click the 'play' button and watch the ball travel across the table.
Does the ball always drop in a pocket? How many times does it rebound off the cushions? Which pocket does it drop in? How far does the ball travel?
A knowledge of ratio will help.


Investigate how far a spring will stretch.
Change the size of the weight and the strength of the spring. Can you predict how far the spring will stretch?

Investigations 2 

Investigate the number of diagonals of a polygon.
Change the number of sides of the polygon and then draw the diagonals.


Investigate the number of lines joining dots round a circle.
Change the number of dots and then draw the diagonals.
Polygon, Mystic Rose and the famous Handshakes problem and work on triangular numbers all go hand in hand!


The mean crunching machine likes working out the mean of two numbers. Input two numbers and the machine will generate a sequence of numbers in which the next term is the mean of the previous two terms.
For example: 2, 5, 3.5, 4.25, 3.875, 4.0625 ....... The sequence will converge to a particular value which the machine will spit out.
Can you predict what the final number will be for any pair of starting numbers? The graph will help you.


The number crunching machine divides and adds over and over again.
For example, start with 37 and divide by 5 and add 1. The sequence of numbers will converge to a final number which the machine will spit out. Try other starting numbers, does it matter what number you start with?
Divide by 4 instead of dividing by 5, what difference does that make? Input any number and predict what will come out.
A little knowledge of the equivalence of decimals and fractions is needed.

Investigations 3 

A blue square can be moved about the grid. A line is drawn from the origin that cuts the square into two sections, one larger than the other. The ratio of the areas of the upper section to the lower is shown. The equation of the "cutting" line can be changed by altering the numerator and denominator. The fractions involved have not been cancelled down to help with sorting out this investigation.
What is the equation of the line that cuts the square in the ratio 2:1? 3:1? 4:1?
A knowledge of equivalent fractions, equations of y=mx+c graphs and ratio is required to successfully tackle this tricky investigation.

