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Problem solvig: Investigations logo

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All the investigations involve using the sliders to input variables and trying to predict the outcomes. Results can be saved in a table.

Investigations 1
link to Concrete Flags

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

spacerlink to Pot the Ball

spacerlink to Rebounds
Investigate the number of rebounds on a frictionless snooker table.
Change the length and width of the snooker 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.

link to Springy Numbers

link to Springy Numbers
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?

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Investigations 2
link to Polygon

link to Polygon
Investigate the number of diagonals of a polygon.

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

spacerLink to Mystic Rose

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Link to Mystic Rose
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!

link to Mean Cruncher
link to Mean Cruncher
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.
link to Number Cruncher

link to Number Cruncher
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.

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Investigations 3
link to Split the Square

link to Split the Square
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.

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