My new applet on Coordinate Geometry concentrates on two important skills for post-16 maths, especially for UK AS levels Core 1 and 2.
Lengths of Line Segments
This topic often seems to be the first useful mathematical application of the Pythagoras Rule (Pythagorean Theorem) that kids come across. Earlier the focus is on contrived right-angled triangles. How many of them are going to find the height or the guy-length of a flagpole?!
It also encourages students to calculate by using a formula rather than a graph — you don’t need to draw or even imagine the triangle.
Mid-points of Line Segments
Once again a simple idea, but one which allows students quickly to ditch the diagrams in favour of an easily-applied formula.
Pretty soon the idea that the coordinates are just the means of the x- and y–values and it is this rather than the diagrams which sticks in the students’ minds.
So why ..
So why haven’t I given the formulae in the applet? This is because of a basic premise of Waldomaths — allow students to see things for themselves. This way the formula seems almost obvious and hence much easier to remember. Students also learn the techniques their own way and apply them with confidence, rather than the all-too-common rote learning of formulae which leads to stress and errors.
Sometimes it’s depressing to think that an applet which has taken me hours of work can achieve its aim within a few seconds of a students time. But then again that’s what Waldomaths is all about.
So why do I show the working? Surely they need to able to work it out for themselves? Well, you can turn the working off!