An idea for ICT in the classroom - getting students started with dynamic geometry software – exploring quadrilaterals formed from triangles
Lots of schools have access to a dynamic geometry software package such as The Geometer’s Sketchpad, Cabri Geometry or Geogebra, and some teachers are using this software to support whole-class teaching on their interactive whiteboards.
Where schools have begun to provide opportunities for their students to use the software for themselves, the following lesson idea has proved to be a successful ‘first lesson’ which generates lots of productive mathematical thinking and does not require the students to have any software skills in order to get started.
You will need to provide the students with a pre-prepared file in which you have already constructed equilateral, isosceles and scalene ‘dynamic’ triangles on separate pages (or you can download these pre-prepared Geometer's Sketchpad or Cabri-Geometry files). You’ll need to have checked out how to reflect bits of the shape in a selected line of symmetry – and be able to show the students how to do this...
The task is a simple one to introduce...
- if you choose one of the sides of the triangle as the line of reflection, and reflect the rest of the shape in this line, what quadrilaterals is it possible to make and why?
- how can you use the angle and side properties of the original triangle to convince somebody else of your theory?
Although you could easily do this task with paper, pencil and card triangles, an advantage of using the dynamic software is that the students can drag the sides and vertices of the triangles to test if their conjecture is ‘always’ true.
And you can pose some more challenging extension questions such as:
- can you say which angles and side are the same?...and how do you know?
- which quadrilaterals can’t you make using this method?...and why?
Whilst working on a variety of challenges within this task, depending on the way that you have presented the task, the students could have opportunities to:
- plot the graphs of linear functions and recognise that equations of the form y = mx + c correspond to straight-line graphs
- appreciate that if lines are parallel, they have the same gradient
- recognise that if lines cross on the y-axis, they have the same intercept value.
Asking questions such as: ‘What is similar about the set of functions that produced the square and the rectangle?’ and ‘What do you notice about the gradients of the four equations that produced each shape?’ will encourage students to extend their mathematical thinking.