Using ICT in mathematics case study 14 - 'Real life gradients'

Headline

A Dynamic Geometry (GSP) resource which students can use to help find the gradient of straight lines on real life objects.

Context

Year 9 introduction to gradient in real life situations.  Year 10 revision of calculating gradient, and investigating the equation of a line.

Teaching and learning objectives

• To be able to generate calculate the gradient of a straight line with positive and negative gradients.
• To understand that the gradient can be calculated from any two points on the straight line.
• To introduce the formal notation for finding the gradient of the line.

Extension

To understand that scale has no effect on the gradient.

ICT resources and context

A GSP file with pictures taken provided by Richard Phillips for the TSM Resource CD that was distributed to all State Secondary Schools in August 2005. More pictures are available to purchase from www.problempictures.co.uk

Pages have buttons to help scaffold the process of finding the gradient of a line.

Explanation of the lesson (including materials used)

The resource is a GSP file where photographs of slides, ladders and buildings have been imported into GSP pages with axes superimposed to enable students to investigate gradients in real life situations.

This resource can be used on an IWB or with a “slate” and data projector as a demonstration tool to illustrate how to calculate the gradient of a line.

It was intended to be used in a computer suite, with students manipulating the points A and B themselves; investigating the different gradients.

Evaluation of the impact of the ICT on the learning

Students were eager to move the points into position and were interested to see how the value was calculated.  They were able to investigate both negative and positive gradients. 

It was easy to see that it did not matter where on the line the points A and B were placed to calculate the gradient.  There was an opportunity for students to investigate what happens when the scale of the axes was changed.  Some students went on to model the various lines using y=mx+c.

Opportunities for further developments

The students had more interesting scenarios to enable them to calculate the gradient of lines.  You could take photos around your own school instead.  This could easily be extended into a task about similar triangles, as an introduction into trigonometric ratios.

You can download this case study below: