An idea for ICT in the classroom - exploring linear graphs dynamically
Many schools have access to an ICT resource that students could use to carry out hands-on tasks to explore functions and graphs dynamically. The new ‘traditional’ approaches tend to focus on students changing certain parameters, and teachers ‘hoping’ that they work systematically to come to wished-for conclusions!
For example, varying ‘m’ and ‘c’ within y = mx + c to learn about gradient and intercept properties of linear functions.
However, this could be seen as an approach that lacks connectivity with other aspects of the mathematics curriculum! What follows is an alternative suggestion, which makes links with the properties of two-dimensional shapes, and can be extended as an introduction to simultaneous linear equations.
Challenge the students to produce on-screen diagrams that show the outlines of different quadrilaterals – you can support this by providing some templates for them to try to match.
The level of difficulty can be varied by positioning the quadrilaterals differently on the page.
So, drawing a rhombus with a line of symmetry on the y-axis is less of a challenge than…
…drawing the outline of the same rhombus ‘shifted’ a little to the right.
Both challenges lead to the need for students to connect ideas concerning gradient and intercept properties of straight-line graphs.
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.