# Real World Algebra: Linear Functions

ACMNA215

This unit is part of the special topic “Bringing the Real World into Algebra”. Using dynamic geometry software students explore the role of each parameter in a linear function rule as line graphs are matched to features of an image (e.g. a playground slide or a scissor lift). Students have the opportunity to take their own photos and to make conclusions about the suitability of the real world objects they photograph (e.g. steepness of access ramps).

### Lesson 1: Linking Graphs and Rules

The link between the position, gradient and orientation of linear function graphs and the corresponding algebraic representation is explored with the help of GeoGebra. In the first activity, focus is given to the change in each parameter in the function rule as the line is manipulated. In the second activity, students use the y=mx+b form of the function rule and systematically vary the parameters “m” and “b” in order to find a line that is a good fit to a feature on a digital image.

### Lesson 2: Gradient, Ramps and Slides

These two tasks explore the real contexts of access ramps and playground slides using linear functions and linking the visual, graphical, symbolic and numeric representations. Students take their own photos of ramps and slides in their school or nearby and fit linear functions to them using GeoGebra. The focus is on gradient shown by the coefficient of x in y=mx+b, and also by rise over run. In the first task, students decide if the ramps match the Australian Standards. The second task uses slides with varying gradient to introduce average gradient. Students also learn to use sliders in GeoGebra to easily vary the line and approximate the steepest and shallowest gradients of the slides.

Last updated December 11 2018.