Tasks | Early Adolescence | Scale Issues

Tasks - Year 8,9

Scale Issues   by Glenys Stade, Hampton Senior High School

Phase of Development:   Early Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understand Graphs Represent Variation
Brief Description:	Explore the issue of how different Windows can effect the appearance of a graph on the calculator screen.
Expected Outcomes:	How to enter and display graphs on a graphics calculator. Learn about the Viewing Window and Zoom functions. Gradient of functions.
Context:	Metropolitan Area Senior High School. Trialed with a Year 9 Maths Enrichment Group. Designed for Year 9 or Year 10.
Learning Activities/ Experience:	Time taken - 1 or 2 lessons. The activity was inspired from the book Graphic Algebra Chapter 3 pp 35 -42. Many function graphs can be deceptive when displayed in a particular viewing window. It is possible to miss features or to get a wrong impression of the graph. Possible Activities F(x) = x(1-x) (x + 10) Start with default Viewing Window Zoom as necessary to find the big picture Sketch the function showing the key features Enter the function y = x and plot Change the View Window No matter what you do the gradient remains constant - despite appearances. (You can even make the gradient appear to be negative - how?) The above activity can also be done with y = xz.
Resources:	Learning Technologies - Graphics Calculators Asp, G. etal (1995). Graphic Algebra, Curriculum Corporation.