Cubic Equations and Their Roots

Using 'real life' data

Lesson idea. Kepler's third law gives an opportunity for students to explore real world data using GeoGebra. Johannes Kepler (1571-1630) was a German astronomer who studied the motion of the planets in the solar system. Based on experimental data he proposed three “laws” – or hypotheses – about the way the planets orbit the sun. Later, Isaac Newton produced mathematical proofs of these laws under the assumption that the force of attraction between the Sun and a planet at any time is proportional to the reciprocal of the square of their distances apart at that time. His third law expresses the relationship between the period of a planet’s orbit (T) and its mean distance from the Sun (D).

Teaching approach. This lesson features a ‘real life’ example for students to explore using visualisation^(ta) via GeoGebra. The focus on ‘real life’ increases student motivation.

The activity engages pupils in group talk^(ta), mathematical thinking^(ta) and vocabulary^(ta). This open ended^(ta) task encourages higher order^(ta) thinking, and encourages whole class^(ta) discussion^(ta)/questioning^(ta) and inquiry^(ta) projects.

Resource details
Title	Cubic Equations and Their Roots
Topic	[[Topics/Statistics|Statistics]]
Teaching approach	[[Teaching Approaches/Group talk|Group talk]],  [[Teaching Approaches/Open ended|Open ended]],  [[Teaching Approaches/Higher order|Higher order]],  [[Teaching Approaches/Questioning|Questioning]],  [[Teaching Approaches/Whole class|Whole class]],  [[Teaching Approaches/Mathematical thinking|Mathematical thinking]],  [[Teaching Approaches/Language|Language]],  [[Teaching Approaches/Visualisation|Visualisation]],  [[Teaching Approaches/Inquiry|Inquiry]],  [[Teaching Approaches/Discussion|Discussion]]
Learning Objectives	By the end of the activity students should be able to understand how a mathematical software modelling and visualisation tool such as GeoGebra can be used to explore 'real life' mathematics.
Format / structure	wiki page with downloadable .doc version
Subject	[[Resources/Maths|Maths]]
Age of students / grade	[[Resources/Secondary|Secondary]],  [[Resources/KS4|KS4]],  [[Resources/KS3|KS3]]
Files and resources to view and download	The first resource is an overall description of the activity with examples. File:Kepler' Third Law with GeoGebra.docx This is the accompanying GeoGebra application: File:Kepler's Third Law.ggb http://mathworld.wolfram.com/CubicEquation.html http://en.wikipedia.org/wiki/Cubic_function