Cubic Equations and Their Roots
Lesson idea. This activity is explore cubic equations and their complex roots, to use Geogebra to find the solution to any cubic equation, given its coefficients, and plot the real and complex roots on an Argand diagram so that as the user changed the coefficients, they could see how that affected the roots of the cubic equation.
The potential age group is for Lower 6th students who are interested and want to learn something outside of their syllabus, and for Upper 6th students for whom it may be relevant to their studies on complex numbers and the relationships between roots of equations. I think my project would appeal to them as it is expanding on the syllabus that is taught
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. ^{(edit)}
Resource details  
Title  Cubic Equations and Their Roots 
Topic  [[Topics/StatisticsStatistics]] 
Teaching approach  [[Teaching Approaches/Group talkGroup talk]], [[Teaching Approaches/Open endedOpen ended]], [[Teaching Approaches/Higher orderHigher order]], [[Teaching Approaches/QuestioningQuestioning]], [[Teaching Approaches/Whole classWhole class]], [[Teaching Approaches/Mathematical thinkingMathematical thinking]], [[Teaching Approaches/LanguageLanguage]], [[Teaching Approaches/VisualisationVisualisation]], [[Teaching Approaches/InquiryInquiry]], [[Teaching Approaches/DiscussionDiscussion]] 
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/MathsMaths]] 
Age of students / grade  [[Resources/SecondarySecondary]], [[Resources/KS4KS4]], [[Resources/KS3KS3]]

Related ORBIT Wiki Resources  This activity was a result of the GeoGebraSTEM exploration day umbrella activity which asked students to develop 'real world' GeoGebra mathematical modeling applications which reach out to a wide range of users both students and teachers. It is described in their own words. 
Files and resources to view and download  This is the accompanying documentation and GeoGebra application:
