Cubics: Difference between revisions

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(Created page with "Category:MathsCategory:SecondaryCategory:ORBIT {{DISPLAYTITLE:Cubic Equations and Their Roots}} {{Rinfo |title=Cubic Equations and Their Roots |tagline=Using 'real...")
 
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|resourcenumber= M0027
|resourcenumber= M0027
|age= Secondary, KS3, KS4
|age= Secondary, KS3, KS4
|content= 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). 
|content= 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
 
|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.|related resources=
|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.|related resources=
|other=
|other=
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|licence=
|licence=
|format= wiki page with downloadable .doc version
|format= wiki page with downloadable .doc version
|resources= The first resource is an overall description of the activity with examples.
|related resources=This activity was a result of the [[GeoGebra STEM Exploration]] 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.
*[[file:Kepler' Third Law with GeoGebra.docx]]
|resources=This is the accompanying GeoGebra application:
This is the accompanying GeoGebra application:
*[[file:Cubic.ggb]]
*[[file:Kepler's Third Law.ggb]]
 
http://mathworld.wolfram.com/CubicEquation.html
http://en.wikipedia.org/wiki/Cubic_function
 
}}

Revision as of 15:25, 25 September 2012


{{Rinfo |title=Cubic Equations and Their Roots |tagline=Using 'real life' data |image=Cubics.jpg |topic=Visualisation, Statistics |subject=Maths |resourcenumber= M0027 |age= Secondary, KS3, KS4 |content= 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

|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.|related resources= |other= |final=yes |licence= |format= wiki page with downloadable .doc version |related resources=This activity was a result of the GeoGebra STEM Exploration 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. |resources=This is the accompanying GeoGebra application: