|
|
| (12 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| Details to follow...
| |
|
| |
| [[Category:Maths]][[Category:Primary]][[Category:ORBIT]] | | [[Category:Maths]][[Category:Primary]][[Category:ORBIT]] |
| {{DISPLAYTITLE:ORBIT/GeoGebra Competition}} | | {{DISPLAYTITLE:ORBIT/GeoGebra Competition}} |
| {{Rinfo | | {{Rinfo |
| |type= Lesson idea | | |type= Lesson idea |
|
| |
| |attribution={{}}
| |
| |title=ORBIT/GeoGebra Competion 2013 | | |title=ORBIT/GeoGebra Competion 2013 |
| |tagline= The 2013 competition has generated five high quality open-ended activities that support interactive teaching and allow children (age 6-10) to explore an element of mathematics for themselves. | | |tagline= The 2013 competition has generated five high quality open-ended activities that support interactive teaching and allow children (age 6-10) to explore an element of mathematics for themselves. |
| |image=Students_shot.jpg | | |image=Geogebralogo.jpg |
| |topic=Visualisation | | |topic=Visualisation |
| |subject=Maths | | |subject=Maths |
| |resourcenumber= M0027
| | |
| |acknowledgement=This was a joint competition between The University of Cambridge Faculty of Education ORBIT project and GeoGebra (a world-wide community developing and using the GeoGebra software). | | |acknowledgement=This was a joint competition between The University of Cambridge Faculty of Education ORBIT project and GeoGebra, run in conjunction with the Cambridge Centre for Innovation in Technological Education (CCITE). On behalf of ORBIT, GeoGebra and CCITE we would like to thank all of the entrants and in particular, the winners, for their interest in the competition and for sharing their excellent Geogebra applets with us. |
| |age= KS1, KS2 | | |age= KS1, KS2 |
| |content= GeoGebra is a free, fun, interactive software environment that can be used with great effect to promote interactive teaching and enquiry based learning. The competition winning GeoGebra applets presented here also come with guidance notes for use in the primary classroom. | | |content= GeoGebra is a free, fun, interactive software environment that can be used with great effect to promote interactive teaching and enquiry based learning. The competition winning GeoGebra applets presented here also come with guidance notes for use in the primary classroom. |
|
| |
|
| |related resources= | | |related resources= |
| |other= | | |other= |
| |final=no | | |final=yes |
| |licence= | | |licence= |
| |format= wiki page with downloadable .doc version | | |format= links to wiki page containing embedded applet, guidance notes (wiki and .doc versions) and, .ggb file |
| |resources= | | |resources= |
|
| |
|
| The winner of the competition was Anthony Or with his pair of complementary applets on perimeter and area. Both applets have in-app spreadsheets for students to record their investigation results. These are excellent applets for visualising area and perimeter, addressing common misconceptions held by primary school students in a fun interactive way. | | The '''winner''' of the competition was '''Anthony Or''' with his pair of complementary applets on perimeter and area. Both applets have in-app spreadsheets for students to record their investigation results. These are excellent applets for visualising area and perimeter and address common misconceptions held by primary school students in a fun and interactive way. |
| | |
| | *[[variety of perimeters with fixed area]] |
| | [[File: Variety of perimeter with fixed area.png]] |
| | *[[variety of areas with fixed perimeter]] |
| | [[File: Variety of areas with fixed perimeter.png]] |
| | |
| | In '''second place''' was '''Irina Boyadzhiev''' with her applet on fractions. This is a great app that requires students to place fractions on a number line. It is easy to use, differentiated (has 3 levels of differentiation i.e. no hint, hint 1 and hint 2), interactive and pedagogically useful as it allows for the visualisation of fractions on a number line: |
| | |
| | *[[positioning fractions on the number line]] |
| | [[File: positioning fractions on the numberline.png]] |
| | |
| | The '''third place''' entrant '''John Golden''' produced a fun interactive game, that can be used by small groups of students, involving two different ways of representing number : |
|
| |
|
| *[[file:material-22723.ggb]] | | *[[number and representation game]] |
| *[[file:material-28888.ggb]]
| | [[File: number and representation game.png]] |
|
| |
|
| | '''Irina Boyadzhiev''' was '''highly commended''' for her entry on perimeter. This clear and easy to use enquiry based activity includes a great visualisation for understanding what is meant by perimeter and how to calculate it: |
|
| |
|
| The ORBIT/GeoGebra competition yielded a further three high quality GeoGebra activities:
| | *[[perimeter of a rectangle]] |
| *[[file:Origami.ggb]] | | [[File: perimeter of a rectangle.png]] |
| *[[file:parabola.ggb]]
| |
| *[[file:Plane.ggb]]
| |
| *[[file:Solar eclipse.ggb]]
| |
| *[[file:Radioactive decay.ggb]]
| |
|
| |
|
| Guidance notes:
| |
| *[[Origami Planes|Flying paper planes]]
| |
| *[[SolarEclipse|Solar and Lunar Eclipse]]
| |
| *[[Radioactive Decay and Carbon Dating]]
| |
| *[[Cubics|Cubic Equations and Their Roots]]
| |
| One student also produced an excellent document with links to GeoGebra files
| |
| *[[file:GeoGebra Software for Technology Enhanced Learning.docx]]
| |
| }} | | }} |
| [[Category:]]
| |
|
| |
|
| <ggb_applet width="720" height="498" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" />
| | |
| | [[Category: Competition]][[Category: GeoGebra]][[Category: CCITE]] |
