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Updated: Jun 2000

Investigating Poyhedra Phase of Development: Early Adolescence The following matrix describes the Mathematics outcomes that were spotlighted in this unit of work. It should be recognised that many other outcomes, from this and other learning areas, will also be achieved during the course of the unit. Learning Area Outcomes Curriculum Framework Strand Statements Outcomes & Standards Framework Working Mathematically Students use mathematical thinking processes and skills in interpreting and dealing with mathematical and non-mathematical solutions. In particular they: show initiative, flexibility and persistence when working mathematically. Direct links to Overarching Learning Outcomes 1, 5 and 6 choose mathematical ideas and tools to fit the constraints in a practical situation, interpret and make sense of the results within the context and evaluate the appropriateness of the methods used. Direct links to Overarching Learning Outcomes 1, 2, 3, 4, 5 and 6 investigate, generalise and reason about patterns in number, space and data, explaining and justifying conclusions reached. Direct links to Overarching Learning Outcomes 1, 3, 5 and 6 Working Mathematically Students use mathematical thinking processes and skills in interpreting and dealing with mathematical and non-mathematical solutions. Space Students describe and analyse mathematically the spatial features of objects, environments and movements. In particular they: visualise, draw and model shapes, locations and arrangements and predict and show the effect of transformations on them. Direct links to Overarching Learning Outcomes 2 and 5 reason about shapes, transformations and arrangements to solve problems and justify solutions. Direct links to Overarching Learning Outcomes 2 and 5 Space Students describe and analyse mathematically the spatial features of objects, environments and movements. Represent Shape Students visualise, draw and model shapes.   Context   Brief Description   Project Duration   Outcomes   Learning Experiences   Step 1         Step 2       Step 3   Reflection Context School A Senior High School, with 1300 students. Teachers within the Mathematics Learning Area generally use traditional teaching and assessment strategies. Class A Year 8 class of 30 students, working at Levels 3 - 5 in the Working Mathematically and Space Strands (but the program can be adapted for Years 8 - 10 classes) Learning Technologies Minimal equipment is available within the learning areas, but students and staff have access via a booking system to 16 computers/Internet within the Library Resource Centre. In this program I also used a notebook computer, projector, dialup Internet account and telephone outlet. Teacher I have had 15 years classroom experiences in Science, Mathematics and Computing within a variety of schools in both metropolitan and country locations. Brief Description of the Program I introduced this task as an extended piece of work (investigation/project) after the students had undertaken studies on polygons in the classroom. Project Duration Approximately 2 week (4 hours) of class time and out of class time Expected Outcomes Students to have an understanding of prisms i.e. what 2-D shapes are used to make them and the names of common prisms. Students to have an understanding of polyhedra, ie what 2-D shapes are used to make them and the names of the platonic solids. Investigate how to construct prisms and polyhedra.   Learning Experiences Background As a traditional teacher within a traditional high school with minimal access to hardware and normal time constraints I wanted a project that would enable students to be extended and also to consolidate prior learning. Students could work independently or within groups (to access the web during class time they were required to work in pairs).   Step 1 I directed students to explore and write a report about the Platonic Solids. to see a copy of the worksheet. Write a report about Platonic Solids. The report should include: what Platonic Solids are. how they are constructed. the net of the platonic solids. any other aspects of polyhedra that you may have discovered. If possible try to construct a polyhedron. Sources of information include: Textbook Library Resources Encyclopedias The Internet (e.g. search strategies/homework helpers and www.georgehart.com/virtual-polyhedra/vp.html) I gave students opportunities to direct their own investigation within this task but, unfortunately, because of constraints within the department, I was not able to negotiate the deadline for submission of the task.   Step 2 After the students had had an opportunity for open exploration and research of polyhedra, I concentrated on the Virtual Polyhedra website by George W. Hart. At this stage of the work I used a notebook computer and projector to demonstrate while all the students watched. Within this site we used VR to build polygons and prisms at www.georgehart.com/virtual-polyhedra/prism-maker.html. We explored some prisms at www.georgehart.com/virtual-polyhedra/prisms-index.html. We explored the platonic solids at www.georgehart.com/virtual-polyhedra/platonic-index.html. Then polyhedra in general at www.georgehart.com/virtual-polyhedra/vp.html.   Step 3 I then gave students the opportunity to explore the Virtual Reality website in pairs and to look at various models.   Assessment They could be many aspects to assessing this task, depending on the demands of the department: Traditional marking guide (e.g. 5 solids, diagrams, polygons that make the shape, nets etc). Anecdotal checklists for the Working Mathematically and Space Strands. Verbal report or a report using PowerPoint or by creating a webpage (Obviously if these types of assessments are to be utilised more time should be allocated). Reflection Hindsight is such a wonderful thing. There would be many aspects that I would do differently. The section on prisms could be used further to enhance students' learning. Being open-ended it enabled students to be extended. The overall task could be modified to suit the local needs of the student population.