Polyhedra Project

Strengths:  The Polyhedra project is a unique way to incorporate geometry, history, and art all into a mathematics classroom.  I think this could be a great introduction/hook project to start off a geometry unit because it has a non numerical and non formulaic approach.  Also, there is endless creativity options for the construction the origami models(Colours, materials, pictures etc).  For the typical math phobes, this could be an effective way to ease their way into geometry.  The artistic and historic type students will find themselves within their comfort zone and for that reason, they may find this project quite appealing and want to do further inquiry on Polyhedrons.  After finding the mathematical relations they might even be more motivated in the mathematics classroom.  For those who are comfortable with your standard homework, crunching out numbers,formula's, and problem sets, this type of project will certainly push them outside of their comfort zone which offers a beneficial challenge to them.  I think in particular, the writing portion of the project is extremely beneficial because we often neglect to do any writing in mathematics and it is such an important life skill.  Also, the presentation part of the project is great because it allows for all of the students in the class to have some knowledge on all of the topic areas.  You end up creating experts in specific fields, but at the end of the project most of the students will have the general knowledge of all the topics.

Weaknesses:  I thought some of the weaknesses of the project was that while there was certainly an artistic and written portion, there seemed to be very little in terms of the actual mathematics.  To a certain extent the historical component achieves this, for example, Euler's polyhedral theorem, but I don't think it offers enough in terms of PLO's and IRP's.  

Modifications, adaptations, extensions:  I think if I were to use this project in my class I would try and modify it to include less of a historical component while having a bigger emphasis on certain mathematical concepts, like surface area for example.  Personally, I think history is important because it offers interesting stories and it may provide a greater appreciation for mathematics, but at the same time, it can become quite boring and hard to find reliable information.  We also found that building five models is actually quite time consuming, especially if you are adding a lot of creativity, so depending on the group sizes you may want to cut down the number of models students have to build.   

For our project we decided to incorporate both surface area and an very basic introduction into probability by turning the polyhedra models into dice.  We also decided to cut out the historical component because we felt that geometry is already an interesting topic without it.  Possibly some of the "drier" topics will better be suited for history.  In addition, instead of having the students do all five of the origami models, we only required two for each pair.  We thought this might be better because on the presentation day, not everyone will have seen all the different types, providing some variety in the classroom.     

New math project outline  EDCP342A Names: Roz and Travis Project title: Polyhedra Dice
Grade level	Grade 9
Purpose	determine the surface area of composite 3-D objects to solve problems To investigate, create, and present findings on regular polyhedra. Introduction and inquiry into basic probability
Description of activities	Students will first be divided into pairs The pairs will then receive two of the four regular polyhedra (Not including tetrahedron) and be required to re-create a 3-D paper model.  Instructions will be provided on how to create the models. Each pair will then number each face/side of the polyhedra to create a set of dice. The pairs will then come up with a formula for calculating surface area for their polyhedra and then provide a numerical answer for their SA Students individually will then answer the following probability questions about their dice. How many sides are there for each of the five regular polyhedra? What can you say about the names of the polyhedra? What is the probability of rolling a 1 for each die? If both dice are rolled at the same time, what is the probability that the sum of the dice will be 10? * Extension:  What is the probability that when both dice are rolled, two 5's will land. * Students will then bring in their creations and surface area answers, and display them in class for all students to see.
Sources (bibliography, websites, etc.)
Length of time project will take (in and out of class)	3 classes for assigning of pairs, polyhedra, and creation of polyhedra dice, and surface area formulas . Students should have enough classtime to finish their models and proceed to inquiry on probability, otherwise it is to be on their own time. 20 mins at beginning of one class to present and display
What students are required to produce	In pairs, two 3-D polyhedra dice models. Surface area formula and numerical answer Individually, answers to probability questions
Marking Criteria:

Part A.(In pairs)  Two 3D polyhedra paper model dice.  /20
                          Proper, correct construction of model
                          Creativity of design (colour, patterns etc)

Part B.(In pairs)  Surface area formula and calculation /15
                         Clear understanding of what surface area is and correct answers

Part C (Individual).  Probability inquiry and answers /10