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Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
Featured UK Key Stage 3-5; US Grades 5-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Classifying Solids Using Angle Deficiency
Stage: 3 and 4
This article takes you through the classification of the Platonic (regular) and Archimedean (semi-regular) solids, to find all of them and prove that there are no more.
I found it difficult to make a choice of article for the NRICH Tenth Anniversary Celebration. I chose this one because it has been the basis of so many enjoyable sessions that I have had both with young learners and also with teachers.
With any age group, from 10 upwards, I find the best approach is to explain the Schlafli code and demonstrate it with an actual Archimedean solid,and then to give individuals different codes with the task of making their solid for that code. According to how much time you have, and how much your group already know, you can structure the session so that they discover the Euler Relation and/or the total Angle Deficiency, you can arrive at a proof that there are only 5 Platonic Solids and you can fill in the tables for all the Archimedean Solids deducing the number of each shape of face as described in the article. There are many possibilities.
In the ATE Maths Superweek where the photos were taken we had a great Holiday Director called Ian Johnston and a very good cook called Mrs Higgins and the children never knew that these were one and the same person. Just before lunch on the morning we spent on this topic Ian (an engineer) joined us and the children, having decided to test him, excitedly showed him their models "Ian look at mine, it's a 466" , "Ian mine is a 3434, can you explain that?" ... and so on. It did not take long for Ian (an engineer) to work it out and the children were impressed.
Perhaps your class can make the models out of card and hang them from the ceiling.
Mathematical reasoning & proof
Manipulating algebraic expressions/formulae
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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