Special Topics in Mathematics I

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Summer classes start the week of June 18 and end the week of July 23

Lisa Fontaine-RainenInstructor: Lisa Fontaine-Rainen

5-10 students, 8-14 years old


Image result for radix number

Mathematics courses often teach students how to solve problems, use algorithms, and number crunch. Our Special Topics and Mathematical Explorations courses teach students how to pose problems, develop algorithms, explore ideas, prove (both formally and informally) their methods and ideas work, and propose next steps. Students can use the skills learned in these classes to stretch their regular math curriculum, challenge their assumptions about mathematics, and truly think like a mathematician.

Special Topics I will base our explorations on patterns such as in the Tower of Hanoi problem, explore advanced ideas in rates, ratios, and proportions, explore representing parts of wholes in different bases, and look at the relationship between mathematics and science. Students will use variables to represent problems – a basic knowledge of variables is useful, but not necessary.

Prerequisites: None


Week 1: Introduction to mathematical thinking and the Tower of Hanoi

Week 2: Tower of Hanoi extension and explorations – discussion: is finding a pattern enough?

Week 3: Sharing Tower of Hanoi explorations, investigating other patterns and asking questions about patterns.

Week 4: More on patterns – Going from a table to an equation, reasoning about patterns

Week 5: More on patterns – Finding patterns in figures, sharing out of pattern explorations

Week 6: Explorations in ratios – what questions can expand our thinking on ratios? Dilutions and paint mixing.

Week 7 Introduction to rates, looking at rates with the eyes of a mathematician, dimensional analysis

Week 8: Trickier rate problems, problem posing and exploration

Image result for euler load

Week 9 Arithmetic in different bases – why and what questions can we pose?

Week 10: Representing parts of wholes in different bases

Week 11: Repeating radix numbers and different bases, and other radix explorations

Week 12: Looking for mathematical relationships in the world around us – Euler loads and elasticity

Week 13: Looking for mathematical relationships in the world around us – soil and student posed problems

Week 14: A flexible day to return to ideas we’ve explored previously and want to explore further, or extended problem solving

Week 15: Student presentations and further explorations

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