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This Resource Package aims to introduce students to mathematical thinking and inquiry. This involves concepts such as axiom, definition, conjecture, proof and theorem. They are also introducted to concepts such as generalisation and extension. The first three chapters are meant to draw in students to mathematical thinking, using examples of situations and objects they are familiar with or can play with. The rest of the package involves students addressing a particular question in a world only inhabited by straight lines. They simulate mathematical research while working on this problem. They setup systems of axioms in different ways, define objects precisely, come up with conjectures, search for counter examples, prove conjectures, come up with conjectures and questions as a result of theorems they prove, and generalise and extend conjectures and theorems.

Learning Objectives

Defining objects precisely and clarifying definitions
Conjecturing and clarifying conjectures
Setting up systems of axioms in different ways
Disproving conjectures through counter examples
Proving conjectures from axioms and definitions
Proving conjectures from axioms, definition and other proved conjectures
Generalising conjectures and proving the more general case
Extending results outside of their domain of applicability
Extending objects and results outside of the world they were created in