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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.

### Modes of Inquiry

### Inquiry Abilities

### 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 |