Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

Curriculum content descriptions

Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)

Elaborations
  • distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
  • performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
  • communicating a proof using a sequence of logically connected statements
General capabilities
  • Numeracy Numeracy
ScOT terms

Shapes (Geometry),  Reasoning,  Congruence (Geometry),  Mathematical proofs,  Similarity (Geometry)

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Proof: Year 10 – planning tool

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Laptop wrap: Geometry gems

A page with a focus on using GeoGebra to enhance student understanding of various geometric properties and the importance of reasoning in proof. A laptop-friendly resource that includes supporting activities and links to resources.

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TIMES Module 22: Measurement and Geometry: scale drawings and similarity - teacher guide

This is a 41-page guide for teachers. It contains an introduction to scale drawings and similarity, and in particular the tests for triangles to be considered similar. Applications of similarity are included throughout the module.

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The geometer's warehouse

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reSolve: Mechanical Linkages: Geometry Proofs

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Work sample Year 10 Mathematics: Proof and conjecture

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My Five Cents: Why borrowing can cost you more

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My Five Cents: What is compound interest?

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In a spin

This resource is a web page containing a short task to explore volume of a solid shape. The task involves calculating the volume of the solid formed by rotating a right angled triangle about its hypotenuse A printable resource and solution is also available to support the task. This resource is an activity from the NRICH ...

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Australia's Trade through Time

Using an interactive timeline created by the Department of Foreign Affairs and Trade, this Teacher guide provides 12 series of learning experiences that engage students in the analysis and interpretation of data about Australian trade from 1900 to the present day. Students study videos, tables, images and texts in order ...

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The Sydney Metro rail project – Stage 5

This inquiry-based unit of work was created, trialled and peer reviewed as part of a professional learning program in inquiry-based learning for school teachers. The professional learning courses were part of a pilot partnership between the NSW Government’s Sydney Metro transport agency and Western Sydney University. The ...

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Waste and materials – sustainability action process (Years 7–10)

This resource guides students through an extended school-based or local investigation focussed on waste and materials using the five-step sustainability action process. The resource supports the investigation of a real-world issue or problem. Students develop and implement a chosen sustainability action and then evaluate ...

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This unit of work students learn about financial planning through the characters Cathy and Dinuka who are Year 10 students planning to go on a holiday together at the end of Year 12. Students learn about goal setting, saving, borrowing, investing, working with compound interest, good and bad credit, depreciation and inflation.

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Desmos Graphing Calculator - Google Play app

Plot functions, create tables, add sliders and animate your graphs. Touch points of interest on the graph to show maximums, minimums and points of intersection. Type in an equation and watch the calculator solve the problem. Free when reviewed on 12/5/2015.

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Water use and efficiency – sustainability action process (Years 7–10)

This resource guides students through an extended school-based or local investigation focussed on water use and efficiency using the five step sustainability action process. The resource supports the investigation of a real-world issue or problem. Students develop and implement a chosen sustainability action and then evaluate ...