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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Work sample Year 10 Mathematics: Proof and conjecture

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 10 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...

Online

Proof: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Proof. Students are familiar with the basics of geometry and have been introduced to proof when looking at similar triangles. They will be extending and applying these skills and using deductive reasoning and geometric theorems to solve spatial problems in relation ...

Interactive

The geometer's warehouse

This web-based, multimedia resource focuses on the geometry of the Stage 4 and Stage 5 Mathematics syllabus. It comprises 70 dynamic html worksheets, each exploring a different outcome in Stage 4 and Stage 5 geometry.

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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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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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reSolve: Mechanical Linkages: Geometry Proofs

This series of six lessons explores geometry proofs using real world contexts focused on the dynamics of linkages and moving joints. Students use physical models and computer simulations, the lessons move from a view of geometry as a study to static diagrams to encompass movement. Each lesson is outlined in detail including ...

Interactive

Renovate, Calculate!

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

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MoneySmart: Reaching goals: What's involved?

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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Work sample Year 10 Mathematics: Mathematics assignment

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 10 Mathematics. The primary purpose for the work sample is to demonstrate the standard, so the focus is on what is evident in the sample not how it was created. The sample is an authentic representation ...

Interactive

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 ...

Interactive

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.

Interactive

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 ...

Online

Pythagoras and trigonometry: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Pythagoras and trigonometry. Students apply their knowledge of Pythagoras' theorem to solve problems involving angles of elevation and depression and direction. They explore how direction can be indicated using true bearings and compass points.

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Voronoi Diagrams - Calculate

This unit of work explores coordinate geometry in the context of Voronoi diagrams. Students use linear coordinate geometry to construct Voronoi diagrams by finding the gradient of a line segment, then finding the midpoint, a perpendicular line and finally the perpendicular bisector.

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Factorising Quadratics and Solving - Calculate

This activity explores the properties of the family of functions and their graphs known as parabolas. The unit includes an AMSI Interactive online module, a range of other AMSI Schools and external links and video tutorials and some extension or enrichment ideas to take their understanding further. A short quiz at the end ...

Online

Volume and surface area: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Volume and surface area. Students extend their application of volume and surface area to solve problems on composite solids. Students will need to be able to visualise the individual elements of the composite solids and identify the areas where these elements touch.

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Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

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Numeracy wrap: Race across transversals

Interactive activities that guide students to explore angles in parallel lines.

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Numeracy wrap: Parallelogram peculiarities

Interactive activities that guide students to investigate properties of parallelograms.

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The Numberline

An interactive tool that can help students explore a number line, including points representing integers, fractions and decimals