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)

Online

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.

Interactive

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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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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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 ...

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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 ...

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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 ...

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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TIMES Module 35: Number and Algebra: the quadratic function - teacher guide

This is a 29-page guide for teachers. It introduces graphing of quadratic functions.

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ABC News: Space debris: the accuracy of space lasers

In space there are thousands of human-made objects (satellites and space junk) orbiting Earth. To avoid collision with space debris, satellites are manoeuvred out of its path. Discover how space debris is tracked using lasers, and about accuracy's effects on the lifetime of the satellite. Find out, using trigonometry, the ...

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Life expectancy PowerPoint

This teacher resource is a PowerPoint presentation designed to address common student misunderstandings about life expectancy. It emphasises that life expectancy is an average, that most people live for much longer or shorter than their life expectancy and that, when life expectancy is low, it is mostly because of a very ...

Interactive

Numeracy wrap: Tell me why

Interactive activities that guide students to consider the use and presentation of geometric reasoning.

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Catalyst: Applying trigonometry: leaning tower

The Leaning Tower of Gingin is the centrepiece of the Gravity Discovery Centre. The Catalyst team of Derek, Simon and Anja drop watermelons from the tower, to examine the rate at which they fall. They are testing Galileo's theory about falling objects. The dimensions of the tower provide an opportunity to apply some basic ...

Interactive

The Numberline

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

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Australia's population: countries of birth - dataset

The dataset provides statistics about the estimated resident population, median age and sex ratio by countries of birth for the latest year of available data. It is periodically updated by the Australian Bureau of Statistics (ABS). The dataset is included in the list of related datasets on the page in MS Excel format.

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TIMES Module 24: Measurement and Geometry: further trigonometry - teacher guide

This is a 32-page guide for teachers. It provides an introduction to the sine rule and cosine rule and their applications.

Interactive

Algebra four

This is an interactive game for two students in which they solve algebraic equations, similar to 'Connect four'. The players can choose from problems that are one- or two-step, quadratic, have distributive properties or have variables on both sides, and more than one problem type can be chosen. The length of time each player ...

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Laptop wrap – a slippery slope

Distance, midpoint and gradient are investigated as students design an Excel spreadsheet and make a Smart Notebook presentation on ski-lifts. Students then contribute to a discussion on the steepest street in the world. 

Interactive

Finding Angles From Ratios

An animated tutorial about using a calculator to find an angle when given a trigonometric ratio. An interactive quiz is included.

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My Five Cents: Why borrowing can cost you more

Think credit cards are basically free money? Gen Fricker will make you think again. Learn how interest rates and fees affect the money you borrow, and why they may be more expensive in the long run. Oh dear! Then test yourself with ASIC MoneySmart's "Things to think about" classroom exercises.  

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Data representation and interpretation - years 9 and 10

This is a teacher resource describing a set of student activities based on temperature and rainfall data and climate graphs for a number of cities in the Asia region, including Australian cities. The activities focus on constructing graphs from climate data and interpreting climate graphs. The resource encourages students ...