Mathematics / Year 10 / Measurement and Geometry / Geometric reasoning

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Curriculum content descriptions

Formulate proofs involving congruent triangles and angle properties (ACMMG243)

Elaborations
  • applying an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal)
General capabilities
  • Numeracy Numeracy
ScOT terms

Angles,  Congruence (Geometry),  Triangles (Shapes),  Mathematical proofs

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6 direct matches to ACMMG243 | 14 other related resources
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The geometer's warehouse

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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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Interactive

Numeracy wrap: It's what's inside that counts

  • TLF-IDM016261

interactive activities that guide students to explore the interior and exterior angle sums of polygons.

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Online

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

  • TLF-IDM009166

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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Online

reSolve: Mechanical Linkages: Geometry Proofs

  • TLF-IDM021852

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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Text

Work sample Year 10 Mathematics: Proof and conjecture

  • TLF-IDA004066

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 ...

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Online

Proof: Year 10 – planning tool

  • TLF-IDA003232

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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Interactive

Renovate, Calculate!

  • TLF-IDM016724

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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Online

TIMES Module 22: Measurement and Geometry: introductory trigonometry - teacher guide

  • TLF-IDM008608

This is a 20-page guide for teachers containing an introduction to the three basic trigonometric ratios. A history of trigonometry concludes the module.

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Interactive

Laptop wrap: Geometry gems

  • TLF-IDM016150

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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Online

Volume and surface area: Year 10 – planning tool

  • TLF-IDA003238

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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Online

TIMES Module 25: Measurement and Geometry: trigonometric functions - teacher guide

  • TLF-IDM009049

This is a 21-page guide for teachers. It provides an introduction to the sine, cosine and tangent functions and applications of these.

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Text

A piece of cake

  • TLF-IDA004931

In this lesson, students build on their skills in finding volumes and surface areas of prisms and cylinders to design a multi-level celebration cake for a party. They use mathematical modelling to vary the size and shape of the component cakes and to calculate how much frosting is needed.

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Voronoi Diagrams - Calculate

  • TLF-IDA004303

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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Text

Factorising Quadratics and Solving - Calculate

  • TLF-IDA004267

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 ...

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Online

Pythagoras and trigonometry: Year 10 – planning tool

  • TLF-IDA003236

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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Video

What are pixels?

  • TLF-IDM020591

Meet Kevin Systrom and Piper Hanson as they explain how digital images work. What are pixels, those tiny dots of light, made from? How are colours created and represented? What does Kevin say about the way mathematical functions are used to create different image filters. What is the difference between image resolution ...

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Interactive

Laptop wrap: Parallelendicular

  • TLF-IDM016249

Students construct a series of GeoGebra applets that investigate the parameters gradient and intercepts of straight lines. They reinforce this knowledge with Microsoft Math 3.0. 

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Interactive

Numeracy wrap: Parallelogram peculiarities

  • TLF-IDM016264

Interactive activities that guide students to investigate properties of parallelograms.

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Video

Catalyst: Applying trigonometry: leaning tower

  • TLF-IDM015448

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 ...

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Interactive

Desmos Graphing Calculator - Google Play app

  • TLF-IDM019620

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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