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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5 direct matches to ACMMG243 | 15 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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TIMES Module 22: Measurement and Geometry: scale drawings and similarity - teacher guide

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

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

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Laptop wrap: Geometry gems

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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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Work sample Year 10 Mathematics: Proof and conjecture

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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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Renovate, Calculate!

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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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Laptop wrap: Talking trigonometry

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In this laptop-friendly resource, students consolidate their understanding of trigonometry by investigating practical applications of the ratios, highlighting the process they used to find a solution.

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Algebra four

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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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Factorising Quadratics and Solving - Calculate

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

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

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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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A piece of cake

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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

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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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What are pixels?

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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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TIMES Module 29: Number and Algebra: introduction to coordinate geometry - teacher guide

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This is a 22-page guide for teachers. This module introduces coordinate geometry. The introduction includes finding the distance between two points, finding the coordinates of the midpoint between two points, determining the gradient of a line and determining the equation of a line.

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Laptop wrap: Parallelendicular

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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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Laptop wrap – a slippery slope

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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. 

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Laptop wrap: Under the surface

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In this laptop-friendly resource, students consider the difference between volume and surface area before posing practical problems. They then consider issues relating to unit conversions and similar figures.

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Numeracy wrap: Tell me why

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

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Desmos Graphing Calculator - Google Play app

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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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