Mathematics / Year 10 / Space

Curriculum content descriptions

apply deductive reasoning┬áto proofs involving shapes in the plane and use theorems to solve spatial problems (AC9M10SP01)

Elaborations
  • distinguishing between a practical demonstration and a proof; for example, demonstrating that triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent
  • developing proofs involving congruent triangles and angle properties, communicating the proof using a sequence of logically connected statements
  • applying an understanding of relationships to deduce properties of geometric figures; for example, the base angles of an isosceles triangle are equal
  • investigating proofs of geometric theorems and using them to solve spatial problems; for example, applying logical reasoning and similarity to proofs and numerical exercises involving plane shapes; using visual proofs to justify solutions
  • using dynamic geometric software to investigate the shortest path that touches 3 sides of a rectangle, starting and finishing at the same point and proving that the path forms a parallelogram
General capabilities
  • Critical and creative thinking Critical and Creative Thinking
ScOT terms

Theorems,  Visual proofs,  Geometry,  Deductive reasoning

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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 ...

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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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The geometer's warehouse

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

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

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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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reSolve: Mechanical Linkages: Geometry Proofs

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A piece of cake

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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Factorising Quadratics and Solving - Calculate

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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 ...

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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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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My Five Cents: Why borrowing can cost you more

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My Five Cents: Why investing can be risky

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My Five Cents: What is compound interest?

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Sustainable agriculture: agri-environmental indicators

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My Five Cents: What is opportunity cost?

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The Sydney Metro rail project – Stage 5

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What are pixels?

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 ...