Mathematics / Year 10 / Measurement

Curriculum content descriptions

solve problems involving the surface area and volume of composite objects using appropriate units (AC9M10M01)

Elaborations
  • determining the volumes and surface areas of composite solids, formed from a range of right prisms and cylinders, by considering the individual solids from which they are constructed
  • estimating the surface area and volume of composite objects in practical contexts
  • using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a roof top and the optimal shape and dimensions for rainwater storage based on where it will be located on a property; determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community
General capabilities
  • Critical and creative thinking Critical and Creative Thinking
  • Numeracy Numeracy
ScOT terms

Units of measurement,  Surface area,  Cubic metres,  Volume (Dimensions),  Square metres

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Geometry of water sources and landforms

Indigenous cultures have always been deeply aware of the location of water and its significance. In this resource students will apply geometric, trigonometric, and algebraic techniques to analyse idealised water body shapes and associated landforms. They will calculate surface areas, volumes, angles, and heights of these ...

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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.

Interactive

Laptop wrap: Under the surface

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.

Interactive

Laptop wrap: Talking trigonometry

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.

Video

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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Off the scale

This lesson introduces students to the idea of a log scale, a seemingly perplexing way to present data. The lesson begins with an exploration of examples when a linear scale is inappropriate and concludes with a plotting activity using authentic data from the COVID-19 pandemic.

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

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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Amp up the volume

This set of learning activities challenges students to build a portable amplifier that passively amplifies the sound produced by a smartphone. The module includes a comprehensive teacher guide, curriculum links, materials lists, design process guides and printable student resource sheets. The resource also provides an editable ...

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.

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.