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

Online

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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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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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 ...

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.

Online

Secondary mathematics: using real data

These seven learning activities, which focus on the use of 'real data' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use the three content strands ...

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In a spin

This resource is a web page containing a short task to explore volume of a solid shape. The task involves calculating the volume of the solid formed by rotating a right angled triangle about its hypotenuse A printable resource and solution is also available to support the task. This resource is an activity from the NRICH ...

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Volume of a Pyramid and a Cone

This resource is a web page containing an investigative task to explore volume. Derive the formulae for the volumes of a square-based pyramid and a cone, using mathematical concepts. A printable resource is also available to support the task. This resource is an activity from the NRICH website.

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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 ...

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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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Logarithmic scale: Year 10 – planning tool

This planning resource for Year 10 is for the topic of Logarithmic scale. Students read and interpret different types of scales. They understand that that a logarithmic scale uses powers 10 and how it appears on a graph. Students know when the use of such a scale is appropriate and where logarithmic scales are used for ...

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Sustainable agriculture: agri-environmental indicators

This is a web resource that provides a database of agri-environmental indicators for environmental performance of agriculture in OECD countries between 1990 and 2008. The data table can be customised, with options to view by country or by theme: land, energy, air, nutrients, soil, biodiversity, pesticides, water, farm management ...

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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.  

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.

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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 ...

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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Catalyst: Graham's number

If you were asked what the biggest number you can think of is, what would you say? Infinity? Well, what about the biggest finite number you can think of? Mathematician Ron Graham came across such a gigantic number in his research that, to capture its massive size, he and his colleagues needed to come up with new methods ...

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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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 ...

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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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Stateline: Mapping farmland: using area and trigonometry

In northern Queensland's Gulf region, some farmers use GPS mapping to help manage their extensive properties. Use this clip as a context for applying your understanding of area, in particular your understanding of conversion between square kilometres and hectares. Apply trigonometry and Pythagoras' theorem.