Mathematics / Year 9 / Measurement and Geometry / Using units of measurement

Curriculum content descriptions

Calculate the surface area and volume of cylinders and solve related problems (ACMMG217)

Elaborations
  • analysing nets of cylinders to establish formulas for surface area
  • connecting the volume and capacity of a cylinder to solve authentic problems
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
  • Critical and creative thinking Critical and creative thinking
ScOT terms

Volume (Dimensions),  Cylinders,  Surface area

Online

reSolve: Tree Biomass

In this sequence of two lessons, students investigate how many trees would be required to supply paper for their school for a year. Students use similar triangles, Pythagoras' Theorem and algebra to design and construct a Biltmore stick, used to measure the diameter and height of a tree. They measure trees, calculate their ...

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

Surface area and volume of prisms and cylinders

This is a website designed for both teachers and students, which addresses the surface area and volume of prisms and cylinders from the Australian Curriculum for year 9 students. It contains material on calculating the surface area and volume of prisms and cylinders. There are pages for both teachers and students. The student ...

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Work sample Year 9 Mathematics: Cylinder volume

This work sample demonstrates evidence of student learning in relation to aspects of the achievement standards for Year 9 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

Volume and surface area: cylinders: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Volume and surface area: cylinders. Students calculate the surface area, volume and capacity of cylinders and solve related problems.

Downloadable

Measurement: Foundation to Year 9

This comprehensive resource describes the progression of measurement ideas. The resource demonstrates examples of relevant teaching strategies, investigations, activity plans and connected concepts in measurement including teaching and cultural implications.

Online

Volume and surface area: prisms: Year 9 – planning tool

This planning resource for Year 9 is for the topic of Volume and surface area: prisms. Students solve problems involving the surface area and volume of right prisms.

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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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Indigo Interior

This resource is a web page containing a problem solving task that requires an understanding of Pythagoras' theorem. The task involves finding the area of shaded region with a circle with a known area. To solve the problem students need to establish a right angled triangle and apply Pythagoras' theorem. A printable resource ...

Interactive

Surface area of prisms

This is a five-page HTML resource about solving problems concerning surface areas of prisms. It contains one video and five questions, two of which are interactive. The resource discusses and explains solving problems involving determining surface areas of prisms to reinforce students' understanding.

Online

reSolve: Mechanical Linkages: Similar Triangles

This sequence of lessons explores the geometry of similar triangles using two real world objects: ironing boards and pantographs. In the first lesson, students investigate different ironing board leg lengths and pivot positions using similar and congruent triangles. In the second lesson, they use their knowledge of parallelogram ...

Online

reSolve: Gradient and Tangent

This sequence of two lessons investigates gradient and angle by applying the tangent ratio to find the angles represented by a road sign or the angle of a street. In the first lesson, students research what a road grade is and determine the actual angle of a road given its grade. They then construct their own road sign ...

Online

reSolve: Pythagoras' Theorem - Lunch Lap

In this sequence of two lessons, students apply Pythagoras' Theorem to explore a practical problem involving optimising paths to lunch carts. In the first lesson, students investigate the length of a path that touches three sides of a rectangle, starting and finishing at the same point. They model the problem, use Pythagoras' ...

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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.

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 ...

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.

Interactive

The Mathematical Toolkit

A 2D Shapes tool that can be used to create geometric objects such as quadrilaterals, circles, triangles, lines, arcs, rays, segments and vectors on a coordinate grid. Plot and label the vertices to reveal the internal angles, side lengths, area and perimeter, then manipulate the shapes on a grid to transform their shape ...

Video

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.

Interactive

Finding Angles From Ratios

An animated tutorial about using a calculator to find an angle when given a trigonometric ratio. An interactive quiz is included.

Online

reSolve: Pythagoras' Theorem - Phone finding

This lesson challenges students to apply Pythagoras' Theorem to explore a practical real-world problem. Students explore technology reliant on mathematical concepts. The lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, discussion points and student resources such as ...