Mathematics / Year 8 / Measurement

Curriculum content descriptions

solve problems involving the area and perimeter of irregular and composite shapes using appropriate units (AC9M8M01)

Elaborations
  • determining the area of composite shapes by composing or decomposing shapes
  • using arrays and rectangles to approximate the area of irregular shapes in situations such as a council needing to work out how much mosquito spray to use for a swamp area or a farmer needing to work out how much seed, fertilizer and herbicide are required to cover a paddock
  • determining the perimeter and area of irregular shapes by sums of increasingly accurate covering measurements, such as line segments and grids; for example, using millimetres or square millimetres as opposed to centimetres or square centimetres
General capabilities
  • Numeracy Numeracy
ScOT terms

Area,  Metres,  Square metres,  Irregular polygons,  Perimeter

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Making triangles

In this lesson, students study the concept of triangle inequality, which determines if three positive numbers can serve as the side lengths of a triangle. Students experiment with various combinations of three natural numbers. They investigate whether these numbers can form a triangle and classify and construct the corresponding ...

Video

Maths inside bees and beehives

Bees are necessary for assisting many plants to produce the food we eat, including meat and milk. Colony collapse disorder, which describes the disappearance of beehives, could have catastrophic effects on food production. Australian scientists are applying their maths and science knowledge to build up a picture of a healthy ...

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TIMES Module 11: Measurement and Geometry: area, volume and surface area - teacher guide

This is a 15-page guide for teachers containing explanations of the derivation of formulas for the areas of parallelograms, trapeziums, rhombuses and kites. Formulas for the volumes and surface areas of prisms and cylinders are obtained. Applications of these formulas are given. A history of the development of these concepts ...

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Making a large wicking bed

Wicking beds are a fantastic invention, allowing crops to be watered more efficiently. Making a large wicking bed does involve a few steps and some preparation, however the benefits of this extra effort are water conservation, improved plant growth and better crops. The design of the wicking bed also provides opportunities ...

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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reSolve: Polygon Pieces

This lesson explores the geometry of cutting polygons in different ways and using algebra to express subsequent findings. Students use one straight cut to divide a convex polygon into two new polygons. They make generalisations about the total number of sides of the two new polygons, and about the number of different combinations ...

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reSolve: Quarter Cartons

This lesson challenges students to use algebra and proportional reasoning to investigate how changing the size of a paper square or rectangle impacts the dimensions of a box folded from that paper. Students apply knowledge about nets of 3D objects and explore algebraic relationships through a set of hands-on activities ...

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reSolve: Circumference

This sequence of three lessons explores the properties of circles, in particular the relationship between the diameter and circumference. In the first lesson, students use a cylinder containing three tennis balls to understand that a circumference is 'three and a bit' times the diameter. They then complete five different ...

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reSolve: Area of a circle

This lesson explores the formula for calculating the area of a circle. Students estimate the area of a circle using inscribed and circumscribed squares, and investigate proofs of the area formula. Each lesson is outlined in detail including curriculum links, vocabulary, materials needed, sample answers, supporting PowerPoint ...

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reSolve: Mechanical Linkages: Quadrilaterals

This series of six lessons explores geometry using real world contexts focussed on the dynamics of linkages and moving joints of everyday tools and objects. Students use physical models and computer simulations, the lessons move from a view of geometry as a study static diagrams to encompass movement. Each lesson is outlined ...

Video

Mystery man Pythagoras meets his match

What do you know about Pythagoras? Join Vi Hart as she not only explains his theorem but raises some legends about his dark past! Follow Vi's timeline of famous mathematicians to find out in which century Pythagoras lived. See how Vi shows a proof of his theorem and raises what was a big dilemma for Pythagoras: the irrational ...

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Comparing fuel consumption

Is it more fuel efficient to drive or fly between two places? Watch this clip and learn how to calculate the answer. What are the various factors that need to be taken into account? This video was made using the American measurement of gallons per hour, American firgures for the average number of passengers in a car and ...

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MathXplosion, Ep 50: How to use a tetrahedron to solve the tree problem

How can you place four trees exactly the same distance apart from one other? By making a model! By using miniature trees to make a model of the problem, it becomes clear that a 2D solution is impossible. We learn how objects can help us visualise the problem situation, which in this case requires a 3D solution: a tetrahedron.

Interactive

Numeracy wrap: Tell me why

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

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TIMES Module 15: Measurement and Geometry: Pythagoras's theorem - teacher guide

This is a 24-page guide for teachers. It contains proofs of Pythagoras's theorem and its converse, applications of Pythagoras's theorem and a discussion of Pythagorean triads. A history of Pythagoras's theorem concludes the module.

Interactive

Surface area and volume

This is an interactive resource about investigating the surface areas and volumes of rectangular and triangular prisms. The resource can be used in one of two modes. In the Explore mode, the student can vary the height, width and depth of the prism, and the surface area and volume are calculated automatically. In the Compute ...

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TIMES Module 20: Measurement and Geometry: parallelograms and rectangles - teacher guide

This is a 17-page guide for teachers. It contains the definitions, properties and tests for parallelograms and rectangles. Proofs of the properties and tests are given. Constructions for parallelograms and rectangles are given.

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Circles

This is a website designed for both teachers and students that refers to the properties of circles including the circumference and area from the Australian Curriculum for year 8 students. It contains material on finding circumferences and areas of circles, and the areas and perimeters of shapes formed from circles and other ...

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TIMES Module 17: Measurement and Geometry: the circle - teacher guide

This is a 15-page guide for teachers. In the module the formulas for finding the circumference and area of a circle are introduced. The history and significance of the number pi is also included in this module.

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Volumes of prisms

This is a website designed for both teachers and students that refers to volumes of prisms and using formulas to find the volumes of prisms. It contains material on rectangular and triangular prisms and finding the volumes of these by using formulas. There are pages for both teachers and students. The student pages contain ...