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Teacher resource

TIMES Module 21: Measurement and Geometry: rhombuses, kites and trapezia - teacher guide

This is a 32-page guide for teachers. It contains the definitions, properties and tests for rhombuses, kites and trapezia. Proofs of the properties and tests are given. Constructions for rhombuses, kites and trapezia are provided.

Teacher resource

TIMES Module 26: Measurement and Geometry: circle geometry - teacher guide

This is a 44-page guide for teachers. It contains theorems on chords, arcs, angles and secants associated with circles.

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Measuring our coastline

How long is the Australian coastline? See Dr Derek Muller and Simon Pampena discussing the perimeter of the Australian coastline. Find out how the accuracy of that measurement depends on the length of the 'measuring stick' used. They discuss how a coastline is much like a fractal such as 'Koch's Snowflake'!

Teacher resource

Primary mathematics: open-ended tasks

These seven learning activities, which focus on 'open-ended tasks' 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 investigations in order ...

Assessment resource

Toby jigsaw puzzle: assessment

Test your ability to complete a 2D jigsaw puzzle of twelve pieces. Look carefully at a photo of a puppy, then reassemble the picture by moving puzzle pieces and rotating them if necessary. Complete the puzzle in the fastest possible time, the least number of moves and without looking at the reference picture.

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Triangle pavers - mathematics activities

This photograph of triangular tiles inlaid in a pavement suggests explorations of the several relationships of these tiles relative to the background square regions. Size relationships and symmetry may be explored. Teachers are encouraged to scan all the ideas suggested here as relevant to the various year level groupings, ...

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Zebra markings - mathematics activities

This photograph of zebras shows the natural markings on the animals. The origin and purpose of the zebras' pelt markings may intrigue many students. The scientific explanation (the work of gifted mathematicians, biologists and chemists) is quite sophisticated. These images provide an opportunity to address concepts of symmetry, ...

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Flower symmetry - mathematics activities

The photograph shows the flowers of a five-petalled weed common in southern Australia, where it is called a soursob. The symmetry in this plant, and in many other naturally occurring examples, contributes to the human understanding of 'beauty'. The mathematical interest in the pentagon and its correlate, the pentagram, ...

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A second hand - mathematics activities

The photograph depicts a humorous approach to advertising a 'second-hand' store. It suggests a range of comparisons from the various patterns detectable here. The photograph has the potential to be considered as a 'self-replicating' process that provides a lead-in to so-called 'L systems', and to the concepts of fractals ...

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Islamic tiling patterns - mathematics activities

This photograph of Islamic tiling suggests descriptions and explorations of the symmetry as well as the irregularity (or 'imperfection') deliberately included in accordance with traditional Islamic craftsmanship. Islamic tradition does not encourage pictorial representations in artwork so beautiful tiling patterns evolved. ...

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Garden at the Red Fort - mathematics activities

This photograph of a section of the garden at the Red Fort in Agra, India, suggests explorations of several relationships relative to the background 'square' regions. Teachers are encouraged to scan all the ideas suggested here as relevant to the various year level groupings, as there is clearly an increasing mathematical ...

Teacher resource

Places for polygons - unit of work

This unit of work investigates the geometric properties of buildings to develop students’ understanding of polygons.

Teacher resource

Properties of polygons - unit of work

This unit of work develops students’ understanding of polygons.

Teacher resource

Symmetry: mobile devices - teacher resource

This teacher resource illustrates how students can create symmetrical patterns using mobile devices. Images can be selected, annotated and placed within applications (apps) loaded on mobile devices. The example demonstrates how a sequence of images can be created from a photograph of the Victory Gate in Vientiane, Laos. ...

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'Subway escalator', 1953

This is a tempera painting by Frank Hinder (1906-92), dated 1953. Measuring 92.8 cm x 72.5 cm, this largely abstract work is dominated by a centrally placed lozenge-shaped unit consisting of a mass of variously sized and blue-coloured crystalline shapes. This central unit runs diagonally from the bottom right to the top ...

Interactive resource

EagleCat: rotasym

Explore rotational symmetry. Observe how many times a shape will fit exactly into itself as it is rotated through 360° about its centre. Explore rotational symmetry in numbers, letters, regular polygons and other shapes. Relate the order of symmetry to the factors of 360°.

Interactive resource

Finding symmetry: three lines: city

Explore a futuristic city to find shapes with at least three lines of symmetry. Look for shapes that are hidden in objects, for example a pentagon, square and triangle. Use the testing wand to fold the shapes into matching halves. Check your prediction. Find and test more hidden shapes. This learning object is one in a ...

Interactive resource

Trig radians: tangent tool

Use a unit circle tool to explore tangent values in different quadrants. Determine the values of tangent for angles between 0 and 2π radians. Use the information to determine what the graph of tan Ø will look like. This learning object is one in a series of seven objects. Three objects in the series are also packaged as ...

Interactive resource

Trig radians: cosine tool

Use a unit circle tool to explore cosine values in different quadrants. Determine the values of cosine for angles between 0 and 2π radians. Observe how the graph represents the values. This learning object is one in a series of seven objects. Three objects in the series are also packaged as a combined learning object.

Assessment resource

Trigonometry: assessment

Test your understanding of angles and their sine, cosine and tangent values. Use a unit circle tool to find sine, cosine and tangent values in different quadrants. Use the tool to find the angle when given sine, cosine or tangent values. Determine the values for angles between 0° and 360°. Solve problems by using the unit ...