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Practising Mathematics: Developing the mathematician as well as the mathematics

How can your students work like mathematicians?

An engaging selection of tasks contain activities from many areas of mathematics including: Number work, Ratio and Proportion, Algebra, Geometry, Probably and Statistics.

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Home > Better teaching > Classroom resources > Maths Inside > Stargazing with the SKA

Stargazing with the SKA

Proficiencies

7

8

9

10

11

number

measurement

geometry

understanding

problem solving

reasoning

The Square Kilometre Array (SKA) is a multi-radio-telescope project that when complete will be the largest and most capable radio telescope available to scientists. It will allow scientists to study and collect information about the universe.

Radio telescopes detect the radio waves that are produced by physical occurrences in space, and then translate these waves into data and imagery which can be used by astronomers, often in conjunction with optical and other types of telescopes.

In its first phase, the SKA will be made up of three telescopes, each made up of thousands of small antennas—which will cover a total area of one square kilometre.

Teacher notes

The teacher notes contain: an overview of each of the activities; curriculum links and suggested year levels; background information; prompting questions and key mathematical points; practical suggestions for running the activity; a list of resources needed; and further ideas.

Activity 1: Heavenly bodies

Years 7–9

Students investigate the physical properties of different planets in the Solar System concentrating on using appropriate units. They then compare some of the properties (for example, mass) in raw figures, and then by using a unit base measure.

Students may also investigate the use of the Southern Cross in navigation.

Activity 2A: How big is a square kilometre?

Years 7–9

Students will construct a square metre and work out how many of these are needed to make a square kilometre. They will then use maps to determine the extent of a square kilometre in a familiar area.

There are also several questions requiring calculations of circular areas in the context of telescopes located in Australia.

Activity 2B: Very large numbers

Years 8–10

Students complete a table to establish the pattern of expressing very large numbers in scientific notation. Relevant examples are used.

Activity 2C: Things that go very fast

Years 8–10

Students investigate doubling as the basis for counting data quantities. They produce a spreadsheet which shows the rapidity of increase when doubling.

Activity 3A: Playing around with parabolas

Years 9–11

Students fold paper to produce parabolic curves and compare the characteristics of the different parabolas. This leads to a more formal analysis where an equation for the curve of the Sydney Harbour Bridge is calculated.

Activity 3B: Practical parabolas

Years 9–11

Students create a parabolic trough which can boil water (or cook a sausage). Students create a parabolic paper dish to improve the sound on a mobile phone. Further explorations are suggested.

Activity 3B: Parabolic solar trough sausage sizzle

Instructions for building a parabolic solar trough for cooking.

Activity 4: Seeking spirals

Years 8–10

Students investigate Archimedean and logarithmic spirals. They then draw both types of spiral by hand, before using technology to draw and change a logarithmic spiral.

Students simulate selecting random points to reduce redundancy firstly by hand, and then using spreadsheets.

Years 8–10

Students are able to quickly generate 50 sets of 10 points by using the ‘refresh’ function. The distance is determined by using the formula for the distance between two points (x1, y1) and (x2y2).

Years 8–10

This spreadsheet explores the means to convert polar coordinates to Cartesian coordinates and hence investigates points on a spiral.

Activity 5: Stars and parallax

Years 10–11

Students calculate the distances to various stars using right angled trigonometry and parallax angles. They use astronomers’ measures such as the Astronomical Unit, parsecs and light years.

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