Laptop wrap: Spherical geometry

Teaching notes

Approaching the tasks

This resource is designed to give students studying General Mathematics Stage 6 a visual experience that will help them consolidate their understanding of the key concepts from the Spherical Geometry unit.

Google Earth provides an effective simulation of the Earth’s rotation. By creating their own simulation using Google Earth and Adobe Captivate students develop their skills in applying technology to enhance and show their learning of spherical geometry.

Students complete a spreadsheet to find and apply the angular dfference formula for calculating time differences between cities on Earth. They demonstrate their understanding of Greenwich Mean Time and of how longitude coordinates impact on these time differences.

Each spreadsheet is designed to help students locate and calculate the angular difference between two points and then implement the arc length formula and time calculations.

When calculating the furthest point from their current position students should:

  • change the value of the latitude from either N to S or vice versa and

  • subtract the latitude from 180 and change East to West or vice versa depending on their position.

The Amazing Race activity allows students to show their learning through the virtual application of Spherical Geometry in a realistic scenario.

The FreeMind mind mapping activity will help students to create a visual scaffold to help them understand how Spherical Geometry can be used to solve practical and mathematical problems.

For students who may not have used FreeMind before, a YouTube Tutorial video has been embedded in the resource. If access to YouTube is blocked to students on the school network it may need to be accessed through the teacher’s login.

Other activities listed in the Syllabus Suggested applications and modelling tasks (M7) could be explored further here.

Curriculum links

This resource is designed for use with the following syllabus:

HSC M7: Spherical geometry.

In this unit, geometry and trigonometry are applied to solve problems relating to the Earth as a sphere. Applications include locating positions on the Earth, using latitude and longitude, and calculating time differences.

A student:

H1 - appreciates the importance of mathematics in her/his own life and its usefulness in contributing to society

H2 - integrates mathematical knowledge and skills from different content areas in exploring new situations

H6 - analyses two-dimensional and three-dimensional models to solve practical and mathematical problems

H7 - interprets the results of measurements and calculations and makes judgements about reasonableness

H11 - uses mathematical argument and reasoning to evaluate conclusions drawn from other sources, communicating his/her position clearly to others.

  • calculating arc lengths of a circle

  • using the Equator and the Greenwich Meridian as lines of reference for locations on the Earth’s surface

  • locating positions on the globe using latitude and longitude

  • calculating distances between two points on the same great circle in nautical miles and kilometres (radius of the Earth to be taken as 6400 km)

  • using time zones and the International Date Line in solving problems

  • calculating time differences given the difference in longitudes
    (Apply 15° = 1 hour and 1°= 4 minutes time difference. Daylight-saving time is to be considered.)

  • Calculate the present time in all the capital cities of Australia.

  • Investigate which states in Australia have daylight-saving, and if so, when it starts and finishes.

  • Students collect data to enable them to discuss and present information on the popularity of daylight-saving.

  • Students find three cities with the same time, say a given number of hours earlier and later than local time. These could be marked on a world map and displayed to reinforce the concept of time zones.

  • Find the coordinates of the point on the Earthʼs surface that is at maximum distance from your current location.

Extract from General Mathematics Stage 6 syllabus, 2011, ©Board of Studies, NSW.

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Learning resources for DER NSW

For a more comprehensive list and detailed support on the complete suite of resources visit DER-NSW laptop resources.

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