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 video¹ 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.

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.

Syllabus outcomes

Students learn and acquire the following skills, knowledge and understanding

Suggested applications and modelling tasks (M7)

Extract from General Mathematics Stage 6² syllabus, 2011, ©Board of Studies³, NSW.

Intellectual quality

• Deep knowledge

• Deep understanding

• Higher-order thinking

Quality Learning Environment

• Engagement

• High expectations

• Student direction

Significance

• Background knowledge

• Inclusivity

• Connectedness