Pythagoras' Theorem

Preparation and Planning

This lesson requires students to have prior familiarity with Pythagoras' Theorem.
Students will benefit most from this lesson if you have access to a whiteboard and PC with broadband access or projector. Minimal further preparation is required other than photocopying of Student Worksheets and preparation of associated multi-media resources. Students will need a calculator for this lesson.
Able students will enjoy the opportunities that this lesson provides for role-play and teamwork, and to begin to visualise more complex mathematical / trigonometric constructions.
Google provides an online, satellite mapping service that can be used to support the exercises in this lesson and help students identify landmarks and features in their area. Google Maps can be accessed via: http://maps.google.co.uk/maps

Note: To ensure accurate completion of the Worksheets, they must be printed with no margins. Go to your printer settings and select 'none' on page scaling. Map scales used are not representative. You should make students aware of this.

About the MOD Topic

A no-fly zone is a territory over which aircraft are not permitted to fly without authorisation. This is usually for security reasons, though efforts to limit noise pollution and ensure privacy can also give rise to restrictions on routes. Responsibility for enforcing no-fly zones in the UK and on UK-led operations, lies with RAF Air Command.

No-fly zones are in effect over many sites in the world, including the following:
United Kingdom:
- Buckingham Palace
- Flights over Whitehall need extensive clearance
- Some RAF bases
- Royal Houses and Senior Politician's houses
- Other sites according to need.

Falkland Islands:
- On-going restrictions in place following the Falklands War in 1982. This is a Control Terminal Region (CTR).*

Peru:
- Macchu Picchu.

India:
- Taj Mahal, Agra
- Parliament Building, New Delhi.

US:
Temporary flight restrictions over:
- Disneyland
- Florida
- The White House
- US Capitol Hill
- Washington.

* CTR restrictions differ from military no-fly zones in that non-military aircraft can enter the area, but only after submitting flight plans to the RAF. If any unexpected air craft appear in a CTR, an RAF team will be immediately scrambled to receive them.

Further Opportunities for Learning

Use Google Earth or a local map to invite students to design their own 'no fly zone' in their local area. This could be over a football match, a prison or other secure site or to preserve the privacy of local celebrities.

Invite students to research other no-fly zones, for example the ones implemented over the Balkans in 1993, to establish the criteria and rationale for implementation and to draw maps of the zones. If possible to then use Pythagoras' Theorem to establish the land mass to be protected in this way.

Invite students to design a 'dummies guide' to Pythagoras' Theorem for presentation to their peers. This should assume no knowledge of the subject and list a variety of day-to-day applications.

Students may wish to consider defining a no-fly zone for their local area, assuming the area was to host a Royal visit, a major sporting event of music festival.

The topic of no-fly zones receives considerable media attention. Students may want to debate the merits of imposing such zones unilaterally over military sites in the UK (which would involve severe curtailing of civilian activity as these are widespread) or the opportunities that such zones give a country to afford protection to its civilians (e.g. over the Queens' Jubilee celebrations in the Mall, 2006).

Student worksheet answers

Download the teachers notes PDF to access the answers for this lesson.