Constructions

Preparation and Planning

This lesson requires minimal pre-planning other than the preparation of student materials and the ability to project slides. You may want to ensure that you know the meaning of all of the language used in the word bank on the Student Worksheets.

This is an ideal lesson for revision of the maths topics. Alternatively, the sufficient and varied examples allow topics to be introduced as student's progress through the lesson.

Material might prompt classroom discussion of the history of mathematics or developments in targeting as a result of more accurate planning tools. The military context can be widened to include sports and orienteering (just two examples).

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

The use of mathematics in analysing complex real-world systems is commonly known as Operations research. The term Operations research came into use in the Second World War. Faced with terrible losses from U-boat attacks, the admiralty began to search for new approaches. Patrick Blackett, a mathematician and former naval officer, brought together teams of academics and military experts who made a number of crucial contributions to the war effort.

Blackett's greatest success was to get the planes used in carpet-bombing reassigned to anti-submarine duty. Using statistics, a few estimates and some simple calculations, he showed that the planes would do far more for the war effort patrolling sea-lanes than bombing German cities. This proposal met fierce resistance from Air Marshal 'Bomber' Harris, who demanded of Churchill, 'Are we fighting this war with the sword or the slide rule?!'. Churchill puffed on his cigar. 'That's a good idea,' he replied. 'Let's try the slide rule.'

This lesson helps students to understand the crucial role that mathematics has played in warfare since the 9th century and to apply some of their skills to real-life case-studies. Drawing on historical and contemporary real-life examples students solve a number of problems faced by different branches of the armed forces and gain an understanding of the need to overlay a practical interpretation of events (i.e. taking into account external events).

In Episode 2 students tackle similar mathematical problems to those presented to the boys at the Rochester Mathematical School, Rochester, Kent, near Chatham naval dockyard. Set up partly to support the recruitment of young men into the Royal Navy and ensure the requisite skills, boys at the Mathematical School were taught proficiency in mathematics (specifically constructions, navigation and geometry) and astronomy. The Mathematics School still exists today though is now co-educational and follows a mainstream curriculum, with no formal ties to the Royal Navy.

Further Opportunities for Learning

Students should consider other contexts for application of construction skills, specifically using a ruler and protractor and should devise their own case-studies to this effect, e.g. fly fishing, orienteering and ball sports.

Invite citizenship-based discussion of the importance of investment in weaponry technologies and the sharing of skills between nations. Students should weigh up the benefits of accuracy (less unnecessary destruction, ability to provide a better line of defence) against cost (weaponry needing to be replaced, men needing to be retrained.

Students may wish to conduct further research into the historical competition between warring sides and the history of mathematics in the race to develop the most accurate and cost effective weapon delivery systems. Consideration of the tools and materials available to men over time will have influenced developments.

Students proficient in ICT might develop a simple programme for forecasting the anticipated maximum height and distance of a projectile assuming consistent missile weight, flat terrain and no wind etc.

Invite students to explore the impact of error on targeting e.g. the impact of a 1 degree increase in elevation at firing point.

Student worksheet answers

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