# Red October

*Keywords:*

AO elaboration and other teaching resources

In the film The Hunt For Red October, at one point the escaping Russian submarine has to navigate a complicated underwater trench. This unit is built around that idea and brings in the measurement of angle and distance. It is expected at this stage that the students will know how to use protractors.

- follow directions given in bearings
- invent their own maps using bearings
- use a protractor to produce maps

Angle can be seen as and thought of in at least three ways. These are as:

- the spread between two rays
- the corner of a 2-dimensional figure
- an amount of turning

The final one of these underpins the others and leads on naturally to the definition of degree and the ability to measure angles with a standard unit. This leads students on to being able to apply their knowledge of angle in a variety of situations.

We see angle as developing over the following progression:

Level 1: quarter and half turns as angles

Level 2: quarter and half turns in either a clockwise or anti-clockwise direction

angle as an amount of turning

Level 3: sharp (acute) angles and blunt (obtuse) angles

right angles

degrees applied to simple angles – 90°, 180°, 360°, 45°, 30°, 60°

Level 4: degrees applied to all acute angles

degrees applied to all angles

angles applied in simple practical situations

Level 5: angles applied in more complex practical situations

The concept of angle is something that we see students developing gradually over several years. As their concept matures, they will be able to apply it in a range of situations including giving instructions for directions and finding heights. In the secondary school angle is used extensively in trigonometry (sine, cosine, tangent, etc.) to measure unknown or inaccessible distances. This deals with situations where only right-angled triangles are present in 2-dimensional situations through to more complicated triangles in 3-dimensional applications.

Surprisingly these trigonometric functions are used in abstract settings too. At Level 8 and above they are used extensively in the calculus as a means to integrate certain functions in calculus.

Outside school and university, angle is something that is used regularly by surveyors and engineers both as an immediate practical tool and as a means to solve mathematics that arises from practical situations. So angle is important in many applications in the ‘real’ world as well as an ‘abstract’ tool. This all means that angles have a fundamental role to play in mathematics and its application.

#### Getting started

Tell the story of The Hunting of Red October. (If the students have seen the film then they can be asked to give the main points of the film.) Sean Connery plays a Russian submarine captain who decides to defect with a new submarine. At one point in the film he has to navigate through a natural trench in the Atlantic Ocean. He can’t see where he is going and relies on his navigator to give him directions. We are going to recreate this part of the film in this unit.

*Today you are going to draw a map of the Norwegian Ravine in the Atlantic Ocean from the instructions that I am about to give you *(Copymaster 1)*. The important thing here is that you should end up at the right place and not hit the sides of the Ravine. So I will give you co-ordinates and bearings so that you can construct a map of the Ravine.*

In their groups of two, let the students draw the Norwegian Ravine using graph paper. The co-ordinates of the various points are

B = (0, 5); C = (8, 5); D = (8, 11); E = (4, 11); F = (4, 8); G = (2, 8).

When they have finished that exercise let them devise their own Ravine map using only the four points of the compass. They should draw their maps and then list the instructions needed to recreate the maps. Pairs of students then swap instructions so that a different pair draws the map. Get the two pairs to check each other’s work. You may need to support some pairs.

#### Exploring

Session 1

We have drawn the Newfoundland Net (see Copymaster 2). Using protractors and ruler the students are to draw it to scale so that 1 km is 1 cm on their drawing. When they have finished they should determine the co-ordinates of the points A, B, C, D, E and F. They should also measure the straight line distance from the start to the finish of the Net.

Session 2

In this session use the map in Copymaster 3. The students work in pairs to navigate the Russian Graveyard.

One student is the navigator and has the map from Copymaster 3. The other student is the coxswain who steers the Red October. The coxswain rolls a dice. The navigator tells the coxswain how much of that roll the Red October can move forward by until a turning point in the Russian Graveyard is reached. At these points the navigator tells the coxswain the new heading and the coxswain moves forward by the amount of the last roll that is unused. The coxswain then rolls again.

The coxswain marks the turning points on graph paper and joins them up. The co-ordinates of the turning points should be read off of the graph paper at the end to see if the coxswain has got the Red October safely through the Russian Graveyard.

Interchange the navigator and the coxswain. Turn Copymaster 3 upside down and repeat the above game.

Session 3

The Scandinavian Sweep

Use Copymaster 2 in this version of the game where there are two navigators and two coxswains manning two submarines – the Red October and Konovalov. The Konovalov is chasing the Red October. Repeat the scenario in the Russian Graveyard but give Red October two rolls start. Can the Konovalov catch the Red October?

The pairs can swap submarines and can start moving through the Sweep from either end. Check co-ordinates at the end to make sure that no submarine has collided with the wall of the Sweep.

#### Reflecting

In the final lesson of this unit allow the students to produce their own maps with instructions for navigating the maps. The channels should be such that the submarines are never moving in the direction of any of the major points of the compass.

Groups should interchange their instructions and try to recreate each other’s maps.

Dear Family and Whānau,

This week we have been looking at the construction of routes on a map. We would like you to work together with your child to choose two points on a map and then make a list of instructions on how to go along that route from beginning to end using a protractor and compass.

We would like to see these instructions to see if we can follow them in class. Try to find routes where the sections are straight lines.

Attachment | Size |
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redoctoberCM1.pdf | 44 KB |

redoctoberCM2.pdf | 47.57 KB |

redoctoberCM3.pdf | 48.07 KB |