MATHEMATICAL LITERACY GRADE 12 CAPS TOPIC 3 Maps

*MATHEMATICAL LITERACY GRADE 12 CAPS TOPIC 3: Maps, plans and other representations of the physical world Section 3. 3: Compass Directions

*Topic 3: Maps, plans and other representations of the physical world The following sections will be covered: 3. 1. Scale 3. 2. 1 Map Work(1) 3. 2. 2 Map Work(2) 3. 3 Compass Directions 3. 4. Plans (floor, elevation and design plans) 3. 5. Models

*Section 3. 3: Compass Directions *In section 3. 3, learners will be able to: ØGive the direction of one point on a map in relation to another point using compass directions. ØGive a set of directions that describe a given route on a map. ØInterpret correctly information on road signboards. ØUse compass directions in house construction.

*Compass Directions It is not always useful to use directions such as left and right when you are working with maps. For example, it is not very accurate to say that Mozambique is to the right of South Africa, because the directions left and right depend on which way you are facing. The two learners in the picture on the next slide are looking at the same map, but Mozambique is to the left of South Africa in one view and to the right in the other view.

*. *Compass Directions

*Compass Directions You can use compass directions to give accurate directions. The main compass points are north(N), south(S), east(E), west(W).

*Compass Directions between the main compass points are also named: northwest(NW), southwest(SW), northeast(NE) and southeast(SE).

*Compass Directions Maps usually include compass directions. In many cases, only the direction of north is shown and you need to use that to work out the other directions. These directions are always in the same position relative to each other, so north is always opposite south; west is always on the left if north is at the top and east is always opposite west. On a map Mozambique is to the east of South Africa.

*Example 1: Map of Soweto .

*Example 1 1. Describe the route shown on the map of Soweto on the previous slide. 2. What is the direction from : a) Jabulani (N 13) to Dobsonville(M 13) b) Dobsonville(M 13) to Jabulani(N 13) c) Pimeville Golf Course(O 14) to Regina Mundi Church(N 14) d) Eldorado Park(O 15) to Lenasia(P 13)

*Solutions: 1. Example 1 Travel south from Doornkop towards the N 12 and then take the N 12 eastbound. At the N 1, take the N 1 north. Take the forth offramp and eastbound and turn to the north at the first intersection. You will be at the Nasrec Expo Centre. 2. a) north b) south c) northwest d) southwest

* Activity: 1

*Activity: 1 1. In which direction would you be driving if you drive along main street? 2. In which direction would you be cycling if you cycle along Rose Street? 3. In which direction do you turn to turn from Lions Head into Petunia Road? 4. Andile is standing at position A. If the church is on his right, in which direction is he facing? 5. Andile is a courier. He has to deliver parcels to places A, B, C, D and E in that order. He is at point A. Write a set of clear directions, using

*Solutions: Activity 1 1. North 2. West 3. East 4. East 5. Answers will differ. Accept any correct answer.

*Compass directions in everyday life Pilots and ship captains use compass directions and latitude and longitude coordinates to find their way around the world. People who use GPS systems in their cars also use such coordinates because the GPS system finds locations by pinpointing precise latitude and longitude coordinates. Many people encounter compass directions while driving – specifically on some signboards. The example that follows will explore this further.

*Example: 2 The photograph below shows a road sign on William Nicol Drive in Johannesburg The signboard gives a variety of information: *The name of the road- e. g. “witkoppen road” *The name of the suburbs the road will travel to, e. g. “Honeydew” and “Sunninghill” *Number of the road e. g. R 511 or R 564.

*Example: 2 *The compass direction in which a particular road is travelling-e. g. R 564 W indicates that a driver on this road is travelling in a westerly direction on the R 564. *Compass directions are provided on street maps so that when a person arrives at an unfamiliar intersection they can determine in which direction to travel if they know the general direction in which they need to go.

*Activity: 2 The picture below shows another signboard found on a road in Johannesburg.

*Activity 2 1. Explain all the information shown on the sign including road names, names of suburbs and the compass directions that a person will travel in when opting for each of the different possible routes shown. 2. Explain why it is useful for drivers to know the compass direction in which they will be travelling if they choose a particular route.

*Solutions: Activity 2 1. You are currently travelling along the R 55. If you continue along the road, you will continue along the R 55. However, if you take the turning or off-ramp to the left (which is in 150 m), you will be travelling in a Northerly direction towards Parktown. You would also be joining the M 27 which also leads to the M 1 free-way. If you take the ramp to the right(which is in 200 m), you would be travelling in a southerly direction and would also be joining on to the M 27, but heading towards Braamfontein or Johannesburg. 2. If drivers arrive at an unfamiliar intersection, they can still determine in which direction to travel.

*Compass directions in house construction Compass directions are also used in the construction industry. Architects and builders must choose the best position for a building in relation to the sun’s location at different times of the day and during different seasons.

. *Activity: 3

*Activity: 3 1. Towards what compass direction does the sun move during the day? 2. Describe how the position of the sun changes during summer and winter in relation to a house built with the front facing north. 3. Why do you think many people ask for their houses to be built to face north, especially for the winter months. 4. Describe the position in relation to the sun during the day in both summer and winter of a house with the main front built facing: a) west 5. b) south. Write an explanation about the benefits of building a house so that the main front faces north.

*Solutions: Activity 3 1. West 2. Summer: the sun moves from east to west. However, it travels high(perpendicular to the earth’s surface) in the sky, making most of the sun’s rays strike the roof of the house. Winter: the sun moves from east to west. However, it does not travel as perpendicular to the earth’s surface and as a result, a lot of sun’s rays strike the walls of the house, warming the home. 3. It allows for the sun’s rays to warm the walls of the house or to enter the windows thus making the home warmer in winter.

*Solutions: Activity 3 4 a). The front of the house would only have the afternoon sun. 4 b). The same effect as if the house were facing north, however, the back rooms (facing north) would be warmer. 5. Summer: the sun moves from east to west. However, it travels high (perpendicular to the earth’s surface) in the sky, making most of the sun’s rays strike the roof of the house thus making the home cooler in summer. Winter: the sun moves from east to west. However it does not travel as perpendicular to the earth’s surface and as a result, a lot of the sun’s rays strike the walls of the house warming the home.

*Final Assessment Questions 1 -10

*Final Assessment Questions 1 -10

*Final Assessment Questions 1 -10 Use the road map of the Free State on the previous slide to answer questions 1 - 4. Hint: Remember, road maps usually have kilometre distances printed on them. The distances are printed on each stretch of the road. There is usually markers to show where each distance starts and ends.

*Question 1 Nandi leaves Bethlehem and travels on the N 5 west. What is the first town on her way? A. Senekal B. Paul Roux C. Clarens

*Question 2 Susan leaves Theunissen and travels southeast for 34 km. She then travels southwest for 46 km before travelling 32 km southeast again. At which place will she arrive. A. Brandfort B. Allandale C. Excelsior

*Question 3 *What is the compass direction from Maseru to Bethlehem? A. North East. B. South West C. North.

*Question 4 Give the compass direction of Bradfort from Verkeerdevlei. A. Northwest B. East C. Southeast

*Questions 5 - 7 A family needs to decide which side of a hill to build their house.

*Question 5 If they build the house on the side of the hill facing eastwards, how would the house be positioned in relation to the sun during the day? A. The house would face too much sun in the afternoon making the home very hot during summer months. B. The house would face the morning sun, but it would be cool in the afternoon, making it nice for the summer months but very cool for the winter. C. The house would not face any sun throughout the day making it cool all the time.

*Question 6 If they build the house on the side of the hill facing westwards, how would the house be positioned in relation to the sun during the day? A. The house face the morning sun, but it would be cool in the afternoon, making it nice for summer months but very cool for the winter. B. The house would not face any sun throughout the day making it cool all the time. C. The house would face the afternoon sun, but it would be cool in the morning , making it nice for summer months but very cool for the winter.

*Question 7 Where would you build the house. Explain your answer. A. North side. Summer: the sun moves from east to west. However, it travels high (perpendicular to the earth’s surface) in the sky, making most of the sun’s rays strike the roof of the house thus making the home cooler in summer. Winter: the sun moves from east to west. However it does not travel as perpendicular to the earth’s surface and as a result, a lot of the sun’s rays strike the walls of the house warming the home. B. C. South side. It will always be cool in summer West side. It will always be warm in winter.

*Questions 8 - 10 On which road and in what compass direction would you be driving to get to Honeydew? A. On R 511 North B. On R 564 East C. On R 564 West

*Question 9 From which direction are you driving as you approach Hartbeespoort on R 511? A. West B. North C. South

*Question 10 If you travel along R 564 eastwards, which suburban area do you get to? A. Sunninghill B. Hartbeespoort C. Witkoppen

*Solutions Final Assessment Questions 1. B 2. C 3. A 4. A 5. B 6. C 7. A 8. C 9. C 10. A