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SUBJECT & GRADEMATHEMATICAL LITERACY, GRADE 11TERM 1WEEK 7TOPICWORKING WITH MAPS (DIRECTIONS AND POINT LOCATIONS):AIMS OF LESSONThe week’s lesson will focus on the following aspects of Maps (directions and point locations): Describing the position of an object in relation to surrounding objects.Describe the position of a building in relation to surrounding buildings.Find locations, follow directions and develop directions for travelling between two or more locations using the following mapping reference systems and/or techniques:Directional indicators – “left’, “right”, “straight”, etc.House or building numbering systems.Seat numbers in a sport stadium or theatre.Grid reference systems.Estimate the following when working with maps:Distances using measurement and a given scale.The time it will take to travel between two or more locations.The amount and cost of fuel that will be used in travelling between two or more locations.Average speed travelled during a trip.Determine appropriate stopping locations with consideration of petrol consumption and/or fatigue.RESOURCES Paper based resourcesDigital resources The Answer Series: Pages 129 – 137 Via Afrika: Pages 128 – 149 Study & Master: Pages 327 – 346 is expected that the skills and knowledge gained in Gr 10 must now be used in order to:Make sense of the information shown on various maps.Follow and describe a set of directionsUse grid reference systemsUse scales (number and bar) to estimate the distances between objects or places.Plan trips, including estimating travelling times, travelling costs and travelling speeds.In Grade 11 we will work with the same maps as in Grade 10, but we will also include street maps, national, provincial road and rail maps and residential or housing estate maps.CONCEPTS AND SKILLSWORKING WITH MAPS (DIRECTIONS AND POINT LOCATIONS):REQUIRED TERMINOLOGY:Map – it is a two-dimensional representation of an area of the Earth’s surface.Plan – it is a more detailed representation of a smaller area, often showing landmarks or objects.Scale - The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground.Relative position – used when describing your position or directions to someone in relation to surrounding landmarks.Grid reference maps – label the area using a grid reference number (e.g. B5) locating the area of interest within a specific block on the map.Transport maps – Indicates the transport routes that a bus/train/taxi takes, together with the stops (to pick up or drop off passengers) along the route.MAPS:Maps are a representation of reality, they use a scale to keep everything in relation to the actual size. This is represented by the scale factor that can be represented by a numeric scale (ratio scale) or a bar scale.Below is a quick summary of how to use the difference scales (previous lesson on scales)RATIO SCALEBAR SCALEExample: 1 : 2 000Measure the length on the mapMultiply the length measured by the scale factor (from map to real-life)Your answer will be in the same unit as your measurement.Convert unit into the required units as indicated in the question.Example:A bar scale shows ratio in a graphic form. The conversion has been done for you.Determine the distance covered in one block on your scale.Measure the length on the map.Multiply the length on the map by the distance shown in the bar.The answer will be in the unit as indicated on the bar scale.GRID REFERENCES:Most maps will have a grid over the map that will make it easier for you to pinpoint a point of interest. This is often used in map books to make it easier to find the point of interest. They will give you a page number as well as a grid reference (a letter and a number, e.g. A5) to help you find your point of interest.3717018301640428392465123801431371112079114311175507764932221120791Horizontal gridlines00Horizontal gridlines5273040164828Vertical gridlines00Vertical gridlines26485933013943201950100330a)00a)3438302462701 Certain maps give us the letters on the vertical gridlines and others on the horizontal gridlines. Irrespective where it is, it is common practice to write the letter first and then the number.The point indicated with a) will be grid reference B3. MAP KEYS:When we work with maps, we will also be exposed to a map key. We use icons to convey certain information on the map. The map key interprets what the icons on the maps represent in real life.It is important that you can interpret the information given on the key. It will make it easier for you to retrieve information from maps.EXAMPLE QUESTIONS:QUESTION 1:Study the map of Woodlands and answer the questions that follow:KEY: = School1.1:Write down how many schools are in the Woodlands area?1.2:If I stayed on the corner of Sycamore and Syringa Streets (?), describe how to get to the Woodlands Hospital.1.3:If the scale on the map is 1 : 80 000, determine the distance (in km) if the distance on the map from Sycamore and Syringa streets (?) to Woodlands Hospital is 53 mm.ANSWERS:1.1:3 Schools (Woodlands primary, Raisethorpe Primary and Alston Primary)1.2:Turn left up Syringa Street. Follow the road which turns to the left (still part of Syringa Street). Pass Melsetter and Mulberry Roads on your left. Turn right into Camphor Road. Woodlands Hospital will be on your left.1.3:Actual distance = 53 mm × 80 000Actual distance = 4 240 000 mmActual distance = 4 240 000 mm ÷10 ÷ 100 ÷ 1 000Actual distance = 4,24 kmQUESTION 2:Study the map of the library below and answer the questions that follow:2.1:Write down in which room you would make use of a computer.2.2:Write down how many copiers the library has.2.3:Write down how many rooms contains issues of journals.2.4:Describe how to get to the group study room from the entrance.ANSWERS:2.1:Room H – Computer Study Room.2.2:5 (indicated by ●)2.3:Two rooms (Room B and E)2.4:As you enter the library, turn right and walk towards the circulation desk and information counter. Then turn left and walk up the stairs. Turn right and walk through Room B and thereafter you will walk directly into Room A, which is the group study room.QUESTION 3:Refer to the map below and answer the following questions:3.1:Write down the town with a Grid Reference I4.3.2:Write down the grid reference of Hoedspruit.3.3:If a car was travelling in a southerly direction from Hoedspruit, and down past Hazyview; write down the next town that they will reach if they remain on the same road.ANSWERS:3.1:Baberton3.2:E43.3:White RiverQUESTION 4:Beverly is a die-hard Rodriquez fan, so she goes into Computicket to book her ticket for the upcoming show.Study the booking layout to answer the questions.4.1:Write down the venue where the show “AN EVENING WITH RODRIQUEZ” will be held.4.2:Write down the number of block of seats are in the venue.4.3:Write down the difference in price of a seat in Block A and Block B.ANSWERS:4.1:Grand Arena, Grand West4.2:11 Blocks4.3:Difference in price = Price of Block B – Price of Block ADifference in price = R565,00 – R510,00Difference in price = R55.QUESTION 5:Magnus is a German tourist who wants to explore the Western Cape. He books his accommodation in Paarl and uses the basic distances between the towns and cities (as shown on the map below) to plan his adventures.Use the map provided and answer the questions that follow.5.1:Write down the distance of a return trip if Magnus decides to go Franschhoek for the day.5.2:Magnus decided that he wants to go and explore Worcester as well. Calculate how long it will take (in minutes) Magnus to drive to Worcester if he drives at an average speed of 80 km/h. Use the following formula:Speed = distance ÷ time5.3:Calculate how much fuel he will need for a return trip to Worcester if his car has a fuel efficiency of 7,8 litres/100 kilometres. 5.4:Calculate how much it will cost Magnus if he uses 9,36 litres of fuel and the fuel costs R 14,45 per litre.ANSWERS:5.1:A return trips means there and back.? 25 km × 2 = 50 km5.2:Speed = distance ÷ timeTime = Distance ÷ SpeedTime = 60 ÷ 80Time = 0,75 hoursTime = 45 minutes5.3:Return trip = 120 kilometres 5.4:Cost of fuel = 9,36 litres × R14,45 ? (120 ÷ 100) × 7,8 Cost of fuel = R135,25= 9,36 litresCAN YOU DO THE FOLLOWING?Make sense of the information shown on various maps.Follow and describe a set of directionsUse grid reference systemsUse scales (number and bar) to estimate the distances between objects or places.Plan trips, including estimating travelling times, travelling costs and travelling speeds.ACTIVITIES/ASSESSMENTWORKING WITH MAPS (DIRECTIONS AND POINT LOCATIONS):QUESTION 1:Carlos Valderrama was a Columbian footballer and is now studying to become a doctor. He is currently on an exchange programme in South Africa where he will be based at Polokwane Hospital. He will also attend some training courses at Pietersburg Medi-Clinic.Use the map (on the next page) of the centre of Polokwane in Limpopo to answer the following questions:1.1:Write down the grid reference for the Polokwane Hospital.1.2:Thabo Mbeki Street is a one-way street going from east to west. Write down the other street shown on the map that is a one-way street going from east to west.1.3:The Pietersburg Medi-Clinic takes up a whole block. Write down the names of the four streets around the Medi-Clinic block.1.4:Give directions to Carlos as to how to get to the Polokwane Hospital whose entrance is in Hospital Street if he is currently on the corner of Grobler and Plein Street.1.5:Calculate the distance between Polokwane Hospital and Pietersburg Medi-Clinic if the map distance in 92 mm and the scale is 1 : 22 500. Give the answer in kilometers.QUESTION 2:Jaco and Louise booked a holiday in the Northern cape. They decided to stay at the Thota Lodge & Boma. Study the area map below and answer the question that follow:2.1:What is the closest town to Thota Lodge & Boma?2.2:The information desk at Frylinckspan recommends that they travel to either Van Zylsrus or Black Rock for shopping. Write down which town would be closer for them to go shopping.2.3:Calculate their average speed if they travelled from Kuruman to Olifantshoek on a day trip which took them 1 hour 30 minutes. Round your answer off to the nearest km/h.Use the following formula:Speed = Distance ÷ TimeQUESTION 3:The plan for a rugby stadium is given below. Seats are organized in sections, with a range of seat numbers available in each section.Refer to the plan and answer the questions that follow.3.1:Harry wants to sit above the players as they run out of the tunnel. In which section should he book a seat?3.2:After the match Harry must meet up with one of his friends that was also at the match. If Harry exits the stadium by entrance/exit 9 and his friend is waiting for him by the entrance/exit 13. Describe a set up directions to help Harry use the shortest route to his friend.3.3:If the length of the rugby field is 100 m and measures 57 mm on the plan. Calculate the scale (rounded to the nearest whole number) in the form 1: ___ that was used for the map of the rugby stadium.ANSWERS OF ACTIVITIES:QUESTION 1:1.1:A21.2:Devenish Street1.3:Grobler Street, Thabo Mbeki Street, Plein Street and Burger Street1.4:Move upwards in Plein Street, passing Jorrisen, Devenish, Rissik and Van Boeschoten up to Hospital Street. Turn left into Hospital street and the entrance will be on your right.1.5:92 mm × 22 500= 2 070 000 mm? 2 070 000 ÷ 10 ÷ 100 ÷ 1 000= 2,07 kmQUESTION 2:2.1:Frylinckspan2.2:Frylinckspan to Van Zylsrus = 62 kmFrylinckspan to Black Rock = 54 km? Thota Lodge & Boma is between Frylinckspan and Black Rock so Black Rock will be the closer town.2.3:From Kuruman to Olifantshoek:52 + 33 + 48= 133 kmTime: 1 hour 30 minutes = 1,5 hours? Speed = Distance ÷ TimeSpeed = 133 ÷ 1,5 hoursSpeed = 88,67 km/hSpeed = 89 km/hQUESTION 3:3.1:West Side of stadium, Section 63.2:Harry must turn right as he exits the stadium and walk past the East entrance’s numbers 10 – 12 and then the next entrance will be entrance/exit 13. He will find his friend there.3.3:57 mm = 100 m? 57 mm = 100 000 mm (now that the units are the same, we can write it as a ratio)5757 : 100 000571: 1 754,39=1 : 1754CONSOLIDATIONEssence of lesson:Make sense of the information shown on various maps.Follow and describe a set of directionsUse grid reference systemsUse scales (number and bar) to estimate the distances between objects or places.Plan trips, including estimating travelling times, travelling costs and travelling speeds.VALUES By mastering the subject content, you will feel more positive about learning and becoming a lifelong learner. ................
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