NCV 4 Mathematical Literacy Hands-On Support Slide Show - Module 4


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This slide show complements the learner guide NCV 4 Mathematical Literacy Hands-On Training by San Viljoen, published by Future Managers Pty Ltd. For more information visit our website

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NCV 4 Mathematical Literacy Hands-On Support Slide Show - Module 4

  1. 1. Mathematical Literacy 4
  2. 2. Module 4: Space, Shape and Orientation
  3. 3. Module 4: Space, Shape and Orientation <ul><li>After completing this outcome, you will be able to: </li></ul><ul><ul><li>perform space, shape and orientation calculations to solve problems </li></ul></ul><ul><ul><li>read, interpret and use representations to solve problems </li></ul></ul><ul><ul><li>make physical and diagrammatical representation to investigate and illustrate solutions </li></ul></ul>
  4. 4. Activity 1 <ul><li>It is assumed that you know what the following words mean. Explain to each other what the following words mean and complete the table: </li></ul>
  5. 6. <ul><li>Explain the meaning of the words, all of which you should have already have encountered. Work in groups. </li></ul>
  6. 7. Activity 2 <ul><li>What is the force of attraction between masses such as the earth and the moon called? </li></ul><ul><li>What is the unit of measurement of weight? </li></ul><ul><li>a. Calculate the weight of a man on the moon if his mass on earth is 90kg. (Gravitational force /acceleration on the moon is 1,57 m/s²). </li></ul><ul><li>b. Calculate this same man’s weight on earth. </li></ul><ul><li>Calculate the gravitational acceleration constant (gravitational force on Jupiter if the same man has a weight of 4628,57 N there. </li></ul>141.3 Newtons gravity Newtons 882N 51.43m.s -1
  7. 8. 2. PERFORM SPACE, SHAPE AND ORIENTATION CALCULATIONS <ul><li>At the end of this outcome, you will be able to calculate: </li></ul><ul><ul><li>Area </li></ul></ul><ul><ul><li>Volume </li></ul></ul><ul><ul><li>Distance </li></ul></ul>
  8. 9. 2.1 Dimensions
  9. 10. 2.2 Perimeter calculations <ul><li>The perimeter of a shape is the total distance around the edges, defining the outline of the shape </li></ul><ul><li>Perimeter is one dimensional </li></ul><ul><li>Perimeter is always given in a measurement of length </li></ul><ul><li>Perimeter of a circle is called the circumference </li></ul>
  10. 11. Activity 3 <ul><li>Calculate the amount of skirting board that has to be ordered in building Ashley’s house – see Summative Assessment Example at end of this module for the plan view of this house. </li></ul>
  11. 12. 2.3 Area calculations <ul><li>A square is a quadrilateral (four-sided figure) with the four sides with the same length and with four right angles, e.g. the common bathroom tile which is stuck against the wall. </li></ul><ul><li>If the sides of the tile are all 10 cm, then the area of the tile will be: </li></ul><ul><ul><li>10cm x 10cm = 100 cm² (read as 100 square centimeters). </li></ul></ul><ul><ul><li>100 is known as a square number, as are the following numbers: 4; 9; 16; 25; 36; 49; 81; 121; 144; 169. </li></ul></ul><ul><ul><li>What is the common trait in this sequence of numbers? </li></ul></ul><ul><ul><li>They can all be written in the square root form with 2 as an index: 2² ; 3² ; 4² ; 5² ; etc… </li></ul></ul>
  12. 13. Area of rectangles <ul><li>If a book measures 7cm in length and 5cm in breadth, then there are seven rows of five centimetres each and the surface area will amount to 7 x 5 square centimetres or 35 cm² the index two indicating the two dimensions. </li></ul><ul><li>Thus: Area of a rectangle = length x breadth of rectangle </li></ul><ul><li>Area of the book = 7 x 5 = 35 cm² </li></ul>
  13. 14. Formula for areas
  14. 15. Activity 4 <ul><li>Write a formula for the perimeter of a rectangle and then calculate it for the rectangles with the following dimensions. Give answers in metres. </li></ul><ul><ul><li>length = 145,46 cm; breadth = 88,95 cm. </li></ul></ul><ul><ul><li>length = 2014 mm; breadth = 258,63 cm. </li></ul></ul><ul><ul><li>length = 125,25 m; breadth = 5 238 cm. </li></ul></ul>Perimeter of rectangle = 2(l+b) 468.82cm = 4.68m 6.614m 355.76m
  15. 16. Activity 4 <ul><li>2. Now do the same for the areas of the rectangles with the dimensions in the previous question. Give answers in square metres. </li></ul><ul><ul><li>length = 145,46 cm; breadth = 88,95 cm. </li></ul></ul><ul><ul><li>length = 2014 mm; breadth = 258,63 cm. </li></ul></ul><ul><ul><li>length = 125,25 m; breadth = 5 238 cm. </li></ul></ul>1.29m 2 5.21m 2 6560.60m 2
  16. 17. Activity 4 <ul><li>3. Calculate the circumference of circles with the following radii. Look at the explanation of the origin of the value for π above to establish the formula for the perimeter of a circle: </li></ul><ul><ul><li>Radius = 125,4 cm </li></ul></ul><ul><ul><li>Radius = 1286,54 mm </li></ul></ul><ul><ul><li>Radius = 621,4 cm </li></ul></ul>Perimeter=  d or 2  r 787.9cm 8083.57cm 3904.37cm
  17. 18. Activity 4 <ul><li>4. Calculate the area of the above three circles. Find the formula elsewhere in the module. </li></ul><ul><ul><li>Radius = 125,4 cm </li></ul></ul><ul><ul><li>Radius = 1286,54 mm </li></ul></ul><ul><ul><li>Radius = 621,4 cm </li></ul></ul>Area of circle =  r 2 49402.04 cm2 = 4.94m 2 5.20m 2 121.31m 2
  18. 19. 2.4 Volume calculations <ul><li>Where length is a measurement in one dimension, and area is a measurement in two dimensions, volume is a measurement in three dimensions, and will always be given in cubic units. It is therefore a measure of the length, breadth and height of a container. Count the cubic content of the following rectangular prism </li></ul>
  19. 20. Example <ul><li>If a carton of fruit juice measures 5cm in the length of the base, 3cm in the breadth of the base and 8cm in the height, then the volume of fluid that the carton can contain will be: </li></ul><ul><li>5 x 3 x 8 cm or cc or ml, i.e. = 120 cubic centimetres. </li></ul><ul><li>Volume of a box = length times breadth times height. </li></ul><ul><li>But you know that the base of the box is a rectangle and that length times breadth of a rectangle = area of the rectangle. </li></ul><ul><li>So you can say that: </li></ul><ul><li>Volume of a box = (base area) times height </li></ul>
  20. 21. Volume formulae
  21. 22. 2.5 Total external surface area
  22. 23. 2.5 Total external surface area
  23. 24. 2.5 Total external surface area
  24. 25. 2.5 Total external surface area
  25. 26. Activity 5 <ul><li>1. Calculate the area in square units of: </li></ul><ul><ul><li>a rectangle with length 134,65cm and breadth 512,74cm </li></ul></ul><ul><ul><li>a circle with radius 258 mm </li></ul></ul><ul><ul><li>a triangle with base length 341cm and perpendicular height 128cm </li></ul></ul>6.90m 2 0.209m 2 2.1824m 2
  26. 27. Activity 5 <ul><li>2. Calculate the total external surface areas of the following right prisms </li></ul>
  27. 28. Activity 5 <ul><li>SA (rectangle) = 2lb + 2la + 2ab = 2(216)(91.8) + 2(216)(450) + 2(450)(91.8) = 316 677.6cm 2 = 31.66m 2 </li></ul><ul><li>Triangle height = By Pythagoras: hypotenuse = 18; base = 9, height =  (18 2 – 9 2 ) =  243 = 15.59cm </li></ul><ul><li>SA (Equilateral triangle prism) = 2(1/2 base x height) + 3(ba) = 2170.62cm2 </li></ul>
  28. 29. Activity 6 <ul><li>Decide on a suitably sized gift box which you can make to hold a small gift and / or: Use the given net to make a toy soccer ball. Enlarge the supplied net to your preferred size. Add flaps on every other side for attaching the sides with glue. </li></ul><ul><li>Steps in the making of the small model: </li></ul><ul><li>Sketch the net of your gift box or soccer ball on an A4 sheet of paper. </li></ul><ul><li>Make a copy of the net to place in your portfolio of evidence. </li></ul><ul><li>Add small attachment flaps by which the sides can be glued to each other. Experiment to determine where these flaps should be – usually on every other side. </li></ul><ul><li>Cut the net out and make the small box or the toy soccer ball with wood glue. </li></ul><ul><li>Place the gift box or that which another group member made in front of you on the table and sketch it in depth, i.e. as a holder with capacity or volume. </li></ul><ul><li>  </li></ul><ul><li>You have now made a rectangular right prism and you have sketched it in three dimensions. This kind of sketch is also called a perspective sketch. </li></ul>
  29. 30. Activity 7 <ul><li>Calculate the total external surface areas and the volumes of the right prisms in the sketches given below. </li></ul>Length of base = 12m, breadth of base =9,2m height = 520cm SA (rectangle) = 2lb + 2la + 2ab = 2(12)(9.2) + 2(12)(5.2) + 2(5.2)(9.2) = 441.28m 2
  30. 31. Activity 7 <ul><li>Calculate the total external surface areas and the volumes of the right prisms in the sketches given below. </li></ul>Sides of triangle all = 150cm; altitude of prism = 260cm Triangle height = By Pythagoras: hypotenuse = 1.5; base = 0.75, height =  (1.5 2 –0.75 2 ) =  1.6875 = 1.30cm SA (Equilateral triangle prism) = 2(1/2 base x height) + 3(ba) = 13.65m2
  31. 32. Activity 7 <ul><li>Calculate the total external surface areas and the volumes of the right prisms in the sketches given below. </li></ul>Radius of circle = 100cm , altitude of prism = 3m , = 3,1415. Cylinder = 2  r 2 + 2  rh = 2  r(r+h) = 25.132m 2
  32. 33. Activity 7 <ul><li>2. Bring any empty container which you bought in a grocery store, to class, e.g. shampoo bottle. Some of the containers must represent volume and others mass. Place the containers on a table and estimate the capacity of each holder. Make a table and compare your estimates to the correct values. </li></ul>
  33. 34. Activity 7 <ul><li>3. Sketch the following right prisms with measurements marked on the correct sides. Work out the volume and the total external surface area of each prism. </li></ul><ul><ul><li>Rectangular prism with length of base = 500cm; breadth of base = 200cm, and altitude of prism = 3000mm. </li></ul></ul><ul><ul><li>Cylinder with radius of the circular base = 180,566cm, and altitude of cylinder = 5300mm. </li></ul></ul>Volume = lbh = 5m x 2m x 3m = 30m 3 SA = 2(lb) + 2(lh) + 2(bh) = 2(5)(2) + 2(5)(3) + 2(2)(3) = 62cm 2 Volume of a cylinder =  r 2 h =  (1.80566) 2 (5.3) =54.28m 2 Surface area =2  r(r+h) =2  (1.80566)(1.80566+5.3) =80.62m 2
  34. 35. Activity 7 <ul><li>4. Calculate the volume of fruit juice in two pipes of 19,25m length: </li></ul><ul><ul><li>The first pipe has a diameter of 18 cm </li></ul></ul><ul><ul><li>The second pipe has a diameter of 6,5 cm. </li></ul></ul>Volume =  r 2 h Volume (pipe 1) =  (0.18) 2 (19.25 ) = 1.96m 2 Volume (pipe 2) =  (0.065) 2 (19.25) = 1.96m 2 =0.26m 2
  35. 36. Activity 7 <ul><li>5. A worker in a wine packing shed knows that there is still 10 000 litres of wine remaining in a tank. He has to requisition sufficient bottles of 750 ml capacity from the store to complete the bottling process. Do the calculation of bottles. </li></ul>Number of bottles = (Wine to be bottled) / Size of bottles = 10 000 / 0.75 = 13 333 bottles
  36. 37. Activity 8 <ul><li>To remind people about the value of water, a municipality reports the following on water wastage in a local newspaper: </li></ul><ul><li>With 6000 litres of water you can fill one and a half mini-bus taxis. </li></ul><ul><li>With 6000 litres of water you can fill the sink to wash dishes 200 times. </li></ul><ul><li>With 6000 litres of water you can boil 4000 kettles of water. </li></ul><ul><li>With 6000 litres of water you can flush a toilet 500 times. </li></ul><ul><li>Check on this municipality’s calculations. Decide in your group how to do each of these estimations. </li></ul><ul><li>Explain in three steps how you can check for water leaks where you stay or work </li></ul>
  37. 38. 2.6 Cones and spheres <ul><li>A cone is the three-dimensional shape – like an ice-cream cone!! </li></ul><ul><li>It is formed by a straight line when one end is moved around a simple closed curve, while the other end of the line is kept fixed at a point, which is not in the plane of the curve. A sheet of paper can be wrapped around a cone. When it is unwrapped it is a sector of a circle. </li></ul><ul><li>Any sector of a circle (cut along any two radii) can be twisted to form a cone. </li></ul><ul><li>A right circular cone is a cone with a circle as its base. </li></ul><ul><li>The height of a cone is the perpendicular distance of its vertex/tip above the base. </li></ul><ul><li>Slant height of a cone is the length of any straight line from the circumference of its base to the vertex/tip. </li></ul><ul><li>Slant height = square root of the sum of the squares of the radius and the perpendicular height (by the theorem of Pythagoras). </li></ul><ul><li>Curved surface of a right circular cone is the sector which could be bent around (until the edges meet) to form the cone. </li></ul><ul><li>Area of the curved surface = x base radius x slant height of cone. </li></ul><ul><li>Volume of a cone = pi times radius squared divided by 3 </li></ul><ul><li>Frustum of a cone is a part of a cone cut off between the base and a plane, which is parallel to the base. </li></ul>
  38. 39. 2.6 Cones and spheres
  39. 40. Activity 9 – Make a cone <ul><li>Draw a circle with a protractor </li></ul><ul><li>Use a graduated arc to divide the circle in three equal parts. </li></ul><ul><li>Cut out one of the thirds – make a copy of this cut-out to include with the portfolio of evidence. </li></ul><ul><li>Add a thin flap along the one side of the cut-out. </li></ul><ul><li>Fold into a cone. </li></ul><ul><li>Identify and measure the slant height, the perpendicular height and the radius of the base and also mark these on the cone which will go into your portfolio of evidence. </li></ul><ul><li>Calculate the total surface area of the cone. </li></ul><ul><li>Can you think of another way to calculate this area? </li></ul>
  40. 41. Cones and spheres
  41. 42. Activity 10 <ul><li>1. Find the area of a quadrilateral with vertices/corners at (Use the Cartesian co-ordinate system and work with trapezia): </li></ul><ul><li>Area of a trapezium = height / 2 x (sum of the two parallel sides) </li></ul><ul><li>a. (2;8), (5;9), (9; 6), (7;2) </li></ul><ul><li>b. (12;8), (9;6), (6; 5), (4; 3) </li></ul>
  42. 43. Activity 10 <ul><li>2. Calculate the area of the triangle with vertices as follows: </li></ul><ul><li>a. (1;2), (6; 6), (8;3) </li></ul><ul><li>b. (4;2), (8;6), (12;8) </li></ul>
  43. 44. Activity 10 <ul><li>3. The figure shows a section along the length of a swimming pool. If the pool is 8 m wide, how many kilolitre of water would be needed to fill it? (Conversion factor from feet to metres = 0,3048.) </li></ul>
  44. 45. Activity 10 <ul><li>4. A water pipe has an internal diameter of 5 cm. What volume of water is in a pipe length of one metre? If the water flows at 1m/s, what volume of water (given in cubic metres) flows through this pipe in one minute? How long will it take this pipe to fill a tank, 3 m high and 2m in diameter. </li></ul>Volume =  r 2 h Volume (pipe) =  (5) 2 (100) = 7852m 3 Amount of water passing through pipe = 1m.s -1 x 60 = 60m Volume =  (0.05) 2 (60) = 0.4712m 3 =471.2 litres Volume of tank =  r 2 h =  (2) 2 (3) =37.70 m 3 Time taken = 37.70 / 0.4712 = 80 minutes
  45. 46. Activity 10 <ul><li>5. If steel has a mass of 484lbs/cubic foot (conversion factor from pounds/cubic foot to kg/cubic metres = 16,0187), find the mass of 1000 ft (conversion factor from feet to metres = 0,3048) of girder with cross section as in the figure. (Conversion factor of inches to cm = 2,54). </li></ul>
  46. 47. Activity 10 <ul><li>6. A circular hole for a tunnel is bored 0,75 mile long (conversion factor from miles to km = 1,609344). If the hole is 25 ft in diameter, how many cubic metres of earth have to be removed? If one truck carries 25 cubic metres, how many truck loads are moved? </li></ul>0.75 miles = 1.207km 25 feet = 7.62m Volume =  (7.62) 2 (1207) = 28 894m 3 Truck loads = 28 894 / 25 = 1156 trucks
  47. 48. Activity 10 <ul><li>7. The radius of the earth is approximately 6,36 x 10³ km. </li></ul><ul><ul><li>Calculate the approximate volume of the earth. </li></ul></ul><ul><ul><li>Calculate the total external surface area of the earth. </li></ul></ul><ul><ul><li>If two thirds of the surface of the earth comprises water, calculate the area of land on earth (in square kilometers). </li></ul></ul>
  48. 49. Activity 10 <ul><li>Calculate the approximate volume of the earth. </li></ul><ul><li>V = 4/3  r 3 </li></ul><ul><li>V = 4/3  (6360) 3 </li></ul><ul><li>V = 1.078 x 10 12 km 3 </li></ul><ul><li>b. Calculate the total external surface area of the earth. </li></ul><ul><li>SA = 4  r 2 </li></ul><ul><li>SA = 4  (6360) 2 </li></ul><ul><li>SA = 5.08 x 10 8 m 2 </li></ul><ul><li>c. If two thirds of the surface of the earth comprises water, calculate the area of land on earth (in square kilometers). </li></ul><ul><li>1.69 x 10 8 m 2 </li></ul>
  49. 50. Activity 10 <ul><li>8. Suppose one cube has twice the edge length of another. Calculate how many times more the volume of concrete is in the larger cube. </li></ul>Double the amount
  50. 51. Activity 11 <ul><li>Tim is doing the Argus Cycle Tour. He aims to finish the 109 km route it in 3h30. His race starts according to plan, however, after 1hr 13 minutes, he has a puncture which takes him 12 minutes to repair. He rides for another 1:24 hours before his chain comes loose which costs him another three minutes. He then rides for another 25 minutes before stopping for a final water break. He finishes the race 23 minutes later. Questions: 1.      What was his total time to finish the race? 2.      What was his total time in stops? 3.      What would his time have been without stops? 4.      Did he archive his objective? 5.      Would he have achieved his objective without the puncture and water stop? 6.      What was his average speed when including the stops 7.      What was his average speed when excluding the stops? 8.      The fastest time in the Argus was that of Robbie Hunter who completed the race in 2 hours 27 minutes. What was his average speed? 9        What was the difference in time between Robbie Hunter and Tim? </li></ul>3h40 15 min 3h25 No Yes 29,72km/h 31.90km/h 44,49km/h 1h13
  51. 52. 3. READ, INTERPRET AND USE REPRESENTATIONS TO SOLVE PROBLEMS IN THE WORKPLACE AND OTHER AREAS OF RESPONSIBILITY <ul><li>At the end of this outcome, you will be able to: </li></ul><ul><ul><li>Use maps </li></ul></ul><ul><ul><li>Use plans </li></ul></ul><ul><ul><li>Use diagrams </li></ul></ul><ul><ul><li>Sequence activities </li></ul></ul>
  52. 53. Maps <ul><li>Road maps </li></ul><ul><li>Compass points </li></ul>
  53. 54. Direction in four compass directions <ul><li>A full circle is measured as 360 degrees. </li></ul><ul><li>A straight line is measured as 180 degrees. </li></ul><ul><li>A right angle equals 90°. </li></ul><ul><li>Direction is determined by a compass. </li></ul><ul><li>Direction on a compass is measured with reference to a line that points to the north. </li></ul><ul><li>The four main compass directions are north, south, east and west. </li></ul><ul><li>North is written as 000°. </li></ul><ul><li>South is written as 180° </li></ul><ul><li>East is 090° </li></ul><ul><li>West is 270°. </li></ul><ul><li>Direction is always given clockwise from a north pointing line. </li></ul><ul><li>Direction angles are always given in three digits e.g. 57 degrees is written 057° </li></ul>
  54. 55. Activity 11 <ul><li>1. Sketch the following angles by using a graduated arc. </li></ul>
  55. 56. 135  35  180  270  250  310  35 
  56. 57. Activity 11 <ul><li>1. An aircraft flies in the direction 065° for 700km. It then changes course and flies in the direction (on a bearing of) 155° for 300 km. Let 10mm on your page represent 100km of real distance. </li></ul><ul><li>Sketch this and fill in the angles and the distances. </li></ul><ul><li>Work out the scale factor for this sketch. </li></ul>65  135  Scale factor: 10mm:100km 10mm:100000000mm 1:10000000
  57. 58. Activity 12 <ul><li>The map comes from the Map Studio book of Cape Town. </li></ul><ul><li>The scale of the map is 1 : 20 000 </li></ul><ul><li>Can you see the foot path which is indicated by dashed lines on the mountain region? </li></ul><ul><li>You are a tour operator and have two German tourists who want to spend the whole day hiking on this part of the mountain. </li></ul><ul><li>They want to go onto the footpath at Military Road. Hike up to the Signal Hill Road and turn right to hike to the top of Signal Hill . </li></ul><ul><li>They then want to walk back down and carry on with the road up to the Lion’s Head turn off – they then want to walk to the top of Lion’s Head. </li></ul><ul><li>They will reverse their steps and go back to the Signal Hill Road, turn left and take the foot path to reach Tamboerskloof in Upper Albert Road. </li></ul>
  58. 60. Activity 12 <ul><li>They ask you to calculate: </li></ul><ul><ul><li>how far this hike is – use a piece of string to measure the distance and the scale to calculate the distance </li></ul></ul><ul><ul><li>how long it will take them </li></ul></ul><ul><ul><li>at what time they have to start </li></ul></ul><ul><ul><li>how long they can lunch </li></ul></ul><ul><ul><li>how do they get from Upper Albert Road’s tip to the Mount Nelson Hotel where they are staying. </li></ul></ul><ul><li>The two tourists also ask you the horizontal and vertical co-ordinate values of and the main wind of compass directions within the grid block of: </li></ul><ul><ul><li>SA Museum </li></ul></ul><ul><ul><li>Old Malay Cemetery </li></ul></ul><ul><ul><li>Green Point Track </li></ul></ul><ul><ul><li>Three Anchor Bay </li></ul></ul><ul><ul><li>The City </li></ul></ul>
  59. 61. Case study 1 <ul><li>The picnic table out of wood could be a special Christmas present for your parents, and the model that you will build here, could make a very nice Christmas present for you sister or daughter to play with. </li></ul><ul><li>Necessary to build the model: craft knife; reasonably sturdy cardboard; wood glue; pencil; ruler. </li></ul><ul><li>The following sketches come from the website: </li></ul><ul><li>One of the comments sent in by people who have built this table reads: “I built this table in one hour.” </li></ul><ul><li>File this information. Some day you will want to use it. There are no instructions as everything is pretty much self-explanatory. </li></ul>
  60. 62. Case Study 1 <ul><li>Your task is to build a scale model of this table. </li></ul><ul><li>Sketch one of each of the separate pieces of wood that will be used. </li></ul><ul><li>List how many of each piece will be necessary. </li></ul><ul><li>Calculate the total length of wood necessary for the real table. </li></ul><ul><li>Decide on an appropriate scale and calculate the lengths and widths of your strips of wood. </li></ul><ul><li>Use a craft knife to cut the cardboard into the correct shapes and sizes. </li></ul><ul><li>Plan the sequence necessary to assemble the parts. </li></ul><ul><li>Use wood glue to fit the pieces together. </li></ul><ul><li>In the module on finance you will work out the cost to build this table. </li></ul><ul><li>Why do the legs of the table lie at an angle to the horizontal? Which factors determined this angle? Discuss in a paragraph. </li></ul>
  61. 66. Activity 13 <ul><li>Planning the job: </li></ul><ul><li>List the sequence of activities for building the table in Case study 3. </li></ul><ul><li>Present the sequence in the form of a flow diagram. </li></ul><ul><li>If one of the activities consists of a few different steps, bring these steps in from the side of the flow chart. </li></ul>
  62. 67. Activity 14 <ul><li>This classical style bank front is built out of matches. </li></ul><ul><li>But now a different question: </li></ul><ul><li>Move two matches in this pattern and make 11 squares. </li></ul><ul><li>Move 4 matches and get 15 squares. </li></ul>
  63. 68. 4.3 Rough sketches and final plans/sketches <ul><li>A front view: This is a view of the object or building, looking at it from the front. </li></ul><ul><li>A side view : This is a view of the object or building, looking at it from the side. </li></ul><ul><li>A plan or top view: This is view of the plan or object, looking at it from above. </li></ul>
  64. 69. Definitions <ul><li>A first angle orthographic projection has the front view in the top left-hand corner of a page and next to it, the side view. Directly beneath the front view is the top or plan view of the object or building. </li></ul><ul><li>A perspective drawing is the art of representing a 3-D object on a 2-D surface so as to convey the impression of height, width, depth and relative distance. </li></ul>
  65. 71. Perspectives
  66. 72. Perspectives
  67. 73. Activity 15 <ul><li>Asanda who has the Shiny Car valet service is now married and his wife Nthabiseng, also has entrepreneurial blood in her veins. She decides to start farming chickens in their backyard. She will start with only 8 hens and is just interested in collecting and selling the eggs. </li></ul><ul><li>She gets the following beautiful sketches from a website called: </li></ul>
  68. 77. Activity 15 <ul><li>1. Nthabiseng does not understand the measurements. Convert all the Imperial Measurements to metric for her. </li></ul>
  69. 78. Activity 15 <ul><li>2. One group in the class must demonstrate to the others groups how big this hen house actually is by measuring it out on the ground. Set out the plan section by packing stones or bricks. Also set out on your floor plan the nesting area. </li></ul>
  70. 79. Activity 15 <ul><li>3. Build a model of this hen house for Nthabiseng out of cardboard. Use a craft knife to do the cutting. Use wood glue to attach everything. The cupola can jus be fitted on top of the house, i.e. don’t actually make it work. The inside need not be built. The purpose of the model is to show Nthabiseng how the hen house will appear from outside. </li></ul>
  71. 80. Activity 15 <ul><li>4. Take a photo of this little model and ask one member of the group or the facilitator to print the photo which then has to go into your portfolio of evidence. </li></ul>
  72. 81. Activity 15 <ul><li>5. In the building of the model: </li></ul><ul><ul><li>Which geometric shapes have been used? </li></ul></ul><ul><ul><li>Which right prisms have been used? </li></ul></ul>
  73. 82. Activity 15 <ul><li>6. What area will be covered by plywood by the: </li></ul><ul><ul><li>Floor </li></ul></ul><ul><ul><li>Cupola </li></ul></ul><ul><ul><li>Nest boxes </li></ul></ul><ul><ul><li>Storage space </li></ul></ul><ul><ul><li>Walls? </li></ul></ul>
  74. 83. Activity 15 <ul><li>7. What is the purpose of the: </li></ul><ul><ul><li>Pressure treated skids? </li></ul></ul><ul><ul><li>12” x 12” cupola with 1 1/4 inch vents covered with screen </li></ul></ul>
  75. 84. Activity 15 <ul><li>8. Calculate the lengths of wood to be bought of the: </li></ul><ul><ul><li>Skids </li></ul></ul><ul><ul><li>Joists </li></ul></ul><ul><ul><li>2 x 2 perches </li></ul></ul><ul><ul><li>Structure lengths to which the plywood will be fixed – called wall studs in the sketch </li></ul></ul><ul><ul><li>Roof rafters </li></ul></ul><ul><ul><li>Cover pieces for outside corners of the plywood. </li></ul></ul>
  76. 85. Activity 15 <ul><li>9. There are no predators in the vicinity and you suggest to Nthabiseng to use screening for the windows and door at first. Calculate the area of screening to be bought. Remember that the vents holes of the cupola (or the extra ventilation method) will also need screening. </li></ul>
  77. 86. Activity 15 <ul><li>Nthabiseng asks you to build the hen house for her. You think that you will be able to do it but you find the building of the cupola too challenging. Why does the ventilation aspect have to be at the top of a building? Think of a different way of ventilating the hen house than with the cupola. </li></ul>
  78. 87. Activity 15 <ul><li>Explain where more nest boxes can be placed in future? How many will fit into this space? </li></ul>
  79. 88. Activity 16 <ul><li>Decide which side is to be the front, which side is to be the side and which the plan view. Decide on an appropriate scale factor. You might have to turn the page through 90 degrees. Roughly work out the position of the views on the page. Leave the same amount of space between the different sketches. The views need to be evenly spaced. Make a rough layout before starting the final sketch. </li></ul><ul><li>  Normally, different parts of the drawing are done in different lines. The main lines are: </li></ul><ul><ul><li>Construction lines - these are faint continuous lines used to plot out the basic shape, as well as for projection and dimension lines . Use a 4H pencil . </li></ul></ul><ul><ul><li>Outlines – these are firm continuous lines used to show the outline of the object. Outlines are often drawn over construction lines. Use a 2H pencil . </li></ul></ul>
  80. 89. Isometric drawings
  81. 90. Activity 17: Isometric drawing <ul><li>Use a graduated arc to get the 30 degree angle from the horizontal. </li></ul><ul><li>Make an isometric sketch of your model of the hen house. Remember the title and the scale. </li></ul><ul><li>Note the object’s measurements and scale them down to your chosen scale </li></ul>
  82. 91. Case study 2: Orthographic sketch of the hen house <ul><li>Nthabiseng has decided to save on costs so she will not have the storage cupboard built. She feels that the time taken to build that cupboard will cost her too much as the carpenter/builder asks R200 per hour for his labour. </li></ul><ul><li>However, she does need storage space for extra feed, and for bins to carry the eggs in. She decides to have only a shelf put up at the storage space indicated on the diagrams. She finds an advertisement for plastic rack bins on the website: </li></ul><ul><li>There are different sizes at different costs: </li></ul>
  83. 92. Case study 2: Orthographic sketch of the hen house <ul><li>Calculate the area of the shelf. </li></ul><ul><li>Make a scaled down plan sketch of this shelf. </li></ul><ul><li>Make plan sketches of the base area of the rackbins at the same scale as the shelf’s plan sketch. </li></ul><ul><li>Cut these base areas out and by moving them around on the sketch of the shelf, decide which rackbins Nthabiseng should buy. </li></ul><ul><li>Investigate the feasibility of rather fitting a shelf along one or two of the other sides of the Hen House. </li></ul><ul><li>Once you have decided which rackbins she should buy, calculate the total cost of the bins to be ordered. </li></ul>
  84. 93. Route maps
  85. 94. Activity 18 <ul><li>Get a road atlas and draw a route map as in the example above of the main road between two major towns/cities in your region. </li></ul>
  86. 95. Activity 18 <ul><li>A city supplies a circular free bus service for its inhabitants. The bus is always on time and can be taken at any bus station at 10-minute intervals during the daylight hours. From the inner-city bus route map (not to scale)(overleaf), and the accompanying clockwise loop time-table, answer the questions: </li></ul><ul><ul><li>What does clock-wise mean? </li></ul></ul><ul><ul><li>For how many hours of the day does this service run? </li></ul></ul><ul><ul><li>How long does one circular route take the bus? </li></ul></ul><ul><ul><li>If the bus travels at an average speed of 25 km/h, how long is the route? </li></ul></ul><ul><ul><li>How many buses must the city supply for this service if there is also an anti-clockwise loop from 7:05 am to 5:55 pm each day? </li></ul></ul><ul><ul><li>What category of young people will probably make use of this bus service on a daily basis? </li></ul></ul><ul><ul><li>Why does the bus not go straight through the city? </li></ul></ul>
  87. 98. Flow diagrams
  88. 99. Activity 19 <ul><li>Make a flow diagram of the steps necessary to make Nthabiseng’s Hen House project work from the start of the idea to the first delivery of eggs. </li></ul>
  89. 100. Summative assessment
  90. 101. Summative assessment <ul><li>Ashley wants to create a low maintenance and water efficient garden around the house. In order to do this he wants a large area without plants. He will pave this area with intermittent pebbles in cement, and with different sizes of square terracotta tiles. </li></ul><ul><li>The tiles are: </li></ul><ul><ul><li>• 30 x 20 cm </li></ul></ul><ul><ul><li>• 10 x 10 cm </li></ul></ul><ul><li>He saw these examples of garden design in a book Small Gardens for South Africa by M. Terblanche. </li></ul>
  91. 102. Summative assessment <ul><li>He wants to have a tile path around the house with spaces between the tiles where he will sow drought resistant wonder-lawn as ground cover. And then he wants to use one of the designs from the book in front of the stoep to enlarge the paved area. He wants to create a rectangular mixed pebble stone and tile area of different geometric shapes. The area has to be twice the depth of the stoep and as wide as the house. </li></ul><ul><li>He also has three succulent plants in medium-sized pots which he can place in the paved area as a focal point. </li></ul><ul><li>Ashley asks your help. </li></ul>
  92. 103. Summative assessment <ul><li>Instructions: </li></ul><ul><ul><li>Redraw the outline of the house as above. The scale is 1 : 100. </li></ul></ul><ul><ul><li>Design and sketch the path to scale around the house. </li></ul></ul><ul><ul><li>Calculate how many tiles of the bigger size he will need. </li></ul></ul><ul><ul><li>Make a rough perspective diagram of your idea of the frontal view of the house with the pavement area in front of it. Include plants in your sketch. </li></ul></ul><ul><ul><li>Draw up a flow chart of everything you did. </li></ul></ul>
  93. 104. Activity 20 <ul><li>Ntombusuko has just completed a three year diploma in photography in Cape Town and wants to visit Rhodes University in Grahamstown to investigate the possibility of doing a post-diploma year there. Once she has completed a fourth year, she will be awarded a degree in photography. She has to decide between renting a car and going by inter-city bus. The bus fare is R320 one way, departing daily at 06h00 or at 18h30 from Cape Town. The trip takes 7 hours by bus. She wants to see the head of the photography department during the morning of a Monday, and has to be back in Cape Town on Thursday at noon. The bus leaves Grahamstown for Cape town on a daily basis at either 05h45 or at 15h50. She has never been to Grahamstown and if possible, she wants to spend some time seeing the town. Overnight accommodation at a guest house in Grahamstown is R250 per person single or sharing. </li></ul>
  94. 105. Activity 20 <ul><li>Questions: </li></ul><ul><ul><li>Decide which bus she should take from Cape Town and on which day. </li></ul></ul><ul><ul><li>Decide which bus she should take from Grahamstown back to Cape Town and on which day. </li></ul></ul><ul><ul><li>Calculate the total cost of the journey, food excluded. </li></ul></ul><ul><ul><li>She might take a friend with her for company and considers the option of renting a car. The car is charged as follows: The first 250km are free and thereafter the charge is R2,25 per kilometre. Ntombusuko sees on a map that it is 837km from Cape Town to Grahamstown. Calculate the cost of the rental for the return trip. </li></ul></ul><ul><ul><li>Added to the car rental is the petrol to be bought along the way. The car has an approximate petrol consumption of 8 litres per 100 km and petrol costs R10,20 per litre. Calculate the cost of petrol for the trip. </li></ul></ul><ul><ul><li>Decide which will be the more economical option for Ntombusuko. </li></ul></ul>