MATHEMATICAL LITERACY GRADE 11 CAPS TOPIC 4 Maps

MATHEMATICAL LITERACY GRADE 11 CAPS TOPIC 4: Maps, plans and other representations of the physical world Section 4. 3: Models

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

Models In Section 4. 3, learners will be able to make and use 3 -D scale models and 2 -D scale cut-outs/pictures of packaging containers in order to: - Investigate and choose the best packaging shape to use for a specific product. - Investigate and determine the amount of material needed. - Investigate the number of furniture items that can fit into a venue. - Estimate quantities of materials needed using perimeter, area and volume calculations. - Final Assessment Questions

Models � Model is a representation of something either as a physical object which I usually smaller than the real object. � A scale model of a container can be built only if the dimensions of the container are known and a scale is given or worked out. � Packaging containers have different shapes and sizes because they are designed for specific purposes. � The shape, fragility and mass of a particular product have an impact on the type of packaging container needed for that product. � Optimal usage of space, quantities of material needed and cost effectiveness are taken into account when packaging is designed.

Example: 1 A chocolate factory makes chocolates and packs them into small boxes. Each chocolate is cube-shaped, which means that length = breadth = height. One chocolate Triangular based box Square box Discuss the triangular-shaped and square-based and the effectiveness of each in packaging according to the shapes of the chocolates above.

Solutions: Example 1 Only one chocolate can fit into the height of each box. The square-based box will be much more efficient when packaging chocolates, as more chocolates will fit into the box. Nine chocolates can fit into the square-based box

Solution: Example 1 Packaging the chocolates into a triangular-based box will be problematic as the cube-shaped chocolates will not fit properly, and a lot of space will be empty and hence wasted.

Activity: 1 1. Liqui fruit can be bought in either a can or a small box. Juice cans and boxes are filled up to 80% of the total volume of a container.

Activity: 1 Use the information in the previous slide to answer the following questions: (a) Calculate the volume of the liquifruit can. (b) Calculate the volume of the liquifruit box. (c) If each can is filled up to 80% of the total volume of the container, determine the juice’s volume in a can. (d) If each can is filled up to 80% of the total volume of the container, determine the juice’s volume in a box. (e) Determine if the can or box is a cheaper option.

Solutions: Activity 1 �

Solutions: Activity 1 �

Example: 2 Tuna cans are cylindrical and the tin needed to manufacture the can is cut from large sheet of metal. Dimensions of a tuna can: Diameter = 7, 4 cm Height = 3, 7 cm Dimensions of one sheet of metal: Length = 2 m Breadth = 1 m

Example: 2 �

Solutions: Example 2 �

Solutions: Example 2 �

Activity: 2 Pynmed is a syrup for children for the relief of pain and fever. The base of the bottle has a diameter of 4 cm. The base length of the box is 10% more than the diameter of the base of the bottle. The base of the box is a square. The height of the box is 13 cm.

Activity: 2 �

Solutions: Activity 2 �

Example: 3 �

Example: 3 (b) Determine the volume of one ream of paper. (c) Determine the volume of each box. (d) How many reams of paper can fit into box A? (e) How many reams of paper can fit into box B? (f) Why are the boxes 0, 5 cm bigger in length that the paper?

Solutions: Example 3 �

Solutions: Example 3 �

Solutions: Example 3 �

Activity: 3 A tile company manufactures floor and wall tiles and exports them to other countries. The tiles are packed into boxes and the boxes are packed into wooden crates before they are shipped. Dimensions of floor tile: Dimensions of a wall tile; Length = 33 cm Length = 32 cm Breadth = 33 cm Breadth = 15, 5 cm Width = 0, 7 cm Dimensions of one box: Length = 68 cm Breadth = 35 cm Height = 50 cm

Activity: 3 Use information in the previous slide to answer the following questions; (a) Determine the volume of a floor tile. (b) Determine the volume of a wall tile. (c) Determine the volume of one box. (d) Determine how many floor tiles can fit into a box. (e) Determine how many wall tiles can fit into a box.

Solutions: Activity: 3 �

Solutions: Activity: 3 �

Estimation �

Example: 4 The model in the figure below is a representation of Johan’s living area.

Example: 4 Use the model in the previous slide to answer the following questions: (a) Estimate how many couches can fit comfortably into the living area. (b) Each couch is 2 metres long. An average child needs approximately 0, 6 m to sit on the couch comfortably. Estimate how man children will be able to fit onto one couch. (c) The curtain rail above the sliding door is 3, 5 m long and 2, 2 m above the ground. Johan wants to make a curtain to cover the sliding door and she has to buy double the material. Estimate the area of the material needed to make the curtain.

Solutions: Example 4 �

Activity: 4 A container is used to pack soccer balls and transport the balls to different sports stores. The container is represented below:

Activity: 4 (c) Estimate the number of containers in slide 31 that will fit into the storeroom above.

Solutions: Activity 3 �

Final Assessment Questions 1 -10 Question 1 If the height of a compact disk is 1, 2 mm and a spindle CD holder with lid has a height of 8 cm. Determine how many compact disks can fit into a spindle. A. 67 B. 66 C. 65 D. 68

Question 2 �

Question 3 If the height of a compact disk is 1, 2 mm and a cubed box holder has a height of 10 cm. Determine how many compact disks can fit into the cubed box. A. 82 B. 84 C. 83 D. 82

Question 4 �

Question 5 If a couch is 2 m long. An average child needs approximately 0, 8 m to sit on the couch comfortably. Estimate how many children will be able to fit onto one couch. A. 2 B. 3 C. 2, 5 D. 4

Question 6 �

Question 7 During an event, people will be seated at round tables. If 10 people can be seated at one table. How many tables will be needed if 150 people attend the event. A. 10 B. 150 C. 15 D. 1 500

Question 8 �

Question 9 �

Question 10 The office of Mr Marais is 15 m by 8 m. Calculate how many 50 cm by 50 cm carpet tiles are needed to tile the floor of the office. A. 460 B. 480 C. 400 D. 580

Solutions: Final Assessment Question 1 - 10 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. B A C D A D C B D B