Page 156 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, Workplace Preparation
3. Solving Measurement Problems Using Proportional Reasoning
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
Sample problem: Draw an outline of your hand and estimate the area.
2.4 solve problems involving the areas of rectan- gles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications
Sample problem: A car manufacturer wants to display three of its compact models in a triangular arrangement on a rotating circular platform. Calculate a reasonable area for this platform, and explain your assumptions and reasoning.
2.5 solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related compo- site figures, in situations arising from real- world applications
Sample problem: Compare the volumes of concrete needed to build three steps that are 4 ft wide and that have the cross-sections shown below. Explain your assumptions and reasoning.
2.6 construct a two-dimensional scale drawing of a familiar setting (e.g., classroom, flower bed, playground) on grid paper or using design or drawing software
Sample problem: Your family is moving to a new house with a living room that is 16 ft by 10 ft. Cut out and label simple geometric shapes, drawn to scale, to represent every piece of furniture in your present living room. Place all of your cut-outs on a scale drawing of the new living room to find out
if the furniture will fit appropriately (e.g., allowing adequate space to move around).
2.7 construct, with reasonable accuracy, a three- dimensional scale model of an object or envi- ronment of personal interest (e.g., appliance, room, building, garden, bridge)
a three-dimensional scale model.
2.8 investigate, plan, design, and prepare a budg- et for a household improvement (e.g., land- scaping a property; renovating a room), using appropriate technologies (e.g., design or deco- rating websites, design or drawing software, spreadsheet)
Sample problem: Plan, design, and prepare a budget for the renovation of a 12-ft by 12-ft bedroom for under $2000. The renovations could include repainting the walls, replacing the carpet with hardwood flooring, and refurnishing the room.
By the end of this course, students will:
3.1 identify and describe applications of ratio and rate, and recognize and represent equivalent ratios (e.g., show that 4:6 represents the same ratio as 2:3 by showing that a ramp with a height of 4 m and a base of 6 m and a ramp with a height of 2 m and a base of 3 m are equally steep) and equivalent rates (e.g., rec- ognize that paying $1.25 for 250 mL of tomato sauce is equivalent to paying $3.75 for 750 mL of the same sauce), using a variety of tools (e.g., concrete materials, diagrams, dynamic geometry software)
3.2 identify situations in which it is useful to make comparisons using unit rates, and solve problems that involve comparisons of unit rates
Sample problem: If 500 mL of juice costs $2.29 and 750 mL of the same juice costs $3.59, which size is the better buy? Explain your reasoning.
3.3 identify and describe real-world applications of proportional reasoning (e.g., mixing con- crete; calculating dosages; converting units; painting walls; calculating fuel consumption; calculating pay; enlarging patterns), distinguish between a situation involving a proportional relationship (e.g., recipes, where doubling the quantity of each ingredient doubles the num- ber of servings; long-distance phone calls
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2.3 estimate the areas and volumes of irregular Sample problem: Design an innovative combi- shapes and figures, using a variety of strat- nation of two appliances or two other consu- egies (e.g., counting grid squares; displacing mer products (e.g., a camera and a cellphone, water) a refrigerator and a television), and construct