Page 144 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, College Preparation
1. solve problems involving measurement and geometry and arising from real-world applications;
2. explain the significance of optimal dimensions in real-world applications, and determine optimal
dimensions of two-dimensional shapes and three-dimensional figures;
3. solve problems using primary trigonometric ratios of acute and obtuse angles, the sine law, and the cosine law, including problems arising from real-world applications, and describe applications of trigonometry in various occupations.
1. Solving Problems Involving Measurement and Geometry
2. Investigating Optimal Dimensions
Deck
Cottage
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 perform required conversions between the imperial system and the metric system using a variety of tools (e.g., tables, calculators, online conversion tools), as necessary within applications
1.2 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 triangu- lar arrangement on a rotating circular platform. Calculate a reasonable area for this platform, and explain your assumptions and reasoning.
1.3 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.
By the end of this course, students will:
2.1 recognize, through investigation using a variety of tools (e.g., calculators; dynamic geometry software; manipulatives such as tiles, geoboards, toothpicks) and strategies (e.g., modelling; making a table of values; graphing), and explain the significance of optimal perimeter, area, surface area, and volume in various applications (e.g., the minimum amount of packaging material, the relationship between surface area and heat loss)
Sample problem: You are building a deck attached to the second floor of a cottage, as shown below. Investigate how perimeter varies with different dimensions if you build the deck using exactly 48 1-m x 1-m decking sections, and how area varies if you use exactly 30 m of deck railing. Note: the entire outside edge of the deck will be railed.
C. GEOMETRY AND TRIGONOMETRY OVERALL EXPECTATIONS
By the end of this course, students will:
142