Page 155 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

C. APPLICATIONS OF MEASUREMENT OVERALL EXPECTATIONS
By the end of this course, students will:
1. determine and estimate measurements using the metric and imperial systems, and convert measures within and between systems;
2. apply measurement concepts and skills to solve problems in measurement and design, to construct scale drawings and scale models, and to budget for a household improvement;
3. identify and describe situations that involve proportional relationships and the possible consequences of errors in proportional reasoning, and solve problems involving proportional reasoning, arising in applications from work and everyday life.
SPECIFIC EXPECTATIONS
1. Measuring and Estimating
By the end of this course, students will:
1.1 measure, using a variety of tools (e.g., meas- uring tape, metre or yard stick, measuring cups, graduated cylinders), the lengths of common objects and the capacities of com- mon containers, using the metric system and the imperial system
1.2 estimate lengths, distances, and capacities in metric units and in imperial units by applying personal referents (e.g., the width of a finger is approximately 1 cm; the length of a piece of standard loose-leaf paper is about 1 ft; the capacity of a pop bottle is 2 L)
Sample problem: Based on an estimate of the length of your stride, estimate how far it is to the nearest fire exit from your math class- room, and compare your estimate with the measurement you get using a pedometer.
1.3 estimate quantities (e.g., bricks in a pile, time to complete a job, people in a crowd), and describe the strategies used
Sample problem: Look at digital photos that show large quantities of items, and estimate the numbers of items in the photos.
1.4 convert measures within systems (e.g., cen- timetres and metres, kilograms and grams, litres and millilitres, feet and inches, ounces
and pounds), as required within applications that arise from familiar contexts
1.5 convert measures between systems (e.g., cen- timetres and inches, pounds and kilograms, square feet and square metres, litres and U.S. gallons, kilometres and miles, cups and milli- litres, millilitres and teaspoons, degrees Celsius and degrees Fahrenheit), as required within applications that arise from familiar contexts
Sample problem: Compare the price of gaso- line in your community with the price of gasoline in a community in the United States.
2. Applying Measurement and Design
By the end of this course, students will:
2.1 construct accurate right angles in practical contexts (e.g., by using the 3-4-5 triplet to construct a region with right-angled corners on a floor), and explain connections to the Pythagorean theorem
2.2 apply the concept of perimeter in familiar contexts (e.g., baseboard, fencing, door and window trim)
Sample problem: Which room in your home required the greatest, and which required the least, amount of baseboard? What is the difference in the two amounts?
APPLICATIONS OF MEASUREMENT
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Mathematics for Work and Everyday Life
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