Applications of Mathematics 12 -
Shape and Space (Measurement)

This sub-organizer contains the following sections:
Prescribed Learning Outcomes
Suggested Instructional Strategies
Suggested Assessment Strategies
Recommended Learning Resources

PRESCRIBED LEARNING OUTCOMES

It is expected that students will analyse objects, shapes and processes to solve cost and design problems.

It is expected that students will:

• use dimensions and unit prices to solve problems involving perimeter, area and volume
• solve problems involving estimation and costing for objects, shapes or processes when a design is given
• design an object, shape, layout or process within a specified budget
• use simplified models to estimate the solutions to complex measurement problems

SUGGESTED INSTRUCTIONAL STRATEGIES

Real-world activities involving measurement formulae and trigonometry enable students to explore the physical world.

• Have students investigate building costs, technical drawings, and related documents, then invite a builder, architect, interior designer, or other appropriate professional to explain her or his measurement techniques, procedures, and "tricks of the trade."
• Have students work in pairs using two methods to determine the trigonometric ratios of right triangles. One student measures the sides and uses these measurements to calculate the ratios; the other student measures the angles and uses a calculator or trigonometric table to determine the ratios. They then compare their results and identify and discuss discrepancies between calculated and measured results.
• Where possible, have students estimate inaccessible distances or dimensions (e.g., the height of a building, width of a river, gradient of a hill). Have them confirm the estimates by using calculations that include:
  • ratio and proportion
  • the Pythagorean theorem
  • trigonometry

SUGGESTED ASSESSMENT STRATEGIES

Measurement experiences are a powerful application of mathematical theory to everyday phenomena. Students demonstrate their knowledge of measurement concepts by generalizing about patterns and procedures and by solving problems involving area, perimeter, surface area, and volume.

Observe

• While students are working on measurement activities, circulate and provide feedback on:
  • their abilities to match the correct measurement formula to a given figure
  • their abilities to recognize and apply the sine and cosine laws
  • the extent to which they consider the reasonableness of their answers
  • their overall understanding of measurement concepts in solving problems
  • their abilities to select the appropriate trigonometric ratio to solve problems involving right triangles

Collect

• Review students’ written work in solving measurement problems for evidence that they can:
  • explain the method used in finding the area or volume of a composite figure
  • use various methods for finding the answers
  • solve various types of problems based on the interpretation of measurements (e.g., from a set of blueprints)
  • show the connection between a model, its related equation, and the physical situation (e.g., string art, building application, computer animation, business applications, graphic design)

   

RECOMMENDED LEARNING RESOURCES

Print Materials

• Applied Mathematics 12 available June 2001

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Maintained by: Mathematics Coordinator
Revised: November 22, 2000

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