Applications of
Mathematics 12 -
Shape and Space (3-D Objects and 2-D Shapes)
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 solve problems involving polygons and vectors, including both 3-D and 2-D
applications.
It is expected that students
will:
- use appropriate terminology
to describe:
- vectors (i.e., direction,
magnitude)
- scalar quantities
(i.e., magnitude)
- assign meaning to the
multiplication of a vector by a scalar
- determine the magnitude
and direction of a resultant vector, using triangle or parallelogram methods
- model and solve problems
in 2-D and simple 3-D, using vector diagrams and technology
SUGGESTED
INSTRUCTIONAL STRATEGIES
The study of vectors helps
students connect mathematics to the real world. Situations involving forces,
velocities, electricity, and navigation are often best described and resolved
using vectors.
- Help students recognize
a wide variety of situations that can be described using vectors. Provide
students with lists of quantities to classify as either vector or scalar.
- Design experiments where
students use spring balances. For example, have students:
- use two balances
to examine collinear force vectors
- use three balances
to examine an equilibrium situation in two dimensions
- verify the experimental
findings using trigonometry
- Provide opportunities
for students to identify practical situations that can be analysed using vectors
(e.g., ferries crossing a river, guy wires supporting poles, hanging a clothesline).
- Engage students in a
three-way or four-way tug-of-war. Ask students to repeat the exercise using
different angles, and then draw conclusions.
- Ask each student to
research a favourite sport to determine where vectors may be used to understand
the physics of the sport. Have students report their findings to the class.
For example, vectors have significant applications in windsurfing, snowboarding,
and skiing. The force of the wind, the strength and direction of the currents
in the water, and the resistance of the snowboard or skis as they move over
snow can be treated as vectors.
SUGGESTED
ASSESSMENT STRATEGIES
Vectors provide a clear
method for students to model and solve 2-D and 3-D problems. Assessment focuses
on students’ abilities to use vectors to accurately represent physical situations,
select appropriate problem-solving methods, and use trigonometry appropriately.
Observe
- As students conduct
experiments or solve problems involving vectors, observe how effectively they
can:
- relate vector quantities
to the physical world
- use appropriate
vector terminology and associated notation
- use protractors
and other measuring devices effectively
- follow directions
to measure angles and vector lengths
- calculate vector
lengths
- select and use appropriate
trigonometric concepts to solve problems
- explain the problem-solving
processes they use
- communicate their
conclusions
- Work with students to
develop a table of specifications for a test on this organizer. Identify for
them the content categories along a vertical axis and the intellectual levels
along the horizontal axis. After the weighting is identified for each cell,
have students work in groups to develop questions for each cell.
Self-Assessment
- Ask students to describe
to the class ways in which a student might make errors when evaluating vectors.
Ask them to then share how to circumvent those errors by using rules or reminder
systems.
RECOMMENDED
LEARNING RESOURCES
Print Materials
- • Applied Mathematics
12 available June 2001
Software
- Secondary Math Lab Toolkit
©
2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000
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