Essentials of Mathematics
12 -
Variation and Formulas
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 use algebraic and graphical models to generate patterns, make prediction
and solve patterns
It is expected that students
will:
- plot and analyse examples
of direct variation, partial variation, and inverse variation
- given data, graph, or
a situation, recognize the variation represented
- use formulas to solve
problems
SUGGESTED
INSTRUCTIONAL STRATEGIES
The ability to identify
relationships between various quantities is essential to solving most problems.
Students need to develop the ability to visualize and identify the appropriate
variation given a variety of information and situations.
- In a class discussion,
encourage students to determine the relationship between sets of data such
as the following:
- pay to hours worked
- light intensity
to water depth
- profit to fixed
and variable costs
- electrical components
for current, voltage, and resistance
- Have students work in
groups to identify the type of variation represented in each situation (e.g.,
direct, inverse, partial) and develop an appropriate equation representing
the variation. For example, the electrical resistance R of a wire varies directly
as the length L and inversely as the square of the diameter D of the wire:
- Have students use appropriate
technology to create graphs and tables of each variation.
- Provide students with
data from modeling real-life situations (e.g., raising a flag on a pole, pouring
water out of a container) and ask them to draw diagrams, find a formula, and
solve by substitution for an unknown quantity.
- Provide students with
several graphs, and ask them to describe the real-life scenarios that would
have produced them.
- Have students design
a puzzle work sheet of formulas and their answers, together with an answer
key.
SUGGESTED
ASSESSMENT STRATEGIES
As students work with algebraic
and graphical representations, assessment should focus on their competency in
solving problems involving several kinds of variation.
Observe
- As students work with
graphing calculators, observe their abilities to:
- set appropriate
domain and range values
- verify their results
- generate examples
that demonstrate an understanding of the different types of variation
Self-Assessment
- Assign experiments that
require students to demonstrate the type of variation involved in real-life
situations (e.g., intensity of light varies inversely as the square of the
distance from the source). Let students check their own understanding and
accuracy by:
- using graphing calculators
or software.
- checking work against
models that are provided
Peer Assessment
- Have students share the
puzzle worksheets with their peers and have them assess the puzzle by completing
it and checking it against the provided key.
RECOMMENDED
LEARNING RESOURCES
Comprehensive learning resources
for this course are currently under development. As an interim measure, schools
are encouraged to use the teacher-developed learning resources distributed to
schools (student and teacher resources). Please note that the student materials
require photocopying for student use.
Print Materials
- What If ...?: The Straight
Line: Investigations with the TI-81 Graphics Calculator
- What If ...?: The Straight
Line: Investigations with the TI-81 Graphics Calculator
Software
- Green Globs & Graphing
Equations
©
2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000
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