Applications of
Mathematics 12 -
Number (Number Operations)
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 describe and apply operations on matrices to solve problems, using technology
as required.
It is expected that students
will:
- model and solve problems,
including those solved previously, using technology to perform matrix operations
of addition, subtraction, and scalar multiplication as required
- model and solve consumer
and network problems using technology to perform matrix multiplication as
required
SUGGESTED
INSTRUCTIONAL STRATEGIES
Matrices offer an excellent
way for students to explore problem solving, modeling and its limitations, and
interpretations of results. Matrix operations give students the tools to analyse
and solve complex problems that they may have been previously unable to solve.
- As a class, brainstorm
situations that require the use of matrices (e.g., scheduling a tournament,
finding the most direct and economical route to travel to a desired location,
tracing consumer preferences).
- Have students discuss
various ways of organizing raw data so that it can be displayed and analysed
in a data table, diagram, or graph. Ask students to determine when using a
matrix is the most appropriate way to display certain types of data.
- Provide students with
various scenarios that allow them to explore the specific matrix operations
needed to generate new information for (or solutions to) a problem. Have students
analyse the resulting matrix to verify hypotheses or generate new questions.
- Have students work in
groups on projects that require the use of matrices to make informed decisions.
For example, they might determine:
- the type and quantity
of coffee to purchase for a coffee shop, based on consumer preferences
- the number of T-shirts
and baseball caps that should be purchased for the year, given a set school
store budget and a known school population
- Ask each student to develop
a project related to matrices using resources such as the NCTM Addenda Series,
the Internet, or consumer preference surveys of their school or neighborhood.
SUGGESTED
ASSESSMENT STRATEGIES
Matrices provide an effective
way to organize, manipulate, and interpret data in tabular form; assessment
should focus on students’ abilities to solve complex problems using matrix operations.
Observe
- In their oral or written
work, look for evidence that students are able to :
- use matrix terminology
such as elements, rows, columns, dimensions, scalar, scalar product, product,
and identity matrix
- use matrices to
represent and organize information
- generate new information
- use appropriate
technology to perform matrix calculations
- interpret the results
Presentation
- Have students present
data in matrix form generated from business or industry, and have them explain
what problem is being analysed or solved using this model. Look for evidence
that students have:
- accurately represented
the information in matrix form
- chosen and used
appropriate operations
- interpreted results
correctly
- understood the limitations
of the data
Peer Assessment
- Ask small groups of
students to design a test for their classmates, given parameters for the test
such as length, topics, and type of questions. A condition of administering
their tests to other groups is that all students in the author group must
be able to answer each question correctly
RECOMMENDED
LEARNING RESOURCES
Print Materials
Software
- Secondary Math Lab Toolkit
©
2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 22, 2000
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