PREFACE:
USING THIS INTEGRATED RESOURCE PACKAGE
This Integrated Resource
Package (IRP) provides some of the basic information that teachers will require
to implement Applications of Mathematics 10 to 12, Essentials of Mathematics
10 to 12, Principles of Mathematics 10 to 12, and Calculus 12. The information
contained in this IRP is also available through the Internet. Contact the Ministry
of Education’s home page: http://www.bced.gov.bc.ca/
The Introduction
The Introduction provides
general information about the Grade 10 to 12 Mathematics curriculum, including
special features and requirements. It also provides a rationale for the subject—why
mathematics is taught in BC schools—and an explanation of the curriculum organizers.
The Grade 10 to
12 Mathematics
Curriculum
The provincially prescribed
curriculum for Grade 10 to 12 Mathematics is structured in terms of curriculum
organizers. The main body of this IRP consists of four columns of information
for each organizer. These columns describe:
- provincially prescribed
learning outcome statements for Grade 10 to 12 Mathematics
- suggested instructional
strategies for achieving the outcomes
- suggested assessment
strategies for determining how well students are achieving the outcomes provincially
- recommended learning
resources
Prescribed
Learning Outcomes
Learning outcome statements
are content standards for the provincial education system. Learning outcomes
set out the knowledge, enduring ideas, issues, concepts, skills, and attitudes
for each subject. They are statements of what students are expected to know
and be able to do in each grade. Learning outcomes are clearly stated and expressed
in measurable terms. All learning outcomes complete this stem: "It is expected
that students will. . . . "
Outcome statements have
been written to enable teachers to use their experience and professional judgment
when planning and evaluating. The outcomes are benchmarks that will permit the
use of criterion referenced performance standards. It is expected that actual
student performance will vary. Evaluation, reporting, and student placement
with respect to these outcomes depends on the professional judgment of teachers,
guided by provincial policy.
Suggested
Instructional Strategies
Instruction involves the
use of techniques, activities, and methods that can be employed to meet diverse
student needs and to deliver the prescribed curriculum. Teachers are free to
adapt the suggested instructional strategies or substitute others that will
enable their students to achieve the prescribed outcomes. These strategies have
been developed by specialist and generalist teachers to assist their colleagues;
they are suggestions only.
Suggested
Assessment Strategies
The assessment strategies
suggest a variety of ways to gather information about student performance. Some
assessment strategies relate to specific activities; others are general. As
with the instructional strategies, these strategies have been developed by specialist
and generalist teachers to assist their colleagues; they are suggestions only.
Provincially
Recommended Learning Resources
The Ministry of Education
promotes the establishment of a resource-rich learning environment through the
evaluation of educationally appropriate materials intended for use by teachers
and students. The media formats include, but are not limited to, materials in
print, video, and software, as well as combinations of these formats. Learning
resources for Applications of Math 10 to 12 and Principles of Math 10 to 12
were reviewed and recommended as part of the Western Canadian Protocol (WCP)
Mathematics Learning Resource Evaluation. The WCP recommended learning resources
have been approved by the Minister and have been incorporated into the Grade
Collection for each course.
The Grade Collection package
contains a grade collection chart for Applications of Mathematics 10 to 12 and
Principles of Mathematics 10 to 12. These charts list both the comprehensive
and additional resources for each curriculum organizer for the course. Each
chart is followed by an annotated bibliography. Please confirm with suppliers
for complete and up-to-date information.
Provincially recommended
learning resources for Calculus 12 are materials that have been reviewed and
evaluated by British Columbia teachers in collaboration with the Ministry of
Education. Provincially recommended learning resources for Essentials of Mathematics
10 to 12 are being developed and will be identified at a later date. As an interim
measure the ministry has provided schools with photocopy masters of learning
resources developed for a similar curriculum.
It is expected that teachers
will select resources from those that meet the provincial criteria and that
suit their particular pedagogical needs and audiences. Teachers who wish to
use non-provincially recommended resources to meet specific local needs must
have these resources evaluated through a local district approval process.
The Appendices
A series of appendices
provides additional information about the curriculum and further support for
the teacher.
- Appendix
A contains a listing of the prescribed
learning outcomes for the curriculum.
- Appendix
B contains a comprehensive listing
of the provincially recommended learning resources for this curriculum. As
new resources are evaluated, this appendix will be updated.
- Appendix
C outlines the cross-curricular reviews
used to ensure that concerns such as equity, access, and the inclusion of
specific topics are addressed by all components of the IRP.
- Appendix
D contains assistance for teachers related
to provincial evaluation and reporting policy. Curriculum outcomes have been
used as the source for examples of criterion-referenced evaluations.
- Appendix
E acknowledges the many people and organizations
that have been involved in the development of this IRP.
- Appendix
F contains an illustrated glossary of
terms used in this IRP.
- Appendix
G contains illustrated examples, which
show the competencies an average student is expected to demonstrate for each
of the prescribed learning outcomes.
- Appendix H contains
more detailed information related to specific teaching strategies referred
to in the IRP. This information is provided in cases where explanations of
strategies and activities are too extensive to fit in the Suggested Instructional
Strategies column, or where the same activity is referred to several times
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| Curriculum Sub-Organizer as seen on the World Wide Web |
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Principals
of Mathematics 10 - Patterns and Relations (Patterns)
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Internal
links to each
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Prescribed Learning Outcomes
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PRESCRIBED LEARNING OUTCOMES
It is expected that students will generate and analyse number patterns.
It is expected that students will:
- generate number patterns exhibiting arithmetic growth
- use expressions to represent general terms and sums for arithmetic
growth, and apply these expressions to solve problems
- relate arithmetic sequences to linear functions defined over
the natural numbers
- generate number patterns exhibiting geometric growth
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| Navigational
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| Suggested
Instructional Strategies |
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SUGGESTED INSTRUCTIONAL STRATEGIES
Many natural phenmomena and man-made processes grow and shrink according
to easily defined mathematical rules. An understanding of arithmetic
and geometric growth helps students to better understand how the
world around them changes.
- Give students a collection of arithmetic or geometric sequences
with blanks either between the numbers or at the end of the
sequence for students to fill in. Have them state the common
difference or ration and give a word-based rule describing how
one term is calculated from the previous term.
- Have students find three examples of arithmetic or geometric
sequences found in nature or used by people in their day-to-day
lives.
- Ask students to match a column of linear equations to a column
of arithmetic sequences.
- Have students describe or model natural phenomena that incorporate
geometric sequences in their structure (e.g. flowers, spiral
shells, paper folding).
- Give students numerical and non-numerical pasterns and ask
the m to define the rule(s) for each pattern. Have them use
the rules to make predictions and classify the patterns.
- Have students use concepts of arithmetic and geometric growth
to solve problems such as:
- If $1000 is deposited each year into an account that earns
12% compounded annually, how much money will have accumulated
after 25 years?
Then have them:
- generate a model of this situation
- identify it as geometric or arithmetic
- discuss the answer (Is it surprising? Reasonable?)
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| Suggested
Assessment Strategies |
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SUGGESTED ASSESSMENT STRATEGIES
Assessment strategies should demonstrate algebraic skills as well
as holistic pattern recognition. Students should also be able to
articulate methods to aid in pattern discovery.
Observe
- How quickly do students see the patterns in partially completed
sequences:
- with no hints (2, 5, 8...)
- with hints (2, __16, _...-geometric)
- Can students develop a mathematical equation from a sequence?
Question
- Can students articulate what to look for in determining whether
a collection of numbers is an arithmetic sequence, geometric
sequence, or neither?
Collect
- Have students collect five arithmetic, five geometric, and
five other sequences Provide them with equations or descriptions
of how to generate each sequence.
Peer/Self-Assessment
- Have each student develop a connect-the-dots puzzle using
a combination of sequences and linear equations. Ask them to
have another student do the puzzle and check it for accuracy.
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| Recommended
Learning Resources |
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the Ministry of Education Home Page. |
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©
2000 Copyright. All Rights Reserved. BC MOE Curriculum
Branch.
Maintained by: Mathematics Coordinator
Revised: January 23, 2001
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