Mathematics Grades 10 to 12 Program of Studies

Mathematics Grades 10 to 12 Program of Studies
MATHEMATICS
GRADES 10–12
INTRODUCTION
The Mathematics Grades 10–12 Program of
Studies has been derived from The Common
Curriculum Framework for Grades 10–12
Mathematics: Western and Northern Canadian
Protocol, January 2008 (the Common Curriculum
Framework). The program of studies incorporates
the conceptual framework for Grades 10–12
Mathematics and most of the general outcomes
and specific outcomes that were established in the
Common Curriculum Framework. (Note: Some
of the outcomes for Mathematics 20-2 and 30-2 in
this program of studies are different from the
outcomes for Foundations of Mathematics in the
Common Curriculum Framework.)
BACKGROUND
The Common Curriculum Framework was
developed by seven ministries of education
(Alberta,
British
Columbia,
Manitoba,
Northwest Territories, Nunavut, Saskatchewan
and Yukon Territory) in collaboration with
teachers, administrators, parents, business
representatives, post-secondary educators and
others. The framework identifies beliefs about
mathematics, general and specific student
outcomes, and achievement indicators agreed
upon by the seven jurisdictions.
©Alberta Education, Alberta, Canada
BELIEFS ABOUT STUDENTS AND
MATHEMATICS LEARNING
Students are curious, active learners with
individual interests, abilities, needs and career
goals. They come to school with varying
knowledge, life experiences, expectations and
backgrounds. A key component in developing
mathematical literacy in students is making
connections to these backgrounds, experiences,
goals and aspirations.
Students construct their understanding of
mathematics by developing meaning based on a
variety of learning experiences. This meaning is
best developed when learners encounter
mathematical experiences that proceed from
simple to complex and from the concrete to the
abstract. The use of manipulatives, visuals and a
variety of pedagogical approaches can address the
diversity of learning styles and developmental
stages of students. At all levels of understanding,
students benefit from working with a variety of
materials, tools and contexts when constructing
meaning about new mathematical ideas.
Meaningful student discussions also provide
essential links among concrete, pictorial and
symbolic representations of mathematics.
Mathematics (10–12) /1
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The learning environment should value, respect
and address all students’ experiences and ways of
thinking, so that students are comfortable taking
intellectual risks, asking questions and posing
conjectures. Students need to explore mathematics
through solving problems in order to continue
developing personal strategies and mathematical
literacy. It is important to realize that it is
acceptable to solve problems in different ways and
that solutions may vary depending upon how the
problem is understood.
FIRST NATIONS, MÉTIS AND INUIT
PERSPECTIVES
First Nations, Métis and Inuit students in northern
and western Canada come from diverse
geographic areas with varied cultural and
linguistic backgrounds. Students attend schools in
a variety of settings, including urban, rural and
isolated communities. Teachers need to
understand the diversity of students’ cultures and
experiences.
First Nations, Métis and Inuit students often have
a holistic view of the environment—they look for
connections in learning and learn best when
mathematics is contextualized. They may come
from cultures where learning takes place through
active participation. Traditionally, little emphasis
was placed upon the written word, so oral
communication and practical applications and
experiences are important to student learning and
understanding. By understanding and responding
to nonverbal cues, teachers can optimize student
learning and mathematical understanding.
A variety of teaching and assessment strategies
help build upon the diverse knowledge, cultures,
communication
styles,
skills,
attitudes,
experiences and learning styles of students.
Research indicates that when strategies go beyond
the incidental inclusion of topics and objects
unique to a culture or region, greater levels of
understanding can be achieved (Banks and Banks,
1993).
2/ Mathematics (10–12)
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AFFECTIVE DOMAIN
A positive attitude is an important aspect of the
affective domain and has a profound effect on
learning. Environments that create a sense of
belonging, support risk taking and provide
opportunities for success help students to develop
and
maintain
positive
attitudes
and
self-confidence. Students with positive attitudes
toward learning mathematics are likely to be
motivated and prepared to learn, to participate
willingly in classroom activities, to persist in
challenging situations and to engage in reflective
practices.
Teachers, students and parents need to recognize
the relationship between the affective and
cognitive domains and to nurture those aspects of
the affective domain that contribute to positive
attitudes. To experience success, students must be
taught to set achievable goals and to assess
themselves as they work toward these goals.
Striving toward success and becoming
autonomous and responsible learners are ongoing,
reflective processes that involve revisiting the
setting and assessing of personal goals.
GOALS FOR STUDENTS
The main goals of mathematics education are to
prepare students to:
• solve problems
• communicate and reason mathematically
• make connections between mathematics and its
applications
• become mathematically literate
• appreciate and value mathematics
• make informed decisions as contributors to
society.
Students who have met these goals:
• gain an understanding and appreciation of the
role of mathematics in society
• exhibit a positive attitude toward mathematics
• engage and persevere in mathematical problem
solving
©Alberta Education, Alberta, Canada
• contribute to mathematical discussions
• take risks in performing mathematical tasks
• exhibit curiosity about mathematics and
situations involving mathematics.
In order to assist students in attaining these goals,
teachers are encouraged to develop a classroom
atmosphere that fosters conceptual understanding
through:
• taking risks
• thinking and reflecting independently
• sharing and communicating mathematical
understanding
• solving problems in individual and group
projects
• pursuing greater understanding of mathematics
• appreciating the value of mathematics
throughout history.
©Alberta Education, Alberta, Canada
Mathematics (10–12) /3
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CONCEPTUAL FRAMEWORK FOR GRADES 10–12 MATHEMATICS
The chart below provides an overview of how mathematical processes and the nature of mathematics
influence learning outcomes.
GRADE
10
TOPICS
11
12
The topics of study vary in the courses
for grades 10–12 mathematics. Topics
in the course sequences include:
Algebra
Geometry
Logical Reasoning
Mathematics Research Project
Measurement
Number
Permutations, Combinations and
Binomial Theorem
Probability
Relations and Functions
Statistics
Trigonometry
GENERAL OUTCOMES
AND
SPECIFIC OUTCOMES
MATHEMATICAL PROCESSES:

NATURE
OF
MATHEMATICS:
Change, Constancy,
Number Sense,
Patterns,
Relationships,
Spatial Sense,
Uncertainty
Communication, Connections, Mental Mathematics
and Estimation, Problem Solving, Reasoning,
Technology, Visualization
Achievement indicators for the prescribed program of studies outcomes are provided in the companion
document The Alberta 10–12 Mathematics Program of Studies with Achievement Indicators, 2008.
Mathematical
Processes
The seven mathematical processes are critical aspects of learning, doing and
understanding mathematics. Students must encounter these processes
regularly in a mathematics program in order to achieve the goals of
mathematics education.
This program of studies incorporates the following interrelated
mathematical processes. They are to permeate the teaching and learning of
mathematics.
Communication [C]
Connections [CN]
Mental Mathematics
and Estimation [ME]
Problem Solving [PS]
Reasoning [R]
Technology [T]
Visualization [V]
Students are expected to:
• use communication in order to learn and express their understanding
• make connections among mathematical ideas, other concepts in
mathematics, everyday experiences and other disciplines
• demonstrate fluency with mental mathematics and estimation
• develop and apply new mathematical knowledge through problem
solving
• develop mathematical reasoning
• select and use technology as a tool for learning and for solving problems
• develop visualization skills to assist in processing information, making
connections and solving problems.
All seven processes should be used in the teaching and learning of
mathematics.
Each specific outcome includes a list of relevant
mathematical processes. The identified processes are to be used as a
primary focus of instruction and assessment.
4/ Mathematics (10–12)
(2008)
©Alberta Education, Alberta, Canada
COMMUNICATION [C]
Students need opportunities to read about,
represent, view, write about, listen to and discuss
mathematical ideas. These opportunities allow
students to create links among their own language
and ideas, the language and ideas of others, and
the formal language and symbols of mathematics.
Communication is important in clarifying,
reinforcing and modifying ideas, attitudes and
beliefs about mathematics. Students should be
encouraged to use a variety of forms of
communication while learning mathematics.
Students also need to communicate their learning
by using mathematical terminology.
Communication can play a significant role in
helping students make connections among
concrete, pictorial, symbolic, verbal, written and
mental representations of mathematical ideas.
Emerging technologies enable students to engage
in communication beyond the traditional
classroom to gather data and share mathematical
ideas.
MENTAL MATHEMATICS AND ESTIMATION
[ME]
Mental mathematics is a combination of cognitive
strategies that enhance flexible thinking and
number sense. It involves using strategies to
perform mental calculations.
Mental mathematics enables students to determine
answers without paper and pencil. It improves
computational fluency by developing efficiency,
accuracy and flexibility in reasoning and
calculating.
“Even more important than performing
computational procedures or using calculators is
the greater facility that students need—more than
ever before—with estimation and mental math”
(National Council of Teachers of Mathematics,
May 2005).
Students proficient with mental mathematics
“become liberated from calculator dependence,
build confidence in doing mathematics, become
more flexible thinkers and are more able to use
multiple approaches to problem solving”
(Rubenstein, 2001, p. 442).
CONNECTIONS [CN]
Contextualization and making connections to the
experiences of learners are powerful processes in
developing mathematical understanding. When
mathematical ideas are connected to each other or
to real-world phenomena, students begin to view
mathematics as useful, relevant and integrated.
Learning mathematics within contexts and making
connections relevant to learners can validate past
experiences and increase student willingness to
participate and be actively engaged.
The brain is constantly looking for and making
connections. “Because the learner is constantly
searching for connections on many levels,
educators need to orchestrate the experiences
from which learners extract understanding.…
Brain research establishes and confirms that
multiple complex and concrete experiences are
essential for meaningful learning and teaching”
(Caine and Caine, 1991, p. 5).
©Alberta Education, Alberta, Canada
Mental mathematics “provides a cornerstone for
all estimation processes, offering a variety of
alternative algorithms and nonstandard techniques
for finding answers” (Hope, 1988, p. v).
Estimation is used for determining approximate
values or quantities, usually by referring to
benchmarks or referents, or for determining the
reasonableness of calculated values. Estimation is
also used to make mathematical judgements and to
develop useful, efficient strategies for dealing
with situations in daily life. When estimating,
students need to learn which strategy to use and
how to use it.
Mathematics (10–12) /5
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PROBLEM SOLVING [PS]
Problem solving is one of the key processes and
foundations within the field of mathematics.
Learning through problem solving should be the
focus of mathematics at all grade levels. Students
develop a true understanding of mathematical
concepts and procedures when they solve
problems in meaningful contexts. Problem solving
is to be employed throughout all of mathematics
and should be embedded throughout all the topics.
When students encounter new situations and
respond to questions of the type, How would
you ...?
or
How
could
you …?,
the
problem-solving approach is being modelled.
Students develop their own problem-solving
strategies by listening to, discussing and trying
different strategies.
In order for an activity to be problem-solving
based, it must ask students to determine a way to
get from what is known to what is sought. If
students have already been given ways to solve the
problem, it is not a problem, but practice. Students
should not know the answer immediately. A true
problem requires students to use prior learnings in
new ways and contexts. Problem solving requires
and builds depth of conceptual understanding and
student engagement. Students will be engaged if
the problems relate to their lives, cultures,
interests, families or current events.
In a mathematics class, there are two distinct types
of problem solving: solving contextual problems
outside of mathematics and solving mathematical
problems. Finding the maximum profit given
manufacturing constraints is an example of a
contextual problem, while seeking and developing
a general formula to solve a quadratic equation is
an example of a mathematical problem.
Problem solving can also be considered in terms
of engaging students in both inductive and
deductive reasoning strategies. As students make
sense of the problem, they will be creating
conjectures and looking for patterns that they may
be able to generalize. This part of the
problem-solving process often involves inductive
reasoning. As students use approaches to solving
the problem, they often move into mathematical
reasoning that is deductive in nature. It is crucial
that students be encouraged to engage in both
types of reasoning and be given the opportunity to
consider the approaches and strategies used by
others in solving similar problems.
Problem solving is a powerful teaching tool that
fosters multiple, creative and innovative solutions.
Creating an environment where students openly
look for, and engage in, finding a variety of
strategies for solving problems empowers students
to explore alternatives and develops confident,
cognitive mathematical risk-takers.
REASONING [R]
Both conceptual understanding and student
engagement are fundamental in moulding
students’ willingness to persevere in future
problem-solving tasks.
Problems are not just simple computations
embedded in a story, nor are they contrived. They
are tasks that are rich and open-ended, so there
may be more than one way of arriving at a
solution or there may be multiple answers. Good
problems should allow for every student in the
class to demonstrate his or her knowledge, skill or
understanding. Problem solving can vary from
being an individual activity to a class (or beyond)
undertaking.
6/ Mathematics (10–12)
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Mathematical reasoning helps students think
logically and make sense of mathematics. Students
need to develop confidence in their abilities to
reason and to justify their mathematical thinking.
Questions that challenge students to think, analyze
and synthesize help them develop an
understanding of mathematics. All students need
to be challenged to answer questions such as, Why
do you believe that’s true/correct? or What would
happen if ….
Mathematical experiences provide opportunities
for students to engage in inductive and deductive
reasoning. Students use inductive reasoning when
they explore and record results, analyze
observations, make generalizations from patterns
©Alberta Education, Alberta, Canada
and test these generalizations. Students use
deductive reasoning when they reach new
conclusions based upon the application of what is
already known or assumed to be true. The thinking
skills developed by focusing on reasoning can be
used in daily life in a wide variety of contexts and
disciplines.
mathematical concepts and make connections
among them.
TECHNOLOGY [T]
Being able to create, interpret and describe a
visual representation is part of spatial sense and
spatial reasoning. Spatial visualization and spatial
reasoning enable students to describe the
relationships among and between 3-D objects and
2-D shapes.
Technology can be used effectively to contribute
to and support the learning of a wide range of
mathematical outcomes. Technology enables
students to explore and create patterns, examine
relationships, test conjectures and solve problems.
Calculators and computers can be used to:
• explore and demonstrate mathematical
relationships and patterns
• organize and display data
• generate and test inductive conjectures
• extrapolate and interpolate
• assist with calculation procedures as part of
solving problems
• increase the focus on conceptual understanding
by decreasing the time spent on repetitive
procedures
• reinforce the learning of basic facts
• develop personal procedures for mathematical
operations
• model situations
• develop number and spatial sense.
Technology contributes to a learning environment
in which the curiosity of students can lead to rich
mathematical discoveries at all grade levels. The
use of technology should not replace mathematical
understanding. Instead, technology should be used
as one of a variety of approaches and tools for
creating mathematical understanding.
VISUALIZATION [V]
Visualization “involves thinking in pictures and
images, and the ability to perceive, transform and
recreate different aspects of the visual-spatial
world” (Armstrong, 1993, p. 10). The use of
visualization in the study of mathematics provides
students with opportunities to understand
©Alberta Education, Alberta, Canada
Visual images and visual reasoning are important
components of number, spatial and measurement
sense. Number visualization occurs when students
create mental representations of numbers.
Measurement visualization goes beyond the
acquisition of specific measurement skills.
Measurement sense includes the ability to
determine when to measure and when to estimate
and involves knowledge of several estimation
strategies (Shaw and Cliatt, 1989, p. 150).
Visualization is fostered through the use of
concrete materials, technology and a variety of
visual representations. It is through visualization
that abstract concepts can be understood
concretely by the student. Visualization is a
foundation to the development of abstract
understanding, confidence and fluency.
Nature of Mathematics
Mathematics is one way of understanding,
interpreting and describing our world. There are a
number of characteristics that define the nature of
mathematics, including change, constancy,
number sense, patterns, relationships, spatial sense
and uncertainty.
CHANGE
It is important for students to understand that
mathematics is dynamic and not static. As a result,
recognizing change is a key component in
understanding and developing mathematics.
Within
mathematics,
students
encounter
conditions of change and are required to search
for explanations of that change. To make
Mathematics (10–12) /7
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predictions, students need to describe and quantify
their observations, look for patterns, and describe
those quantities that remain fixed and those that
change. For example, the sequence 4, 6, 8, 10,
12, … can be described as:
• skip counting by 2s, starting from 4
• an arithmetic sequence, with first term 4 and a
common difference of 2
• a linear function with a discrete domain
(Steen, 1990, p. 184).
A true sense of number goes well beyond the
skills of simply counting, memorizing facts and
the situational rote use of algorithms. Students
with strong number sense are able to judge the
reasonableness
of
a
solution,
describe
relationships between different types of numbers,
compare quantities and work with different
representations of the same number to develop a
deeper conceptual understanding of mathematics.
Students need to learn that new concepts of
mathematics as well as changes to already learned
concepts arise from a need to describe and
understand something new. Integers, decimals,
fractions, irrational numbers and complex
numbers emerge as students engage in exploring
new situations that cannot be effectively described
or analyzed using whole numbers.
Number sense develops when students connect
numbers to real-life experiences and when
students use benchmarks and referents. This
results in students who are computationally fluent
and flexible with numbers and who have intuition
about numbers. Evolving number sense typically
comes as a by-product of learning rather than
through direct instruction. However, number sense
can be developed by providing mathematically
rich tasks that allow students to make connections.
Students best experience change to their
understanding of mathematical concepts as a
result of mathematical play.
PATTERNS
CONSTANCY
Many important properties in mathematics do not
change when conditions change. Examples of
constancy include:
• the conservation of equality in solving
equations
• the sum of the interior angles of any triangle
• the theoretical probability of an event.
Some problems in mathematics require students to
focus on properties that remain constant. The
recognition of constancy enables students to solve
problems such as those involving constant rates of
change, lines with constant slope, or direct
variation situations.
NUMBER SENSE
Number sense, which can be thought of as deep
understanding and flexibility with numbers, is the
most important foundation of numeracy (British
Columbia Ministry of Education, 2000, p. 146).
Continuing to foster number sense is fundamental
to growth of mathematical understanding.
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Mathematics is about recognizing, describing and
working with numerical and non-numerical
patterns. Patterns exist in all of the mathematical
topics, and it is through the study of patterns that
students can make strong connections between
concepts in the same and different topics.
Working with patterns also enables students to
make connections beyond mathematics. The
ability to analyze patterns contributes to how
students understand their environment.
Patterns may be represented in concrete, visual,
auditory or symbolic form. Students should
develop fluency in moving from one
representation to another.
Students need to learn to recognize, extend, create
and
apply
mathematical
patterns.
This
understanding of patterns allows students to make
predictions and justify their reasoning when
solving problems.
Learning to work with patterns helps develop
students’ algebraic thinking, which is foundational
for working with more abstract mathematics.
©Alberta Education, Alberta, Canada
RELATIONSHIPS
Mathematics is used to describe and explain
relationships. Within the study of mathematics,
students look for relationships among numbers,
sets, shapes, objects, variables and concepts. The
search for possible relationships involves
collecting and analyzing data, analyzing patterns
and describing possible relationships visually,
symbolically, orally or in written form.
provides students with an understanding of why
and how to assess the reliability of data and data
interpretation.
Chance addresses the predictability of the
occurrence of an outcome. As students develop
their understanding of probability, the language of
mathematics becomes more specific and describes
the degree of uncertainty more accurately. This
language must be used effectively and correctly to
convey valuable messages.
SPATIAL SENSE
Spatial sense involves the representation and
manipulation of 3-D objects and 2-D shapes. It
enables students to reason and interpret among
3-D and 2-D representations.
Spatial sense is developed through a variety of
experiences with visual and concrete models.
It offers a way to interpret and reflect on
the physical environment and its 3-D or
2-D representations.
Some problems involve attaching numerals and
appropriate units (measurement) to dimensions of
objects. Spatial sense allows students to make
predictions about the results of changing these
dimensions.
Spatial sense is also critical in students’
understanding of the relationship between the
equations and graphs of functions and, ultimately,
in understanding how both equations and graphs
can be used to represent physical situations.
Course Sequences and Topics
The Mathematics Grades 10–12 Program of
Studies includes course sequences and topics
rather than strands as in the Mathematics
Kindergarten to Grade 9 Program of Studies.
Three course sequences are available: “-1,” “-2”
and “-3.” A combined course (Mathematics 10C)
is the starting point for the “-1” course sequence
and the “-2” course sequence. Each topic area
requires that students develop a conceptual
knowledge base and skill set that will be useful to
whatever course sequence they have chosen. The
topics covered within a course sequence are meant
to build upon previous knowledge and to progress
from simple to more complex conceptual
understandings.
UNCERTAINTY
In mathematics, interpretations of data and the
predictions made from data inherently lack
certainty.
Events and experiments generate statistical data
that can be used to make predictions. It is
important that students recognize that these
predictions (interpolations and extrapolations) are
based upon patterns that have a degree of
uncertainty. The quality of an interpretation or
conclusion is directly related to the quality of the
data it is based upon. An awareness of uncertainty
©Alberta Education, Alberta, Canada
Mathematics (10–12) /9
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Mathematics 10C
(combined course)
K to 9
Mathematics 10-3
Mathematics 20-1
Mathematics 30-1
“-1” Course
Sequence
Mathematics 20-2
Mathematics 30-2
“-2” Course
Sequence
Mathematics 20-3
Mathematics 30-3
“-3” Course
Sequence
GOALS OF COURSE SEQUENCES
The goals of all three course sequences are to
provide prerequisite attitudes, knowledge, skills
and understandings for specific post-secondary
programs or direct entry into the work force. All
three course sequences provide students with
mathematical understandings and critical-thinking
skills. It is the choice of topics through which
those understandings and skills are developed that
varies among course sequences. When choosing a
course sequence, students should consider their
interests, both current and future. Students,
parents and educators are encouraged to research
the admission requirements for post-secondary
programs of study as they vary by institution and
by year.
DESIGN OF COURSE SEQUENCES
Each course sequence is designed to provide
students with the mathematical understandings,
rigour and critical-thinking skills that have been
identified for specific post-secondary programs of
study and for direct entry into the work force.
The content of each course sequence has been
based on consultations with mathematics teachers
and on the Western and Northern Canadian
Protocol
(WNCP)
Consultation
with
Post-Secondary Institutions, Business and
Industry Regarding Their Requirements for High
School Mathematics: Final Report on Findings.
10/ Mathematics (10–12)
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“-1” Course Sequence
This course sequence is designed to provide
students with the mathematical understandings
and critical-thinking skills identified for entry into
post-secondary programs that require the study of
calculus. Topics include algebra and number;
measurement;
relations
and
functions;
trigonometry; and permutations, combinations and
binomial theorem.
“-2” Course Sequence
This course sequence is designed to provide
students with the mathematical understandings
and critical-thinking skills identified for
post-secondary studies in programs that do not
require the study of calculus. Topics include
geometry, measurement, number and logic, logical
reasoning, relations and functions, statistics, and
probability.
“-3” Course Sequence
This course sequence is designed to provide
students with the mathematical understandings
and critical-thinking skills identified for entry into
the majority of trades and for direct entry into the
work force. Topics include algebra, geometry,
measurement, number, statistics and probability.
©Alberta Education, Alberta, Canada
Outcomes
The program of studies is stated in terms of
general outcomes and specific outcomes.
General outcomes are overarching statements
about what students are expected to learn in each
course.
Links to the ICT outcomes have been identified
for some specific outcomes. These links appear in
square brackets below the process codes for an
outcome, where appropriate.
The complete
wording of the relevant outcomes for ICT is
provided in the Appendix.
Summary
Specific outcomes are statements that identify the
specific knowledge, skills and understandings that
students are required to attain by the end of a
given course.
In the specific outcomes, the word including
indicates that any ensuing items must be addressed
to fully meet the learning outcome. The phrase
such as indicates that the ensuing items are
provided for clarification and are not requirements
that must be addressed to fully meet the learning
outcome.
The word and used in an outcome indicates that
both ideas must be addressed to fully meet the
learning outcome, although not necessarily at the
same time or in the same question.
Links to Information and Communication
Technology (ICT) Outcomes
Some curriculum outcomes from Alberta
Education’s Information and Communication
Technology (ICT) Program of Studies can be
linked to outcomes in the mathematics program so
that students will develop a broad perspective on
the nature of technology, learn how to use and
apply a variety of technologies, and consider the
impact of ICT on individuals and society. The
connection to ICT outcomes supports and
reinforces the understandings and abilities that
students are expected to develop through the
general and specific outcomes of the mathematics
program.
Effective, efficient and ethical
application of ICT outcomes contributes to the
mathematics program vision.
©Alberta Education, Alberta, Canada
The Conceptual Framework for Grades 10–12
Mathematics describes the nature of mathematics,
the mathematical processes, the course sequences
and topics, and the role of outcomes in
grades 10–12 mathematics. Activities that take
place in the mathematics classroom should be
based on a problem-solving approach that
incorporates the mathematical processes and leads
students to an understanding of the nature of
mathematics.
INSTRUCTIONAL FOCUS
Each course sequence in the Mathematics Grades
10–12 Program of Studies is arranged by topics.
Students should be engaged in making
connections among concepts both within and
across topics to make mathematical learning
experiences meaningful.
Teachers should consider the following points
when planning for instruction and assessment.
• The mathematical processes that are identified
with the outcome are intended to help teachers
select effective pedagogical approaches for the
teaching and learning of the outcome.
• All seven mathematical processes must be
integrated throughout teaching and learning
approaches, and should support the intent of
the outcomes.
• Wherever possible, meaningful contexts
should be used in examples, problems and
projects.
• Instruction should flow from simple to
complex and from concrete to abstract.
Mathematics (10–12) /11
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• The assessment plan for the course should be a
balance of assessment for learning, assessment
as learning and assessment of learning.
The focus of student learning should be on
developing a conceptual and procedural
understanding
of
mathematics.
Students’
conceptual
understanding
and
procedural
understanding must be directly related.
12/ Mathematics (10–12)
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©Alberta Education, Alberta, Canada
MATHEMATICS 10C
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Measurement
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense and
proportional reasoning.
1. Solve problems that involve linear measurement, using:
• SI and imperial units of measure
• estimation strategies
• measurement strategies.
[ME, PS, V]
2. Apply proportional reasoning to problems that involve conversions
between SI and imperial units of measure.
[C, ME, PS]
3. Solve problems, using SI and imperial units, that involve the surface
area and volume of 3-D objects, including:
• right cones
• right cylinders
• right prisms
• right pyramids
• spheres.
[CN, PS, R, V]
4. Develop and apply the primary trigonometric ratios (sine, cosine,
tangent) to solve problems that involve right triangles.
[C, CN, PS, R, T, V]
Mathematics 10C
©Alberta Education, Alberta, Canada
Mathematics (10–12) /13
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Algebra and Number
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic reasoning and
number sense.
1. Demonstrate an understanding of factors of whole numbers by
determining the:
• prime factors
• greatest common factor
• least common multiple
• square root
• cube root.
[CN, ME, R]
2. Demonstrate an understanding of irrational numbers by:
• representing, identifying and simplifying irrational numbers
• ordering irrational numbers.
[CN, ME, R, V]
[ICT: C6–2.3]
3. Demonstrate an understanding of powers with integral and rational
exponents.
[C, CN, PS, R]
4. Demonstrate an understanding of the multiplication of polynomial
expressions (limited to monomials, binomials and trinomials),
concretely, pictorially and symbolically.
[CN, R, V]
5. Demonstrate an understanding of common factors and trinomial
factoring, concretely, pictorially and symbolically.
[C, CN, R, V]
14/ Mathematics (10–12)
(2008)
Mathematics 10C
©Alberta Education, Alberta, Canada
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and
graphical reasoning through
the study of relations.
1. Interpret and explain the relationships among data, graphs and situations.
[C, CN, R, T, V]
[ICT: C6–4.3, C7–4.2]
2. Demonstrate an understanding of relations and functions.
[C, R, V]
3. Demonstrate an understanding of slope with respect to:
• rise and run
• line segments and lines
• rate of change
• parallel lines
• perpendicular lines.
[PS, R, V]
4. Describe and represent linear relations, using:
• words
• ordered pairs
• tables of values
• graphs
• equations.
[C, CN, R, V]
5. Determine the characteristics of the graphs of linear relations, including the:
• intercepts
• slope
• domain
• range.
[CN, PS, R, V]
6. Relate linear relations expressed in:
• slope–intercept form (y = mx + b)
• general form (Ax + By + C = 0)
• slope–point form (y – y1 = m(x – x1))
to their graphs.
[CN, R, T, V]
[ICT: C6–4.3]
Mathematics 10C
©Alberta Education, Alberta, Canada
Mathematics (10–12) /15
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions (continued)
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and
graphical reasoning through
the study of relations.
7. Determine the equation of a linear relation, given:
• a graph
• a point and the slope
• two points
• a point and the equation of a parallel or perpendicular line
to solve problems.
[CN, PS, R, V]
8. Represent a linear function, using function notation.
[CN, ME, V]
9. Solve problems that involve systems of linear equations in two variables,
graphically and algebraically.
[CN, PS, R, T, V]
[ICT: C6–4.1]
16/ Mathematics (10–12)
(2008)
Mathematics 10C
©Alberta Education, Alberta, Canada
MATHEMATICS 20-1
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Algebra and Number
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic reasoning and
number sense.
1. Demonstrate an understanding of the absolute value of real numbers.
[R, V]
2. Solve problems that involve operations on radicals and radical
expressions with numerical and variable radicands.
[CN, ME, PS, R]
3. Solve problems that involve radical equations (limited to square roots).
[C, PS, R]
4. Determine equivalent forms of rational expressions (limited to
numerators and denominators that are monomials, binomials or
trinomials).
[C, ME, R]
5. Perform operations on rational expressions (limited to numerators and
denominators that are monomials, binomials or trinomials).
[CN, ME, R]
6. Solve problems that involve rational equations (limited to numerators
and denominators that are monomials, binomials or trinomials).
[C, PS, R]
Trigonometry
General Outcome
Specific Outcomes
It is expected that students will:
Develop trigonometric reasoning.
1. Demonstrate an understanding of angles in standard position
[0° to 360°].
[R, V]
2. Solve problems, using the three primary trigonometric ratios for angles
from 0° to 360° in standard position.
[C, ME, PS, R, T, V]
[ICT: C6–4.1]
3. Solve problems, using the cosine law and sine law, including the
ambiguous case.
[C, CN, PS, R, T]
[ICT: C6–4.1]
Mathematics 20-1
©Alberta Education, Alberta, Canada
Mathematics (10–12) /17
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and graphical
reasoning through the study of
relations.
1. Factor polynomial expressions of the form:
2
• ax + bx + c, a ≠ 0
•
a 2 x 2 − b2 y 2 , a ≠ 0, b ≠ 0
•
a ( f ( x ) ) + b ( f ( x ) ) + c, a ≠ 0
•
a 2 ( f ( x ) ) − b 2 ( g ( y ) ) , a ≠ 0, b ≠ 0
2
2
2
where a, b and c are rational numbers.
[CN, ME, R]
2. Graph and analyze absolute value functions (limited to linear and
quadratic functions) to solve problems.
[C, PS, R, T, V]
[ICT: C6–4.1, C6–4.3]
3. Analyze quadratic functions of the form y = a ( x − p ) + q and
2
determine the:
• vertex
• domain and range
• direction of opening
• axis of symmetry
• x- and y-intercepts.
[CN, R, T, V]
[ICT: C6–4.3, C7–4.2]
4. Analyze quadratic functions of the form y = ax2 + bx + c to identify
characteristics of the corresponding graph, including:
• vertex
• domain and range
• direction of opening
• axis of symmetry
• x- and y-intercepts
and to solve problems.
[CN, PS, R, T, V]
[ICT: C6–4.1, C6–4.3]
5. Solve problems that involve quadratic equations.
[C, CN, PS, R, T, V]
[ICT: C6–4.1]
6. Solve, algebraically and graphically, problems that involve systems of
linear-quadratic and quadratic-quadratic equations in two variables.
[CN, PS, R, T, V]
[ICT: C6–4.1, C6–4.4]
18/ Mathematics (10–12)
(2008)
Mathematics 20-1
©Alberta Education, Alberta, Canada
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions (continued)
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and graphical
reasoning through the study of
relations.
7. Solve problems that involve linear and quadratic inequalities in two
variables.
[C, PS, T, V]
[ICT: C6–4.1, C6–4.3]
8. Solve problems that involve quadratic inequalities in one variable.
[CN, PS, V]
9. Analyze arithmetic sequences and series to solve problems.
[CN, PS, R]
10. Analyze geometric sequences and series to solve problems.
[PS, R]
11. Graph and analyze reciprocal functions (limited to the reciprocal of
linear and quadratic functions).
[CN, R, T, V]
[ICT: C6–4.1, C6–4.3]
Mathematics 20-1
©Alberta Education, Alberta, Canada
Mathematics (10–12) /19
(2008)
20/ Mathematics (10–12)
©Alberta Education, Alberta, Canada
MATHEMATICS 30-1
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Trigonometry
General Outcome
Specific Outcomes
It is expected that students will:
Develop trigonometric reasoning.
1. Demonstrate an understanding of angles in standard position, expressed
in degrees and radians.
[CN, ME, R, V]
2. Develop and apply the equation of the unit circle.
[CN, R, V]
3.
Solve problems, using the six trigonometric ratios for angles expressed
in radians and degrees.
[ME, PS, R, T, V]
[ICT: C6–4.1]
4.
Graph and analyze the trigonometric functions sine, cosine and tangent
to solve problems.
[CN, PS, T, V]
[ICT: C6–4.1, C6–4.3]
5. Solve, algebraically and graphically, first and second degree
trigonometric equations with the domain expressed in degrees and
radians.
[CN, PS, R, T, V]
[ICT: C6–4.1, C6–4.4]
6.
Mathematics 30-1
©Alberta Education, Alberta, Canada
Prove trigonometric identities, using:
• reciprocal identities
• quotient identities
• Pythagorean identities
• sum or difference identities (restricted to sine, cosine and tangent)
• double-angle identities (restricted to sine, cosine and tangent).
[R, T, V]
[ICT: C6–4.1, C6–4.4]
Mathematics (10–12) /21
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and graphical
reasoning through the study of
relations.
1. Demonstrate an understanding of operations on, and compositions of,
functions.
[CN, R, T, V]
[ICT: C6–4.1]
2. Demonstrate an understanding of the effects of horizontal and vertical
translations on the graphs of functions and their related equations.
[C, CN, R, V]
3. Demonstrate an understanding of the effects of horizontal and vertical
stretches on the graphs of functions and their related equations.
[C, CN, R, V]
4. Apply translations and stretches to the graphs and equations of
functions.
[C, CN, R, V]
5. Demonstrate an understanding of the effects of reflections on the graphs
of functions and their related equations, including reflections through
the:
• x-axis
• y-axis
• line y = x.
[C, CN, R, V]
6. Demonstrate an understanding of inverses of relations.
[C, CN, R, V]
7. Demonstrate an understanding of logarithms.
[CN, ME, R]
8. Demonstrate an understanding of the product, quotient and power laws
of logarithms.
[C, CN, ME, R, T]
[ICT: C6–4.1]
9. Graph and analyze exponential and logarithmic functions.
[C, CN, T, V]
[ICT: C6–4.3, C6–4.4, F1–4.2]
22/ Mathematics (10–12)
(2008)
Mathematics 30-1
©Alberta Education, Alberta, Canada
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions (continued)
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and graphical
reasoning through the study of
relations.
10. Solve problems that involve exponential and logarithmic equations.
[C, CN, PS, R]
11. Demonstrate an understanding of factoring polynomials of degree
greater than 2 (limited to polynomials of degree ≤ 5 with integral
coefficients).
[C, CN, ME]
12. Graph and analyze polynomial functions (limited to polynomial
functions of degree ≤ 5 ).
[C, CN, T, V]
[ICT: C6–4.3, C6–4.4]
13. Graph and analyze radical functions (limited to functions involving one
radical).
[CN, R, T, V]
[ICT: C6–4.1, C6–4.3]
14. Graph and analyze rational functions (limited to numerators and
denominators that are monomials, binomials or trinomials).
[CN, R, T, V]
[ICT: C6–4.1, C6–4.3, C6–4.4]
Permutations, Combinations and Binomial Theorem
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and numeric
reasoning that involves
combinatorics.
Mathematics 30-1
©Alberta Education, Alberta, Canada
1.
Apply the fundamental counting principle to solve problems.
[C, PS, R, V]
[ICT: C6–2.3]
2.
Determine the number of permutations of n elements taken r at a time to
solve problems.
[C, PS, R, V]
3.
Determine the number of combinations of n different elements taken r
at a time to solve problems.
[C, PS, R, V]
4.
Expand powers of a binomial in a variety of ways, including using the
binomial theorem (restricted to exponents that are natural numbers).
[CN, R, V]
Mathematics (10–12) /23
(2008)
24/ Mathematics (10–12)
©Alberta Education, Alberta, Canada
MATHEMATICS 20-2
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Measurement
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense and
proportional reasoning.
1.
Solve problems that involve the application of rates.
[CN, PS, R]
2. Solve problems that involve scale diagrams, using proportional
reasoning.
[CN, PS, R, V]
3. Demonstrate an understanding of the relationships among scale factors,
areas, surface areas and volumes of similar 2-D shapes and 3-D objects.
[C, CN, PS, R, V]
Geometry
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense.
1. Derive proofs that involve the properties of angles and triangles.
[CN, R, V]
2. Solve problems that involve properties of angles and triangles.
[CN, PS, V]
3. Solve problems that involve the cosine law and the sine law, excluding
the ambiguous case.
[CN, PS, R]
Mathematics 20-2
©Alberta Education, Alberta, Canada
Mathematics (10–12) /25
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Number and Logic
General Outcome
Specific Outcomes
It is expected that students will:
Develop number sense and
logical reasoning.
1. Analyze and prove conjectures, using inductive and deductive
reasoning, to solve problems.
[C, CN, PS, R]
2. Analyze puzzles and games that involve spatial reasoning, using
problem-solving strategies.
[CN, PS, R, V]
3. Solve problems that involve operations on radicals and radical
expressions with numerical and variable radicands (limited to square
roots).
[CN, ME, PS, R]
4. Solve problems that involve radical equations (limited to square roots or
cube roots).
[C, PS, R]
Statistics
General Outcome
Specific Outcomes
It is expected that students will:
Develop statistical reasoning.
1. Demonstrate an understanding of normal distribution, including:
• standard deviation
• z-scores.
[CN, PS, T, V]
[ICT: C6–4.1, C7–4.2]
2. Interpret statistical data, using:
• confidence intervals
• confidence levels
• margin of error.
[C, CN, R]
[ICT: C1–4.2, C2–4.2, C7–4.2]
26/ Mathematics (10–12)
(2008)
Mathematics 20-2
©Alberta Education, Alberta, Canada
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and graphical
reasoning through the study of
relations.
1.
Demonstrate an understanding of the characteristics of quadratic
functions, including:
• vertex
• intercepts
• domain and range
• axis of symmetry.
[CN, PS, T, V]
[ICT: C6–4.1, C6–4.3]
2.
Solve problems that involve quadratic equations.
[C, CN, PS, R, T, V]
[ICT: C6–4.1, C6–4.3]
Mathematics Research Project
General Outcome
Specific Outcomes
It is expected that students will:
Develop an appreciation of the
role of mathematics in society.
Mathematics 20-2
©Alberta Education, Alberta, Canada
1.
Research and give a presentation on a historical event or an area of
interest that involves mathematics.
[C, CN, ME, PS, R, T, V]
[ICT: C1–4.2, C1–4.4, C2–4.1, C3–4.1, C3–4.2, C7–4.2, F2–4.7]
Mathematics (10–12) /27
(2008)
28/ Mathematics (10–12)
©Alberta Education, Alberta, Canada
MATHEMATICS 30-2
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Logical Reasoning
General Outcome
Specific Outcomes
It is expected that students will:
Develop logical reasoning.
1. Analyze puzzles and games that involve numerical and logical
reasoning, using problem-solving strategies.
[CN, ME, PS, R]
2. Solve problems that involve the application of set theory.
[CN, PS, R, V]
[ICT: C6–2.3]
Probability
General Outcome
Specific Outcomes
It is expected that students will:
Develop critical thinking skills
related to uncertainty.
1. Interpret and assess the validity of odds and probability statements.
[C, CN, ME]
2. Solve problems that involve the probability of mutually exclusive and
non–mutually exclusive events.
[CN, PS, R, V]
[ICT: C6–2.3]
3. Solve problems that involve the probability of two events.
[CN, PS, R]
4. Solve problems that involve the fundamental counting principle.
[PS, R, V]
[ICT: C6–2.3]
5. Solve problems that involve permutations.
[ME, PS, R, T, V]
6. Solve problems that involve combinations.
[ME, PS, R, T, V]
Mathematics 30-2
©Alberta Education, Alberta, Canada
Mathematics (10–12) /29
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Relations and Functions
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic and graphical
reasoning through the study of
relations.
1. Determine equivalent forms of rational expressions (limited to
numerators and denominators that are monomials and binomials).
[C, ME, R]
2. Perform operations on rational expressions (limited to numerators and
denominators that are monomials and binomials).
[CN, ME, R]
3. Solve problems that involve rational equations (limited to numerators
and denominators that are monomials and binomials).
[C, CN, PS, R]
4. Demonstrate an understanding of logarithms and the laws of logarithms.
[C, CN, ME, R]
[ICT: C6–4.1]
5. Solve problems that involve exponential equations.
[C, CN, PS, R, T]
[ICT: C6–4.1, C6–4.3]
6. Represent data, using exponential and logarithmic functions, to solve
problems.
[C, CN, PS, T, V]
[ICT: C6–4.1, C6–4.3, C6–4.4]
7. Represent data, using polynomial functions (of degree ≤ 3), to solve
problems.
[C, CN, PS, T, V]
[ICT: C6–4.1, C6–4.3, C6–4.4]
8. Represent data, using sinusoidal functions, to solve problems.
[C, CN, PS, T, V]
[ICT: C6–4.1, C6–4.3, C6–4.4]
Mathematics Research Project
General Outcome
Specific Outcomes
It is expected that students will:
Develop an appreciation of the
role of mathematics in society.
30/ Mathematics (10–12)
(2008)
1.
Research and give a presentation on a current event or an area of interest
that involves mathematics.
[C, CN, ME, PS, R, T, V]
[ICT: C1–4.2, C1–4.4, C2–4.1, C3–4.1, C3–4.2, C7–4.2, F2–4.7,
P2–4.1]
Mathematics 30-2
©Alberta Education, Alberta, Canada
MATHEMATICS 10-3
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Measurement
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense through
direct and indirect measurement.
1. Demonstrate an understanding of the Système International (SI) by:
• describing the relationships of the units for length, area, volume,
capacity, mass and temperature
• applying strategies to convert SI units to imperial units.
[C, CN, ME, V]
2. Demonstrate an understanding of the imperial system by:
• describing the relationships of the units for length, area, volume,
capacity, mass and temperature
• comparing the American and British imperial units for capacity
• applying strategies to convert imperial units to SI units.
[C, CN, ME, V]
3. Solve and verify problems that involve SI and imperial linear
measurements, including decimal and fractional measurements.
[CN, ME, PS, V]
4. Solve problems that involve SI and imperial area measurements of
regular, composite and irregular 2-D shapes and 3-D objects, including
decimal and fractional measurements, and verify the solutions.
[ME, PS, R, V]
Mathematics 10-3
©Alberta Education, Alberta, Canada
Mathematics (10–12) /31
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Geometry
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense.
1. Analyze puzzles and games that involve spatial reasoning, using
problem-solving strategies.
[C, CN, PS, R]
2. Demonstrate an understanding of the Pythagorean theorem by:
• identifying situations that involve right triangles
• verifying the formula
• applying the formula
• solving problems.
[C, CN, PS, V]
3. Demonstrate an understanding of similarity of convex polygons,
including regular and irregular polygons.
[C, CN, PS, V]
4. Demonstrate an understanding of primary trigonometric ratios
(sine, cosine, tangent) by:
• applying similarity to right triangles
• generalizing patterns from similar right triangles
• applying the primary trigonometric ratios
• solving problems.
[CN, PS, R, T, V]
[ICT: C6–4.1]
5. Solve problems that involve parallel, perpendicular and transversal
lines, and pairs of angles formed between them.
[C, CN, PS, V]
6. Demonstrate an understanding of angles, including acute, right, obtuse,
straight and reflex, by:
• drawing
• replicating and constructing
• bisecting
• solving problems.
[C, ME, PS, T, V]
[ICT: C6–4.1]
32/ Mathematics (10–12)
(2008)
Mathematics 10-3
©Alberta Education, Alberta, Canada
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Number
General Outcome
Specific Outcomes
It is expected that students will:
Develop number sense and
critical thinking skills.
1.
Solve problems that involve unit pricing and currency exchange, using
proportional reasoning.
[CN, ME, PS, R]
[ICT: F2–4.7]
2.
Demonstrate an understanding of income, including:
• wages
• salary
• contracts
• commissions
• piecework
to calculate gross pay and net pay.
[C, CN, R, T]
[ICT: C6–4.1, C6–4.2, C7–4.2, F2–4.7]
Algebra
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic reasoning.
Mathematics 10-3
©Alberta Education, Alberta, Canada
1. Solve problems that require the manipulation and application of
formulas related to:
• perimeter
• area
• the Pythagorean theorem
• primary trigonometric ratios
• income.
[C, CN, ME, PS, R]
Mathematics (10–12) /33
(2008)
34/ Mathematics (10–12)
©Alberta Education, Alberta, Canada
MATHEMATICS 20-3
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Measurement
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense through
direct and indirect measurement.
1.
Solve problems that involve SI and imperial units in surface area
measurements and verify the solutions.
[C, CN, ME, PS, V]
2.
Solve problems that involve SI and imperial units in volume and
capacity measurements.
[C, CN, ME, PS, V]
Geometry
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense.
Mathematics 20-3
©Alberta Education, Alberta, Canada
1.
Solve problems that involve two and three right triangles.
[CN, PS, T, V]
[ICT: C6–4.1]
2.
Solve problems that involve scale.
[PS, R, V]
3.
Model and draw 3-D objects and their views.
[CN, R, V]
4.
Draw and describe exploded views, component parts and scale diagrams
of simple 3-D objects.
[CN, V]
Mathematics (10–12) /35
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Number
General Outcome
Specific Outcomes
It is expected that students will:
Develop number sense and
critical thinking skills.
1. Analyze puzzles and games that involve numerical reasoning, using
problem-solving strategies.
[C, CN, PS, R]
2. Solve problems that involve personal budgets.
[CN, PS, R, T]
[ICT: C6–4.2, C6–4.4]
3. Demonstrate an understanding of compound interest.
[CN, ME, PS, T]
[ICT: C6–4.1]
4. Demonstrate an understanding of financial institution services used to
access and manage finances.
[C, CN, R, T]
[ICT: F2–4.6]
5. Demonstrate an understanding of credit options, including:
• credit cards
• loans.
[CN, ME, PS, R]
[ICT: F2–4.7]
36/ Mathematics (10–12)
(2008)
Mathematics 20-3
©Alberta Education, Alberta, Canada
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Algebra
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic reasoning.
1.
Solve problems that require the manipulation and application of
formulas related to:
• volume and capacity
• surface area
• slope and rate of change
• simple interest
• finance charges.
[CN, PS, R]
2. Demonstrate an understanding of slope:
• as rise over run
• as rate of change
• by solving problems.
[C, CN, PS, V]
3. Solve problems by applying proportional reasoning and unit analysis.
[C, CN, PS, R]
Statistics
General Outcome
Specific Outcomes
It is expected that students will:
Develop statistical reasoning.
Mathematics 20-3
©Alberta Education, Alberta, Canada
1. Solve problems that involve creating and interpreting graphs, including:
• bar graphs
• histograms
• line graphs
• circle graphs.
[C, CN, PS, R, T, V]
[ICT: C6–4.1, C6–4.2, C6–4.3, P2–4.1]
Mathematics (10–12) /37
(2008)
38/ Mathematics (10–12)
©Alberta Education, Alberta, Canada
MATHEMATICS 30-3
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Measurement
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense through
direct and indirect measurement.
1. Demonstrate an understanding of the limitations of measuring
instruments, including:
• precision
• accuracy
• uncertainty
• tolerance
and solve problems.
[C, PS, R, T, V]
[ICT: C6–4.4, C6–4.5]
Geometry
General Outcome
Specific Outcomes
It is expected that students will:
Develop spatial sense.
1.
2.
Solve problems by using the sine law and cosine law, excluding the
ambiguous case.
[CN, PS, V]
Solve problems that involve:
triangles
quadrilaterals
regular polygons.
[C, CN, PS, V]
•
•
•
3.
Mathematics 30-3
©Alberta Education, Alberta, Canada
Demonstrate an understanding of transformations on a 2-D shape or a
3-D object, including:
• translations
• rotations
• reflections
• dilations.
[C, CN, R, T, V]
[ICT: C6–3.4]
Mathematics (10–12) /39
(2008)
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Number
General Outcome
Specific Outcomes
It is expected that students will:
Develop number sense and
critical thinking skills.
1.
Analyze puzzles and games that involve logical reasoning, using
problem-solving strategies.
[C, CN, PS, R]
2.
Solve problems that involve the acquisition of a vehicle by:
• buying
• leasing
• leasing to buy.
[C, CN, PS, R, T]
3.
Critique the viability of small business options by considering:
• expenses
• sales
• profit or loss.
[C, CN, R]
[ICT: F2–4.7]
Algebra
General Outcome
Specific Outcomes
It is expected that students will:
Develop algebraic reasoning.
1.
Demonstrate an understanding of linear relations by:
recognizing patterns and trends
graphing
creating tables of values
writing equations
interpolating and extrapolating
solving problems.
[CN, PS, R, T, V]
[ICT: C6–4.1, C6–4.3, C7–4.2]
•
•
•
•
•
•
40/ Mathematics (10–12)
(2008)
Mathematics 30-3
©Alberta Education, Alberta, Canada
[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation
[PS]
[R]
[T]
[V]
Problem Solving
Reasoning
Technology
Visualization
Statistics
General Outcome
Specific Outcomes
It is expected that students will:
Develop statistical reasoning.
1.
Solve problems that involve measures of central tendency, including:
mean
median
mode
weighted mean
trimmed mean.
[C, CN, PS, R]
•
•
•
•
•
2.
Analyze and describe percentiles.
[C, CN, PS, R]
Probability
General Outcome
Specific Outcomes
It is expected that students will:
Develop critical thinking skills
related to uncertainty.
Mathematics 30-3
©Alberta Education, Alberta, Canada
1.
Analyze and interpret problems that involve probability.
[C, CN, PS, R]
Mathematics (10–12) /41
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42/ Mathematics (10–12)
©Alberta Education, Alberta, Canada
APPENDIX: INFORMATION AND COMMUNICATION TECHNOLOGY (ICT)
OUTCOMES
The following excerpts from the Information and Communication Technology (ICT) Program of Studies
provide the complete wording for outcomes that are linked to the mathematics program of studies. For
the complete ICT Program of Studies, go to the Alberta Education Web site at http://education.alberta.ca/
teachers/program/ict.aspx.
ICT Outcomes, Division 2
General Outcomes
C6 – Students will use technology to
investigate and/or solve problems.
Specific Outcomes
2.3
use graphic organizers, such as mind mapping/webbing, flow
charting and outlining, to present connections between ideas and
information in a problem-solving environment
ICT Outcomes, Division 3
General Outcomes
C6 – Students will use technology to
investigate and/or solve problems.
Specific Outcomes
3.4
pose and test solutions to problems by using computer
applications, such as computer-assisted design or simulation/
modelling software
ICT Outcomes, Division 4
General Outcomes
Specific Outcomes
C1 – Students will access, use and
communicate information from a
variety of technologies.
4.2
C2 – Students will seek alternative
viewpoints, using information
technologies.
C3 – Students will critically assess
information accessed through the
use of a variety of technologies.
4.1
C6 – Students will use technology to
investigate and/or solve problems.
4.1
4.4
4.2
4.1
4.2
4.2
4.3
4.4
4.5
Appendix
©Alberta Education, Alberta, Canada
select information from appropriate sources, including primary
and secondary sources
communicate in a persuasive and engaging manner, through
appropriate forms, such as speeches, letters, reports and
multimedia presentations, applying information technologies for
context, audience and purpose that extend and communicate
understanding of complex issues
consult a wide variety of sources that reflect varied viewpoints on
particular topics
evaluate the validity of gathered viewpoints against other sources
assess the authority, reliability and validity of electronically
accessed information
demonstrate discriminatory selection of electronically accessed
information that is relevant to a particular topic
investigate and solve problems of prediction, calculation and
inference
investigate and solve problems of organization and manipulation
of information
manipulate data by using charting and graphing technologies in
order to test inferences and probabilities
generate new understandings of problematic situations by using
some form of technology to facilitate the process
evaluate the appropriateness of the technology used to investigate
or solve a problem
Mathematics (10–12) /43
(2008)
General Outcomes
Specific Outcomes
C7 – Students will use electronic
research techniques to construct
personal knowledge and meaning.
4.2
analyze and synthesize information to determine patterns and links
among ideas
F1 – Students will demonstrate an
understanding of the nature of
technology.
4.2
solve mathematical and scientific problems by selecting
appropriate technology to perform calculations and experiments
F2 – Students will understand the role
of technology as it applies to self,
work and society.
4.6
demonstrate an understanding of the basic principles and issues of
e-commerce, including such topics as security and privacy,
marketing, and implications for governments, businesses and
consumers alike
use current, reliable information sources from around the world
manipulate and present data through the selection of appropriate
tools, such as scientific instrumentation, calculators, databases
and/or spreadsheets
P2 – Students will organize and
manipulate data.
44/ Mathematics (10–12)
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4.7
4.1
Appendix
©Alberta Education, Alberta, Canada
REFERENCES
Alberta Education. Mathematics Kindergarten to Grade 9 Program of Studies. Edmonton, AB:
Alberta Education, 2007. http://education.alberta.ca/media/645594/kto9math.pdf
(Accessed February 6, 2008).
Alberta Education, System Improvement Group. Western and Northern Canadian Protocol (WNCP)
Consultation with Post-Secondary Institutions, Business and Industry Regarding Their Requirements
for High School Mathematics: Final Report on Findings. Edmonton, AB: Alberta Education, 2006.
Available at http://www.wncp.ca/math/report_2006.pdf (Accessed February 6, 2008).
Alberta Education. The Alberta 10–12 Mathematics Program of Studies with Achievement Indicators.
Edmonton, AB: Alberta Education, 2008.
Alberta Learning. Information and Communication Technology (ICT) Program of Studies.
Edmonton, AB: Alberta Learning, 2000–2003. http://education.alberta.ca/media/453069/pofs.pdf
(Accessed February 6, 2008).
Armstrong, Thomas. 7 Kinds of Smart: Identifying and Developing Your Many Intelligences.
New York, NY: Plume, 1993.
Banks, J. A. and C. A. M. Banks. Multicultural Education: Issues and Perspectives. 2nd ed.
Boston, MA: Allyn and Bacon, 1993.
British Columbia Ministry of Education. The Primary Program: A Framework for Teaching.
Victoria, BC: British Columbia Ministry of Education, 2000.
Caine, Renate Nummela and Geoffrey Caine. Making Connections: Teaching and the Human Brain.
Alexandria, VA: Association for Supervision and Curriculum Development, 1991.
Hope, Jack A. et al. Mental Math in the Primary Grades. Palo Alto, CA: Dale Seymour Publications,
1988.
McAskill, B. et al. WNCP Mathematics Research Project: Final Report. Victoria, BC: Holdfast
Consultants Inc., 2004. Available at http://www.wncp.ca/math/Final_Report.pdf (Accessed
February 6, 2008).
National Council of Teachers of Mathematics. Computation, Calculators, and Common Sense: A
Position of the National Council of Teachers of Mathematics. May 2005.
http://www.nctm.org/uploadedFiles/About_NCTM/Position_Statements/computation.pdf (Accessed
February 6, 2008).
Rubenstein, Rheta N. “Mental Mathematics beyond the Middle School: Why? What? How?”
Mathematics Teacher 94, 6 (September 2001), pp. 442–446.
Shaw, J. M. and M. J. P. Cliatt. “Developing Measurement Sense.” In P. R. Trafton (ed.), New
Directions for Elementary School Mathematics: 1989 Yearbook (Reston, VA: National Council of
Teachers of Mathematics, 1989), pp. 149–155.
Steen, L. A. On the Shoulders of Giants: New Approaches to Numeracy. Washington, DC:
Mathematical Sciences Education Board, National Research Council, 1990.
References
©Alberta Education, Alberta, Canada
Mathematics (10–12) /45
(2008)
Western and Northern Canadian Protocol for Collaboration in Basic Education (Kindergarten to
Grade 12). The Common Curriculum Framework for Grades 10–12 Mathematics: Western and
Northern Canadian Protocol. January 2008. http://www.wncp.ca/math/math10to12.pdf
(Accessed February 6, 2008).
46/ Mathematics (10–12)
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References
©Alberta Education, Alberta, Canada
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