Knowledge and Employability courses provide students with practical and applied opportunities to develop competencies necessary to meet or exceed the following goals. Knowledge and Employability courses prepare students to:

• earn a senior high school credential
• enter the workplace upon leaving school with employability and occupational skills that meet industry standards
• make successful transitions to other courses or to further education and training
• become responsible and contributing members of society.

Programs of study and resources for Knowledge and Employability courses are distinctive, in part, because they promote cross-curricular, community and workplace connections.

Knowledge and Employability courses promote the integration of subjects to emphasize their interrelationships and connections to other school subjects. The philosophy of Knowledge and Employability courses is that students learn best when they can clearly recognize connections, applications and relevance to a variety of everyday experiences. Organizing for instruction may include thematic units, subject integration within units and/or projects in other subjects.

Knowledge and Employability courses provide students with practical and applied opportunities to develop basic reading, writing and mathematical literacy. Community and workplace connections ensure learning within applied contexts, connecting the school with environments beyond school, and may include tours to local businesses and industries, mentorships, job shadowing and work experience.

Knowledge and Employability courses promote the development of career portfolios that help students connect their school experience to the world beyond school. Each portfolio will include exemplars of the student’s on- and off-campus experiences and can be used when the student is seeking employment or further education/training opportunities. Items appropriate for inclusion in career portfolios include résumés, samples of written work, awards and/or their representations, teacher and self-evaluation checklists, workplace assessment tools and employer letters of recommendation.

Safety is emphasized and relevant information is incorporated throughout Knowledge and Employability courses, including basic safety rules and guidelines and information regarding the safe use of tools, equipment and materials in school, home, community and workplace settings.

Because technology is best learned within an applied context, Information and Communication Technology (ICT) outcomes, and the use of computers and other technologies, are included in Knowledge and Employability courses. This technology integration will help students make the transition to the world beyond school.

Knowledge and Employability courses emphasize universal skills and strategies that are essential to all students, including the following.

• Interpersonal skills promote teamwork and respect for, support of and cooperation with others.
• Critical thinking promotes the analysis and appropriate applications of information.
• Creative thinking promotes the identification of unique connections among ideas and insightful approaches to questions and issues.
• Decision-making processes promote the making of timely and appropriate decisions.
• Problem-solving processes promote the ability to identify or pose problems and apply learning to consider the causes and dimensions of, and the solutions to, problems.
• Metacognition² enables students to become more aware of, and have greater control over, their own thinking and learning processes.

²Metacognition: Learning-to-learn strategies; awareness of processes and strategies one uses when learning.

Each Knowledge and Employability course is consistent with the rationale, philosophy, program foundations and organization of other secondary courses. This consistency enables students, as appropriate, to progress through the Knowledge and Employability course sequence and/or to other secondary courses.

Students may take one or more courses in the sequence at any time during grades 8 through 12. Students may be enrolled in only Knowledge and Employability courses or in a combination of Knowledge and Employability and other secondary courses.

Information regarding the identification of students for enrollment in one or more courses can be accessed in the Knowledge and Employability Courses Handbook, Grades 8–12.

Students will develop the following mathematics competencies in the context of solving everyday problems. Students will:

• identify the problem and select and apply appropriate problem-solving strategies, mathematical operations and tools
• estimate and calculate solutions accurately
• evaluate processes, results and personal/ group performance
• develop teamwork skills and use appropriate vocabulary to reason and communicate mathematically
• apply mathematical literacy to everyday situations.

Knowledge and Employability mathematics courses have similarities with, and linkages to, other mathematics courses. However, Knowledge and Employability mathematics courses and resources are distinctive in that they:

• provide students with practical and applied opportunities to develop mathematical competencies
• promote the integration of curriculum and community partnerships to connect mathematics to other school subjects and to other environments.

Within the context and nature of mathematics, the courses include the development of mathematical processes to assist students in achieving their learning goals and to encourage lifelong learning in mathematics.

The conceptual framework outlined in this section presents:

• a multifaceted view of mathematics
• the discipline as a set of interwoven skills, procedures and concepts.

The following graphic illustrates how student outcomes are organized by strand and are designed to be influenced by mathematical processes and the nature of mathematics.

There are critical components that students must encounter in a mathematics program in order to achieve the goals of mathematics education and to encourage lifelong learning in mathematics. Students in Knowledge and Employability mathematics courses will build on and apply mathematical processes, using everyday home, workplace and community problems.

This program of studies incorporates the following seven interrelated mathematical processes that are intended to permeate teaching and learning.

Knowledge and Employability mathematics courses focus on making connections between the components of mathematics and everyday home, workplace and community applications.

• Change
• Constancy
• Dimension
• Number
• Pattern
• Quantity
• Relationships
• Shape
• Uncertainty

To make predictions, students need to describe and quantify their observations, attempt to build patterns and identify those quantities that remain fixed and those that change.

Students are expected to communicate ideas visually, using diagrams and spoken and written forms, when describing constancy. The most important properties in mathematics and science relate to those properties that do not change when outside conditions do.

Stability, conservation, equilibrium, steady state and symmetry are terms used to describe constancy.

Students need to be aware of the properties that remain fixed so that they can solve problems involving constants; e.g., rates of change, lines with constant slope, direct variation situations or the angle sums of triangles.

The concept of dimension is generally associated with 3-D objects, 2-D shapes or 1-D lines and needs to be developed within an environment of physical objects.

Physical objects can also be described using measurement concepts and pattern recognition, rather than the memorization of formulas.

Number, number systems and number operations are vital to all mathematics learning. The use of number must include number sense. Number sense includes:

• an intuitive feeling about numbers and their multiple relationships
• the construction of the meaning of number through a variety of experiences
• the development of an appreciation of the need for numbers beyond whole numbers
• an appreciation of, and the ability to make, quick and accurate estimations for computation and measurement
• the ability to detect arithmetic errors
• knowledge of place value and the effects of arithmetic operations.

Number sense includes the recognition of number patterns that can be used to count, make predictions, describe shapes and make comparisons.

"Mathematics is an exploratory science that seeks to understand every kind of pattern."⁶

Patterns exist in numbers, geometry, algebra and data. Mathematics becomes a useful tool to assist students in their systematic and intellectual understanding of their environment by helping them recognize, extend, create and use patterns as a routine aspect of their lives.

⁶Lynn Arthur Steen, ed., On the Shoulders of Giants, New Approaches to Numeracy, (Washington, DC: National Academy Press, 1990), p. 8.

In everyday situations, individuals classify, measure and order. Some outcomes therefore address single numbers, numbers attached to units of measure and ordered sets of numbers. Other outcomes address the interpretation of numbers and number systems.

With the growing use of technology to process numerical information, it is essential for students to have a wide range of estimation skills to evaluate whether the numerical output provided by a calculator or a computer is a reasonable solution to a given problem.

The study of mathematics is the development of relationships between and among things. Mathematics should prepare for students to make their own relationships between mathematics in school, at home and in the community. Students should look for relationships among physical things and the data used to describe those things.

Descriptions of the attributes of objects are used to examine symmetry and congruence and to classify things. Relationships will be described visually, symbolically, orally and in written form.

Shape in mathematics is central to geometry but also includes:

• geometric representations of algebraic relations
• the geometry of maps
• the creation of networks of plane figures that can be used to construct 3-D objects.

It is very important for students to look for and use similarities, congruences, patterns, transformations, dilatations and tessellations in the solution of a range of everyday problems.

The use of language to describe shapes is an important aspect of mathematics and allows for the classification of objects according to various attributes and the naming and analysis of objects.

Uncertainty involves data, chance, measurements and errors. Problems dealing with data, together with numbers found in various contexts, can be solved within the school mathematics program as long as the data provided and the problems posed have some meaning and relevance to students.

Chance deals with the predictable and the unpredictable outcomes of events. From an early age, students are expected to deal with the concept of chance. As they mature, the language they use to describe chance becomes more sophisticated and involves the vocabulary of probability theory.

Students will:

• estimate and solve problems using numbers, money, decimals, percents, fractions, ratios and proportion in everyday home, workplace and community contexts, using technology as appropriate
• develop and demonstrate number sense to describe quantities, represent numbers in multiple ways and apply appropriate arithmetic operations
• assess the reasonableness of calculations and problem-solving strategies
• communicate mathematically and investigate the application of number concepts and operations in a variety of career and workplace situations, working individually or as a member of a team.

Students will:

develop and demonstrate a number sense for whole numbers, common fractions, decimals, percents and integers and apply arithmetic operations to solve everyday problems.

Students will:

• 1. use estimation strategies to estimate and round numbers to the nearest unit, tenth and hundredth to solve problems in everyday contexts

Estimation and Mental Mathematics | Problem Solving | Reasoning

• 2. represent and describe the relationships between proper/improper fractions, equivalent fractions and mixed numbers concretely, pictorially and symbolically

Communication | Connections | Reasoning | Visualization

• 3. convert among fractions, decimals and percents concretely, pictorially and symbolically to facilitate the solving of problems

Communication | Connections | Reasoning | Visualization

• 4. represent and explain the meaning of integers in everyday contexts concretely, pictorially and symbolically

Communication | Connections | Reasoning | Visualization

• 5. estimate and apply arithmetic operations to solve everyday problems, using:
• whole numbers
• decimals
• fractions
• mixed numbers
• percents

Connections | Estimation and Mental Mathematics | Problem Solving

• 6. estimate, add and subtract integers concretely, pictorially and symbolically in everyday contexts

Connections | Estimation and Mental Mathematics | Problem Solving

• 7. assess the reasonableness of applied calculations and problem-solving strategies, using a variety of tools and/or strategies, e.g., estimation, charts, graphs, calculators and/or computers

Estimation and Mental Mathematics | Reasoning | Technology | Visualization

• 8. calculate and compare rates and unit prices by writing ratios that involve numbers with different units

Connections | Problem Solving | Reasoning

• 9. determine the value of a power, using a whole number base with exponents of 2 and 3

Connections | Reasoning | Visualization

• 10. recognize and explain numbers in scientific notation form

Communication | Connections | Reasoning | Visualization

Students will:

• recognize that patterns and relationships exist in nature and everyday living
• use patterns and relationships to develop a better understanding of their environments and to solve everyday problems at home, in the workplace and in the community, using technology as appropriate
• assess the reasonableness of calculations and problem-solving strategies
• communicate mathematically and investigate the application of patterns and relationships in a variety of career and workplace situations, working individually or as a member of a team.

Students will:

express and use patterns, variables and expressions, including those used in business and industry, with graphs to solve problems at home, in the community and in the workplace.

Students will:

• 1. identify, describe and draw conclusions about patterns and relationships, in oral and written form, in nature and everyday contexts

Communication | Connections | Reasoning | Visualization

• 2. create expressions, make predictions and develop rules to describe, complete and extend patterns and relationships in everyday contexts

Communication | Connections | Problem Solving | Reasoning

• 3. distinguish between the use of variables and constants in everyday situations

Connections | Reasoning

• 4. graph relationships using everyday home, community and workplace contexts and draw conclusions using patterns and relationships

Connections | Reasoning | Visualization

Students will:

• represent algebraic expressions in multiple ways to solve problems, using technology as appropriate
• communicate mathematically and investigate the application of variables and equations in a variety of career and workplace situations, working individually or as a member of a team.

Students will:

use variables and equations to express, summarize and apply relationships as problem-solving tools in a restricted range of contexts.

Students will:

• 5. use variables, formulas and/or substitutions to solve problems in practical situations

Connections | Problem Solving | Reasoning

• 6. substitute numbers for variables in expressions and graph and examine the relationship

Communication | Problem Solving | Reasoning | Visualization

Students will:

• estimate and take accurate measurements using everyday metric (SI) and Imperial units of measure
• solve problems using appropriate measuring devices, i.e., metric (SI) and Imperial, strategies and technology in home, workplace and community contexts
• communicate mathematically and investigate the application of measurement knowledge and skills in a variety of career and workplace situations, working individually or as members of a team
• assess the reasonableness of calculations and problem-solving strategies.

Students will:

estimate, measure and compare using whole numbers, decimals, fractions and metric (SI) and Imperial units of measure to solve everyday problems.

Students will:

• 1. select and use appropriate metric (SI) and Imperial measuring devices and units to take measurements in home and work-related contexts, including:
• length
• mass (weight)
• volume (capacity)

Connections | Problem Solving | Reasoning | Technology

• 2. measure within acceptable degrees of accuracy

Connections | Reasoning

• 3. compare, convert and apply metric (SI) and Imperial units of measure, as appropriate in everyday contexts

Connections | Reasoning | Technology

• 4. solve problems involving perimeter, area, mass (weight) and volume (capacity)

Connections | Problem Solving | Reasoning | Technology

• 5. use conversion charts, calculators and/or other tools to compare and convert common metric (SI) and Imperial units of measure, as required in everyday contexts

Connections | Problem Solving | Reasoning | Technology

• 6. estimate the measurements of angles in a diagram and in various environments

Estimation and Mental Mathematics

• 7. measure and draw angles using a straight edge, protractor and other technology

Connections | Reasoning

• 8. estimate, measure and calculate the area of a circle

Estimation and Mental Mathematics | Problem Solving

• 9. calculate the unknown when given the circumference, diameter and/or radii of a circle to solve everyday problems

Problem Solving | Technology

• 10. estimate and calculate the area of a circle to solve problems in everyday contexts

Estimation and Mental Mathematics | Problem Solving

• 11. estimate and apply a variety of arithmetic operations, using hours and minutes, in everyday applications

Connections | Estimation and Mental Mathematics | Problem Solving | Technology

• 12. estimate and measure temperature and calculate changes in temperature

Estimation and Mental Mathematics | Problem Solving

Students will:

• create, examine and manipulate 3-D objects and 2-D shapes using transformations and technology, and other tools as appropriate, to better understand shapes and objects at home, in the workplace and in the community
• communicate mathematically and investigate the application of shape and space in a variety of career and workplace situations, working individually or as members of a team.

Students will:

use visualization and symmetry to:

• extend their awareness of objects and shapes
• create and examine patterns and designs using congruence, symmetry, translation, rotation and reflection.

Students will:

• 13. measure and classify pairs of angles as either complementary or supplementary

Connections | Estimation and Mental Mathematics | Reasoning

• 14. represent, examine and describe enlargements and reductions

Connections | Reasoning

• 15. interpret scale models and identify the geometric properties associated with figures and shapes used in representations

Connections | Reasoning | Technology

• 16. reproduce drawings or objects to scale, using a variety of strategies; e.g., grid paper, dot paper and/or computer software

Connections | Reasoning | Technology

• 17. draw designs, using ordered pairs, in all four quadrants of a coordinate grid, with translation and reflection images

Problem Solving | Visualization

Students will:

• collect, generate, interpret, examine and maintain data, charts, graphs and other records for personal use at home, in the workplace and in the community, using technology as appropriate
• use probability, chance and predictions when planning and making everyday decisions
• assess the reasonableness of calculators and problem-solving strategies
• communicate mathematically and investigate, collect and examine information in a variety of career and workplace situations, working individually or as members of a team.

Students will:

develop and implement a plan for the collection, display and examination of data and information, using technology and other strategies as required.

Students will:

• 1. predict, interpret, make comparisons and communicate information from graphs, tables, charts and other sources at home and in the workplace

Connections | Reasoning

• 2. recognize the uses of data and data collection and display tools in life- and work-related situations

Connections | Reasoning

• 3. record information and organize files and directories, using computers and/or other tools

Connections | Problem Solving | Reasoning | Technology

• 4. examine a plan for collecting and processing information and modify as appropriate for everyday situations

Connections | Problem Solving | Reasoning

Students will:

• estimate and solve problems using numbers, money, decimals, percents, fractions, ratios and proportion in everyday home, workplace and community contexts, using technology as appropriate
• develop and demonstrate number sense to describe quantities, represent numbers in multiple ways and apply appropriate arithmetic operations
• assess the reasonableness of calculations and problem-solving strategies
• communicate mathematically and investigate the application of number concepts and operations in a variety of career and workplace situations, working individually or as a member of a team.

Students will:

solve everyday home, community and workplace problems by applying arithmetic operations to whole numbers, decimals, common fractions, percents and integers.

Students will:

• 1. use estimation strategies to estimate and apply arithmetic operations to solve everyday problems, using:
• whole numbers
• integers (add/subtract only)
• decimals
• fractions
• mixed numbers
• percents

Connections | Estimation and Mental Mathematics | Problem Solving | Reasoning

• 2. estimate and round numbers and decimals, e.g., money, to the nearest unit, tenth and hundredth to solve problems in everyday contexts

Estimation and Mental Mathematics | Problem Solving | Reasoning

• 3. assess the reasonableness of applied calculations and problem-solving strategies, using a variety of tools and/or strategies; e.g., estimation, charts, graphs, calculators and/or computers

Estimation and Mental Mathematics | Reasoning | Technology | Visualization

• 4. identify and use appropriate tools, e.g., tables, charts, spreadsheets and calculators, to increase accuracy in everyday and/or work-related problem-solving situations

Connections | Problem Solving | Reasoning | Technology

• 5. create, use and modify a spreadsheet template for a variety of everyday contexts, including the determining of interest rates, vehicle payments, investments or budgets

Connections | Problem Solving | Reasoning | Technology

• 6. use a variety of methods and tools to convert fractional percents to decimal forms

Connections | Problem Solving | Reasoning

• 7. express rates and ratios in equivalent forms to solve problems in everyday contexts

Problem Solving | Reasoning | Technology

• 8. estimate unit costs and compare costs of everyday purchases

Connections | Estimation and Mental Mathematics | Problem Solving | Reasoning

Students will:

• recognize that patterns and relationships exist in nature and everyday living
• use patterns and relationships to develop a better understanding of their environments and to solve everyday problems at home, in the workplace and in the community, using technology as appropriate
• assess the reasonableness of calculations and problem-solving strategies
• communicate mathematically and investigate the application of patterns and relationships in a variety of career and workplace situations, working individually or as a member of a team.

Students will:

express and use patterns, variables and expressions, including those used in business and industry, with graphs to solve problems at home, in the community and in the workplace.

Students will:

• 1. use relationships and patterns to summarize, generalize and predict when problem solving and decision making in life- and work-related contexts

Connections | Problem Solving | Reasoning

• 2. generalize patterns arising from everyday problem-solving contexts, using mathematical expressions and equations and/or verifying by substitution

Connections | Problem Solving | Reasoning

Students will:

• represent algebraic expressions in multiple ways to solve problems, using technology as appropriate
• communicate mathematically and investigate the application of variables and equations in a variety of career and workplace situations, working individually or as a member of a team.

Students will:

use variables and equations to express, summarize and apply relationships as problem-solving tools in a restricted range of contexts.

Students will:

• 3. interpret formulas related to practical situations and solve everyday problems using common arithmetic expressions and relationships; e.g., perimeter and area

Connections | Problem Solving | Reasoning | Visualization

Students will:

• estimate and take accurate measurements using everyday metric (SI) and Imperial units of measure
• solve problems using appropriate measuring devices, i.e., metric (SI) and Imperial, strategies and technology in home, workplace and community contexts
• communicate mathematically and investigate the application of measurement knowledge and skills in a variety of career and workplace situations, working individually or as members of a team
• assess the reasonableness of calculations and problem-solving strategies.

Students will:

estimate, measure and compare using whole numbers, decimals, fractions and metric (SI) and Imperial units of measure to solve everyday problems.

Students will:

• 1. use appropriate metric (SI) and Imperial measuring strategies, tools and units to measure:
• length
• volume (capacity)
• mass (weight)
• angles
• time
• temperature
• 2. measure within acceptable degrees of accuracy as required in life- and work-related situations

Connections | Problem Solving | Reasoning | Technology

• 3. calculate elapsed time in everyday contexts

Connections | Reasoning

• 4. use conversion charts, calculators and/or other tools to compare and convert common metric (SI) and Imperial units of measure, as required in everyday contexts

Reasoning | Technology

• 5. investigate the types and uses of measuring tools and units within the community and workplace

Communication | Visualisation

Students will:

• create, examine and manipulate 3-D objects and 2-D shapes using transformations and technology, and other tools as appropriate, to better understand shapes and objects at home, in the workplace and in the community
• communicate mathematically and investigate the application of shape and space in a variety of career and workplace situations, working individually or as members of a team.

Students will:

use visualization and symmetry to:

• extend their awareness of objects and shapes
• create and examine patterns and designs using congruence, symmetry, translation, rotation and reflection.

Students will:

• 6. read and interpret scale drawings and models in workplace and community situations

Communication | Reasoning | Technology

• 7. use scale diagrams, including enlargements and reductions, to solve construction, renovation and other related problems

Connections | Problem Solving | Reasoning | Technology

• 8. give oral and written directions, applying appropriate communication skills

Communication | Reasoning

• 9. read and interpret maps to locate specific sites, determine distances, give directions or use public transportation

Communication | Connections | Reasoning | Visualization

Students will:

• collect, generate, interpret, examine and maintain data, charts, graphs and other records for personal use at home, in the workplace and in the community, using technology as appropriate
• use probability, chance and predictions when planning and making everyday decisions
• assess the reasonableness of calculators and problem-solving strategies
• communicate mathematically and investigate, collect and examine information in a variety of career and workplace situations, working individually or as members of a team.

Students will:

develop and implement a plan for the collection, display and examination of data and information, using technology and other strategies as required.

Students will:

• 1. use information and data from a variety of sources to make comparisons, predictions, inferences, conclusions and/or decisions in everyday situations

Connections | Estimation and Mental Mathematics | Problem Solving | Reasoning

• 2. record and organize information and data as appropriate in life- and work-related situations

Connections | Reasoning

• 3. use probability and statistics to predict upcoming events and to make decisions in everyday life

Connections | Estimation and Mental Mathematics | Reasoning