ICT: math, sr high

Alberta Learning ICT outcomes: Senior high mathematics

The following occur across senior high mathematics:

P1 (4.1) - Continue to demonstrate the learner outcomes achieved in prior grade and course subjects.

F1 (4.1) — Assess the strengths and weaknesses of computer simulations in relation to real-world problems.
F1 (4.2) — Solve mathematical and scientific problems by selecting appropriate technology to perform calculations and experiments.
F1 (4.3) — Apply terminology appropriate to technology in all forms of communication.
F1 (4.4) — Demonstrate an understanding of the general concepts of computer programming and the algorithms that enable technological devices to perform operations and solve problems.

F2 (4.1) — Use technology outside formal classroom settings.
F2 (4.2) — Analyze how technological innovations and creativity affect the economy.
F2 (4.3) — Demonstrate an understanding of new and emerging communication systems.
F2 (4.4) — Evaluate possible potential for emerging technologies.
F2 (4.5) — Demonstrate conservation measures when using technology.
F2 (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.
F2 (4.6) — Use current, reliable information sources from around the world.
F2 (4.7) — Analyze and assess the impact of technology on the global community.

F3 (4.1) — Demonstrate an understanding of how changes in technology can benefit or harm society.
F3 (4.2) — Record relevant data for acknowledging sources of information, and cite sources correctly.
F3 (4.3) — Respect ownership and integrity of information.

F4 (4.1) — Discriminate between style and content in a presentation.
F4 (4.2) — Evaluate the influence and results of digital manipulation on our perceptions.
F4 (4.3) — Identify and analyze a variety of factors that affect the authenticity of information derived from mass media and electronic communication.

F5 (4.1) — Assess new physical environments with respect to ergonomics.
F5 (4.2) — Identify safety regulations specific to the technology being used.

F6 (4.1) — Continue to demonstrate the outcomes addressed within the previous divisions. Students interested in pursuing advanced study in such areas as electronics, programming, computer-aided design and drafting (CADD), robotics and other industrial applications of technology will find opportunities in Career and Technology Studies (CTS) courses.

a. The teacher knows how to facilitate the communication of ideas and information using computer software writing and graphics tools such that:

Possible Student Activities	Correlation to the Curriculum in Mathematics (Division 4 Outcomes)	Correlation to the Information and Communication Technology Program of Studies for Division 4
Students maintain a journal of mathematical concepts, terms and personal reflections about mathematics.	- Demonstrate and explain the meaning of fractions, concretely, pictorially and symbolically (SO, M 14). - Demonstrate and explain the meaning of ratio concretely, pictorially and symbolically (SO, M 14). - Illustrate and explain the order of operations, using paper and pencil or a calculator (SO, M 14). - Explain and illustrate the structure and the interrelationship of the sets of numbers within the real number system (GO, AM 10, PM 10). - Explain and apply the exponent laws for powers of numbers and for variables with rational exponents (SO, PM 10). - Explain and apply connecting words, such as "and", "or" and "not", to solve problems (SO, PM 20). - Explain the relationship between the laws of logarithms and the laws of exponents (SO, PM 30).	C1 (4.2) - Select information from appropriate sources, including primary and secondary sources. C7 (4.1) - Use appropriate strategies to locate information to meet personal needs. P4 (4.1) - Integrate a variety of visual and audio and information into a document to create a message targeted for a specific audience. P4 (4.2) - Apply principles of graphic design to enhance meaning and audience appeal. P4 (4.3) - Use integrated software effectively and efficiently to reproduce work that incorporates data, graphics and text. P6 (4.1) - Select and use the appropriate technologies to communicate effectively with a targeted audience. C1 (4.4) - Communicate in a persuasive and engaging manner, through appropriate forms, such as speeches, letters, reports and multimedia presentations, applying information technologies for content, audience and purpose that extend and communicate understanding of complex issues. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students produce documents that incorporate a combination of written explanations, tables, graphs, diagrams or mathematical expressions in order to communicate mathematical understanding.	- Demonstrate and explain the meaning of fractions, concretely, pictorially and symbolically (SO, M 14). - Demonstrate and explain the meaning of ratio concretely, pictorially and symbolically (SO, M 14). - Illustrate and explain the order of operations, using paper and pencil or a calculator (SO, M 14). - Use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are related recursively (not calculated and calculated from previous data) (SO, AM 10, PM 10). - Explain and illustrate the structure and the interrelationship of the sets of numbers within the real number system (GO, AM 10, PM 10). Describe a function in terms of: ordered pairs a rule, in word or equation form a graph (SO, AM 10, PM 10). - Explain and apply the exponent laws for powers of numbers and for variables with rational exponents (SO, PM 10). - Plot and describe data of exponential form, using appropriate scales (SO, AM 20, PM 20). - Describe, graph and analyze polynomial and rational functions, using technology (SO, PM 20). - Describe periodic events, including sinusoidal curves, using correct terminology (SO, AM 30). - Describe the three primary trigonometric functions as circular functions with reference to the unit circle and an angle in standard position (SO, PM 30). - Explain the relationship between the laws of logarithms and the laws of exponents (SO, PM 30). - Fit mathematical models to situations described by data sets (SO, M 31).	C7 (4.2) - Analyze and synthesize information to determine patterns among ideas. P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. P3 (4.3) - Apply general principles of graphic layout and design to a document in process. P4 (4.1) - Integrate a variety of visual and audio and information into a document to create a message targeted for a specific audience. P4 (4.2) - Apply principles of graphic design to enhance meaning and audience appeal. P4 (4.3) - Use integrated software effectively and efficiently to reproduce work that incorporates data, graphics and text. P6 (4.1) - Select and use the appropriate technologies to communicate effectively with a targeted audience. C1 (4.2) - Select information from appropriate sources, including primary and secondary sources. C1 (4.4) - Communicate in a persuasive and engaging manner, through appropriate forms, such as speeches, letters, reports and multimedia presentations, applying information technologies for content, audience and purpose that extend and communicate understanding of complex issues. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process.

b. The teacher knows how to enhance communication and research skills using the Internet such that:

Possible Student Activities

Correlation to the Curriculum in Mathematics (Division 4 Outcomes)

Correlation to the Information and Communication Technology Program of Studies for Division 4

Students access current and realistic data for use in classroom activities.

- Develop and implement a plan for the collection, display and analysis of data using technology, as required (SO, M 14).

- Display data by hand or by computer in a variety of ways, including circle graphs (SO, M 14).

- Design different ways of presenting data and analyzing results, by focusing on the truthful display of data and the clarity of presentation (SO, M 24).

- Design different ways of presenting data and analyzing results, by focusing on the truthful display of data and the clarity of presentation (SO, AM 20).

From cyclic data produce a periodic graph (SO, AM 30).

- Estimate, read and record temperature to the nearest degree Fahrenheit or degree Celsius (SO, M 14).

- Plot and describe data of exponential form, using appropriate scales (SO, M 24).

- Draw and validate inferences, including interpolations and extrapolations, from graphical and tabular data (SO, M 24).

- Implement and analyze sampling procedures, and draw appropriate inferences from the data collected. (GO, AM 10, PM 10).

- Plot and describe data of exponential form, using appropriate scales (SO, AM 20, PM 20).

- Find the population standard deviation of a data set or a probability distribution, using technology (SO, AM 30, PM 30).

C6 (4.1) - Investigate and solve problems of prediction, calculation and inference.

C6 (4.2) - Investigate and solve problems of organization and manipulation of information.

P3 (4.2) - Support communication with appropriate images, sounds and music.

P3 (4.3) - Apply general principles of graphic layout and design to a document in process.

C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities.

C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process.

C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.

Students participate in collaborative on-line problem solving activities.

- Communicate a set of instructions used to solve an arithmetic problem (SO, AM 10, PM 10).

- Describe and apply arithmetic operations on tables to solve problems, using technology as required (SO, AM 10, PM 10).

- Apply the principles of mathematical reasoning to solve problems and to justify solutions. (SO, PM 20).

- Use the connections between a given problem and either a simpler or equivalent problem, or a previously solved problem, to solve the given problem (GO, M 31).

C1 (4.4) - Communicate in a persuasive and engaging manner, through appropriate forms, such as speeches, letters, reports and multimedia presentations, applying information technologies for content, audience and purpose that extend and communicate understanding of complex issues.

C5 (4.2) - Participate in a variety of electronic group formats.

P3 (4.2) - Support communication with appropriate images, sounds and music.

P3 (4.3) - Apply general principles of graphic layout and design to a document in process.

P4 (4.1) - Integrate a variety of visual and audio and information into a document to create a message targeted for a specific audience.

P4 (4.2) - Apply principles of graphic design to enhance meaning and audience appeal.

P4 (4.3) - Use integrated software effectively and efficiently to reproduce work that incorporates data, graphics and text.

P5 (4.1) - Create multiple-link documents appropriate to the content of a particular topic.

P5 (4.2) - Post multi-link pages on the World Wide Web or on a local or wide area network.

C2 (4.1) - Consult a wide variety of sources that reflect varied viewpoints on particular topics.

C2 (4.2) - Evaluate the validity of gathered viewpoints against other sources.

C5 (4.1) - Use telecommunications to pose critical questions to experts.

C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem.

C7 (4.1) - Use appropriate strategies to locate information to meet personal needs.

C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.

c. The teacher knows how to collect, process, organize, and report data using spreadsheet and database programs such that:

Possible Student Activities	Correlation to the Curriculum in Mathematics (Division 4 Outcomes)	Correlation to the Information and Communication Technology Program of Studies for Division 4
Students explore data and the interrelationships in tables that are related both recursively and non-recursively, and they create and modify the data in such tables to solve problems.	- Describe and apply arithmetic operations on tables to solve problems, using technology as required (GO, M 24, AM 10, PM 10). - Solve problems involving combinations of tables, using: addition or subtraction within tables multiplication of a table by a real number spreadsheet templates (SO, M 24, AM 10, PM 10). - Solve budget problems, using graphs and tables to communicate solutions (SO, M 24, AM 20, PM 20). - Analyze the numerical data in a table for trends, patterns and interrelationships (GO, AM 10, PM 10). - Use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are not related recursively (not calculated and calculated from previous data) (GO, AM 10, PM 10). - Create and modify tables from both recursive and nonrecursive situations (GO, AM 10, PM 10).	C6 (4.2) - Investigate and solve problems of organization and manipulation of information. P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students plot linear and non-linear data, using appropriate scales.	- Plot linear and nonlinear data, using appropriate scales (SO, AM 10, PM 10). - Represent data, using linear function models. (GO, AM 10, PM 10). - Use direct variation and arithmetic sequences as applications of linear functions (SO, AM 10, PM 10). - Graph linear inequalities, in two variables (SO, AM 20, PM 20). - Solve systems of linear equations, in two variables: algebraically (elimination and substitution) graphically (SO, AM 20, PM 20). - Solve, graphically, systems of linear inequalities, in two variables, using technology (SO, AM 20). - Design and solve linear and nonlinear systems, in two variables, to model problem situations (SO, AM 20). - Solve systems of linear equations, in two and three variables: algebraically with technology (SO, PM 20).	P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students determine the equation of a line of best fit and correlation coefficients for scatter plots.	- Apply line-fitting and correlation techniques to analyze experimental results (GO, AM 10). - Determine the equation of a line of best fit, using: estimate of slope and one point median—median method least squares method with technology (SO, AM 10). - Use technological devices to determine the correlation coefficient r (SO, AM 10). - Interpret the correlation coefficient r and its limitations for varying problem situations, using relevant scatterplots (SO, AM 10).	P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students collect, display and perform a statistical analysis of data to make predictions about a population.	- Collect, display and analyze data to make predictions about a population (GO, M 14, AM 10, PM 10). - Choose, justify and apply sampling techniques that will result in an appropriate, unbiased sample from a given population (SO, AM 10, PM 10). - Defend or oppose inferences and generalizations about populations, based on data from samples (SO, AM 10, PM 10). - Find the population standard deviation of a data set or a probability distribution, using technology (SO, AM 30, PM 30).	P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C1 (4.2) - Select information from appropriate sources, including primary and secondary sources. C1 (4.4) - Communicate in a persuasive and engaging manner, through appropriate forms, such as speeches, letters, reports and multimedia presentations, applying information technologies for content, audience and purpose that extend and communicate understanding of complex issues. C3 (3.1) - Evaluate the authority, reliability and validity of electronic accessed information. C3 (3.2) — Demonstrate discriminatory selection of electronically accessed information that is relevant to a particular topic. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.1) - Use appropriate strategies to locate information to meet personal needs. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students explore patterns and trends by automating and graphically displaying results of a series of repetitive calculations.	- Graph relations, analyze the result and draw a conclusion from a pattern (SO, M 14). - Analyze the numerical data in a table for trends, patterns and interrelationships (SO, AM 10, PM 10). - Generate and analyze number patterns (GO, AM 10). - Generate number patterns exhibiting arithmetic growth (SO, PM 10). - Generate and analyze exponential patterns (GO, PM 30). - Use patterns, variables and expressions, together with their graphs, to solve problems (GO, M 14).	P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem.
Students solve and communicate solutions to problems related to budgets, finance, investments, borrowing etc. by constructing appropriate spreadsheet models and performing appropriate operations.	- Solve consumer problems, using arithmetic operations (GO, M 24, AM 10, PM 10). - Solve consumer problems, such as: wages earned in various situations property taxation exchange rates unit prices personal income tax calculation (SO, M 24, AM 20, PM 20). - Reconcile financial statements, such as: cheque books and electronic bank transactions with bank statements credit card statements with payment receipts (SO, M 24, AM 20, PM 20). - Solve budget problems, using graphs and tables to communicate solutions (SO, M 24, AM 20, PM 20). - Solve investment and credit problems involving simple and compound interest (SO, M 24, AM 20, PM 20). - Analyze car, property or house insurance needs and premiums, using such concepts as loss, compulsory coverage, optional coverage, deductible and claims record (SO, M 24). - Use spreadsheet(s) to analyze an investment or life insurance portfolio, applying such concepts as capital gains, interest rate, inflation rate, risk, total rate of return and after-tax rate of return (SO, AM 30). - Use spreadsheet(s) to analyze an investment or life insurance portfolio, applying such concepts as capital gains, interest rate, inflation rate, risk, total rate of return and after-tax rate of return (SO, AM 30). - Describe and apply arithmetic operations on tables to solve problems, using technology as required (GO, M 24, AM 10, PM 10). - Solve problems involving combinations of tables, using: addition or subtraction within tables multiplication of a table by a real number spreadsheet templates (SO, M 24, AM 10, PM 10). - Modify an existing spreadsheet to make and justify financial decisions (GO, M 24). - Modify a spreadsheet template to allow users to input their own variables (SO, M 24). - Use spreadsheet software applications to analyze leasing or buying a decreasing asset (vehicle, computer) under different sets of circumstances (SO, M 24). - Create and modify tables from both recursive and nonrecursive situations (SO, AM 10, PM 10). - Use and modify a spreadsheet template to model recursive situations (SO, AM 10, PM 10). - Design an object, shape, layout or process within a specified budget (SO, AM 20).	C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C1 (4.1) - Plan and perform complex searches, using more than one electronic sources. C1 (4.2) - Select information from appropriate sources, including primary and secondary sources. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.1) - Use appropriate strategies to locate information to meet personal needs. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students explore and extend number patterns exhibiting arithmetic and geometric growth patterns.	- Generate number patterns exhibiting arithmetic growth (SO, PM 10). - Generate number patterns exhibiting geometric growth (SO, PM 10). - Graph relations, analyze the result and draw a conclusion from a pattern (SO, M 14). - Generate and analyze number patterns (GO, AM 10). - Generate and analyze exponential patterns (GO, PM 30). - Derive and apply expressions to represent general terms and sums for geometric growth and to solve problems (SO, PM 30). - Connect geometric sequences to exponential functions over the natural numbers (SO, PM 30). - Estimate values of expressions for infinite geometric processes (SO, PM 30). - Calculate the sum of an infinite convergent geometric series (SO, M 31).	P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students solve optimization problems using linear programming techniques or built in "solver" functions.	- Use linear programming to solve optimization problems (GO, AM 20). - Apply linear programming to find optimal solutions to decision-making problems (SO, AM 20).	P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students perform matrix calculations.	- Describe and apply operations on matrices to solve problems, using technology as required (GO, AM 30). - Show an understanding of matrices and perform the operations of addition, scalar multiplication and matrix multiplication (SO, AM 30). - Solve problems, using the operations of addition, subtraction, scalar multiplication and matrix multiplication on matrices (SO, AM 30). - Use matrices and matrix operations to model and to solve consumer, network and schedule problems (SO, AM 30).	P2 (4.1) - Manipulate and present data through the selection of appropriate tools, such as scientific instrumentation, calculators, databases and/or spreadsheets. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.

d. The teacher knows how to develop mathematical concepts and facilitate the use of mathematical processes using specialized software such that:

Possible Student Activities	Correlation to the Curriculum in Mathematics (Division 4 Outcomes)	Correlation to the Information and Communication Technology Program of Studies for Division 4
Students use mathematical engines such as MathView, Maple, Mathematica, or Derive to explore and create accurate documentation of mathematical concepts.	- Applicable across the curricula.	C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students use 3-D modeling or CAD programs to assist in visualization and to aid in problem solving related to shape and space.	- Draw the plan and elevations of a 3-D object from sketches and models (SO, M 14). - Enlarge or reduce a dimensioned object, according to a specified scale (SO, M 24). - Determine the relationships among linear scale factors, areas, the surface areas and the volumes of similar figures and objects (SO, AM 10, PM 10).	C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students design web pages, VRML objects, applets and other Internet products to convey information or to allow others to explore and solve problems online.	- Describe and apply arithmetic operations on tables to solve problems, using technology as required (GO, M 24, SO AM 10, PM 10). - Communicate a set of instructions used to solve an arithmetic problem (SO, AM 10, PM 10). - Create and analyze design problems and architectural patterns, using the properties of scaling, proportion and networks (GO, M 14). - Apply the principles of mathematical reasoning to solve problems and to justify solutions. (SO, PM 20).	P5 (4.1) - Create multiple-link documents appropriate to the content of a particular topic. P5 (4.2) - Post multi-link pages on the World Wide Web or on a local or wide area network. P6 (4.1) - Select and use the appropriate technologies to communicate effectively with a targeted audience. C1 (4.2) - Select information from appropriate sources, including primary and secondary sources. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process.

e. The teacher knows how to explore geometric and general mathematical concepts using dynamic geometry software or graphics programs such that:

Possible Student Activities	Correlation to the Curriculum in Mathematics (Division 4 Outcomes)	Correlation to the Information and Communication Technology Program of Studies for Division 4
Students explore concepts in trigonometry and construct models to aid in solving various problems.	- Represent and analyze trigonometric functions, using technology as appropriate (GO, PM 30). - Use trigonometric functions to model and solve problems (SO, PM 30). - Construct mathematical models for situations in a broad range of contexts, using algebraic and trigonometric functions of a single real variable (SO, M 31). - Use vector diagrams and trigonometry to analyze and solve practical problems in 3-D and 2-D (SO, AM 30). - Solve first and second degree trigonometric equations over a domain of length np: algebraically graphically (SO, PM 30). - Verify trigonometric identities: numerically for any particular case algebraically for general cases graphically (SO, PM 30). - Draw (using technology), sketch and analyze the graphs of sine, cosine and tangent functions, for: amplitude, if defined period domain and range asymptotes, if any behaviour under transformations (SO, PM 30).	C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students explore coordinate geometry problems involving lines and line segments.	- Solve coordinate geometry problems involving lines and line segments (GO, AM 10, PM 10). - Solve coordinate geometry problems involving lines and line segments, and justify the solutions. (SO, PM 20). - Solve problems involving distances between points in the coordinate plane (SO, AM 10, PM 10). - Solve problems involving midpoints of line segments (SO, AM 10, PM 10). - Solve problems involving rise, run and slope of line segments (SO, AM 10, PM 10). - Solve problems involving rise, run and slope of line segments (SO, AM 10, PM 10). - Determine the equation of a line, given information that uniquely determines the line (SO, AM 10, PM 10). - Solve problems using slopes of: parallel lines perpendicular lines (SO, AM 10, PM 10). - Solve problems involving distances between points and lines (SO, PM 20). - Verify and prove assertions in plane geometry, using coordinate geometry (SO, PM 20).	C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students explore geometric properties of circles and polygons and solve related problems.	- Use technology and measurement to confirm and apply the following properties to particular cases: the perpendicular from the centre of a circle to a chord bisects the chord the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc the inscribed angles subtended by the same arc are congruent the angle inscribed in a semicircle is a right angle the opposite angles of a cyclic quadrilateral are supplementary a tangent to a circle is perpendicular to the radius at the point of tangency the tangent segments to a circle, from any external point, are congruent the angle between a tangent and a chord is equal to the inscribed angle on the opposite side of the chord the sum of the interior angles of an n-sided polygon is (2n — 4) right angles (SO, AM 20, PM 20). - Solve problems involving the properties of circles and their connections with angles and time zones (GO, M 14). - Measure the diameters, radii and circumferences of circles, and establish the relationships among them (SO, M 14). - Solve problems involving the radii, diameters and circumferences of circles (SO, M 14). - Develop, verify and use rules or expressions for determining the areas and perimeters of polygons (SO, M 14). - Develop and apply the geometric properties of circles and polygons to solve problems (GO, M 24). - Use properties of circles and polygons to solve design and layout problems (SO, M 24). - Develop and apply the geometric properties of circles and polygons to solve problems (GO, AM 20, PM 30). - Develop and apply the geometric properties of circles and polygons to solve problems (GO, AM 20, PM 20). - Use properties of circles and polygons to solve design and layout problems (GO, AM 20). - Solve problems, using a variety of circle properties, and justify the solution strategy used (SO, PM 30). - Describe the three primary trigonometric functions as circular functions with reference to the unit circle and an angle in standard position (SO, PM 30). - Solve problems involving polygons and vectors, including both 3-D and 2-D applications (SO, PM 30).	C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students construct a fractal pattern by repeatedly applying a procedure to a geometric figure.	- Generate and analyze cyclic, recursive and fractal patterns (GO, AM 30). - Construct a fractal pattern by repeatedly applying a procedure to a geometric figure (SO, AM 20). - Use the concept of self-similarity to compare and/or predict the perimeters, areas and volumes of fractal patterns (SO, AM 20).	C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem.
Students explore concepts related to 2D vectors and solve problems related to 2D vectors.	- Use vector diagrams and trigonometry to analyze and solve practical problems in 3-D and 2-D (SO, AM 30). - Solve problems involving polygons and vectors, including both 3-D and 2-D applications (GO, AM 30). - Use and give 3-D and 2-D examples of vector terminology and notation, including: vector (direction, magnitude) scalar unit vector collinear vectors opposite vectors parallel vectors resultant vectors (SO, AM 30). - Assign meaning to the multiplication of a vector by a scalar (SO, AM 30).	C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.

f. The teacher knows how to explore concepts related to the graphing of mathematical functions and relations and the graphical solution of equations using graphing programs such that:

Possible Student Activities	Correlation to the Curriculum in Mathematics (Division 4 Outcomes)	Correlation to the Information and Communication Technology Program of Studies for Division 4
Students use a graphing tool to draw the graph of a function from its equation.	- Represent and analyze quadratic, polynomial and rational functions, using technology as appropriate. (SO, AM 20, PM 20, PM 30). - Draw (using technology), sketch and analyze the graphs of sine, cosine and tangent functions, for: amplitude, if defined period domain and range asymptotes, if any behaviour under transformations (SO, PM 30). - Draw (using technology) and analyze the graphs of secant, cosecant and cotangent functions, for: period domain and range asymptotes behaviour under transformations (SO, PM 30). - Use a graphing tool to draw the graph of a function from its equation (SO, AM 10, PM 10). - Plot linear and nonlinear data, using appropriate scales (SO, AM 10, PM 10). - Describe a function in terms of: ordered pairs a rule, in word or equation form a graph (SO, AM 10, PM 10). - Solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function, using: factoring the quadratic formula graphing (SO, PM 20). - Determine the character of the real and non-real roots of a quadratic equation, using: the discriminant in the quadratic formula graphing (SO, PM 20). - Describe, graph and analyze polynomial and rational functions, using technology (SO, PM 20 PM 30). - Model, graph and apply exponential functions to solve problems (SO, PM 30). - Graph and analyze logarithmic functions with and without technology (SO, PM 30). - Perform, analyze and create transformations of functions and relations that are described by equations or graphs (SO, PM 30). - Draw the graphs of functions by applying transformations to the graphs of known functions (SO, M 31).	C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students determine the domain and range of a relation from its graph.	- Determine the domain and range of a relation from its graph (SO, AM 10, PM 10). - Determine the following characteristics of the graph of a linear function, given its equation: intercepts slope domain range (SO AM 10, PM 10). - Determine the following characteristics of the graph of a quadratic function: vertex domain and range axis of symmetry intercepts (SO, AM 20, PM 20). - Graph and analyze logarithmic functions with and without technology (SO, PM 30). - Draw (using technology) and analyze the graphs of secant, cosecant and cotangent functions, for: period domain and range asymptotes behaviour under transformations (SO, PM 30). - Determine vertical, horizontal and oblique asymptotes, and domains and ranges of a function (SO, M 31).	C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students graph linear inequalities and systems of linear inequalities in two variables.	- Graph linear inequalities, in two variables (SO, AM 20, PM 20). - Solve, graphically, systems of linear inequalities, in two variables, using technology (SO, PM 20). - Represent and analyze situations that involve expressions, equations and inequalities (GO, AM 20, PM 20).	C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students solve non-linear equations using a graphing tool and solve systems of linear and non-linear equations in two variables graphically.	- Solve nonlinear equations, using a graphing tool (SO AM 20, PM 20). - Solve nonlinear equations: by factoring graphically (SO, PM 20). - Determine the solution to a system of nonlinear equations, using technology as appropriate (SO, PM 20).	C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.
Students explore a variety of quadratic, exponential, trigonometric, logarithmic, polynomial, and other functions and relations and their transformations.	- Represent and analyze quadratic, polynomial and rational functions, using technology as appropriate. (SO, AM 20, PM 20, PM 30). - Represent and analyze trigonometric functions, using technology as appropriate (SO, PM 30). - Draw the graphs of functions by applying transformations to the graphs of known functions (SO, M 31). - Model real-world situations, using quadratic functions (SO, PM 20). - Solve quadratic equations, and relate the solutions to the zeros of a corresponding quadratic function, using: factoring the quadratic formula graphing (SO, PM 20). - Determine the character of the real and non-real roots of a quadratic equation, using: the discriminant in the quadratic formula graphing (SO, PM 20). - Describe, graph and analyze polynomial and rational functions, using technology (SO, PM 20, PM 30). - Model, graph and apply exponential functions to solve problems (SO, PM 30). - Graph and analyze logarithmic functions with and without technology (SO, PM 30). - Draw (using technology), sketch and analyze the graphs of sine, cosine and tangent functions, for: amplitude, if defined period domain and range asymptotes, if any behaviour under transformations (SO, PM 30). - Draw (using technology) and analyze the graphs of secant, cosecant and cotangent functions, for: period domain and range asymptotes behaviour under transformations (SO, PM 30). - Sketch continuous and discontinuous functions, using limits, intercepts and symmetry (SO, M 31).	C6 (4.3) - Manipulate data by using charting and graphing technologies in order to test inferences and probabilities. C6 (4.4) - Generate new understandings of problematic situations by using some form of technology to facilitate the process. C6 (4.1) - Investigate and solve problems of prediction, calculation and inference. C6 (4.2) - Investigate and solve problems of organization and manipulation of information. C6 (4.5) - Evaluate the appropriateness of the technology used to investigate or solve a problem. C7 (4.2) - Analyze and synthesize information to determine patterns among ideas.