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Click on any standard to search for aligned resources. This data may be subject to copyright. You may download a CSV of the Ontario Curriculum if your intention constitutes fair use.

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Solving Exponential Equations: By the end of this course, students will:

Determine, through investigation (e.g., by expanding terms and patterning), the exponent laws for multiplying and dividing algebraic expressions involving exponents [e.g., (x^3)(x^2), x^3 / x^5] and the exponent law for simplifying algebraic expressions involving a power of a power [e.g. (x^6 y^2)^2]

Simplify algebraic expressions containing integer exponents using the laws of exponents

Determine, through investigation using a variety of tools (e.g., calculator, paper and pencil, graphing technology) and strategies (e.g., patterning; finding values from a graph; interpreting the exponent laws), the value of a power with a rational exponent (i.e., x^(m/n) , where x is greater than 0 and m and n are integers)

Evaluate, with or without technology, numerical expressions involving rational exponents and rational bases [e.g., 2^-3 , (-6)^3 , 4^1/2 , 1.01^120]

Solve simple exponential equations numerically and graphically, with technology (e.g., use systematic trial with a scientific calculator to determine the solution to the equation 1.05^x = 1.276), and recognize that the solutions may not be exact

Solve problems involving exponential equations arising from real-world applications by using a graph or table of values generated with technology from a given equation [e.g., h = 2(0.6)^n , where h represents the height of a bouncing ball and n represents the number of bounces]

Solve exponential equations in one variable by determining a common base (e.g., 2^x = 32, 4^5x =2^2(x+11) , 3^(5x+8) = 27^x)

Modelling Graphically: By the end of this course, students will:

Interpret graphs to describe a relationship (e.g., distance travelled depends on driving time, pollution increases with traffic volume, maximum profit occurs at a certain sales volume), using language and units appropriate to the context

Recognize that graphs and tables of values communicate information about rate of change, and use a given graph or table of values for a relation to identify the units used to measure rate of change (e.g., for a distance-time graph, the units of rate of change are kilometres per hour; for a table showing earnings over time, the units of rate of change are dollars per hour)

Identify when the rate of change is zero, constant, or changing, given a table of values or a graph of a relation, and compare two graphs by describing rate of change (e.g., compare distance-time graphs for a car that is moving at constant speed and a car that is accelerating)

Recognize that a linear model corresponds to a constant increase or decrease over equal intervals and that an exponential model corresponds to a constant percentage increase or decrease over equal intervals, select a model (i.e., linear, quadratic, exponential) to represent the relationship between numerical data graphically and algebraically, using a variety of tools (e.g., graphing technology) and strategies (e.g., finite differences, regression), and solve related problems

Modelling Algebraically: By the end of this course, students will:

Solve equations of the form x^n = a using rational exponents (e.g., solve x^3 = 7 by raising both sides to the exponent 1/3)

Determine the value of a variable of degree no higher than three, using a formula drawn from an application, by first substituting known values and then solving for the variable, and by first isolating the variable and then substituting known values

Make connections between formulas and linear, quadratic, and exponential functions [e.g., recognize that the compound interest formula, A = P(1 + i)^n , is an example of an exponential function A(n) when P and i are constant, and of a linear function A(P) when i and n are constant], using a variety of tools and strategies (e.g., comparing the graphs generated with technology when different variables in a formula are set as constants)

Solve multi-step problems requiring formulas arising from real-world applications (e.g., determining the cost of two coats of paint for a large cylindrical tank)

Gather, interpret, and describe information about applications of mathematical modeling in occupations, and about college programs that explore these applications

Working With Two-Variable Data: By the end of this course, students will:

Distinguish situations requiring one-variable and two-variable data analysis, describe the associated numerical summaries (e.g., tally charts, summary tables) and graphical summaries (e.g., bar graphs, scatter plots), and recognize questions that each type of analysis addresses (e.g., What is the frequency of a particular trait in a population? What is the mathematical relationship between two variables?)

Describe characteristics of an effective survey (e.g., by giving consideration to ethics, privacy, the need for honest responses, and possible sources of bias, including cultural bias), and design questionnaires (e.g., for determining if there is a relationship between age and hours per week of Internet use, between marks and hours of study, or between income and years of education) or experiments (e.g., growth of plants under different conditions) for gathering two-variable data

Collect two-variable data from primary sources, through experimentation involving observation or measurement, or from secondary sources (e.g., Internet databases, newspapers, magazines), and organize and store the data using a variety of tools (e.g., spreadsheets, dynamic statistical software)

Create a graphical summary of two-variable data using a scatter plot (e.g., by identifying and justifying the dependent and independent variables; by drawing the line of best fit, when appropriate), with and without technology

Determine an algebraic summary of the relationship between two variables that appear to be linearly related (i.e., the equation of the line of best fit of the scatter plot), using a variety of tools (e.g., graphing calculators, graphing software) and strategies (e.g., using systematic trials to determine the slope and y-intercept of the line of best fit; using the regression capabilities of a graphing calculator), and solve related problems (e.g., use the equation of the line of best fit to interpolate or extrapolate from the given data set)

Describe possible interpretations of the line of best fit of a scatter plot (e.g., the variables are linearly related) and reasons for misinterpretations (e.g., using too small a sample; failing to consider the effect of outliers; interpolating from a weak correlation; extrapolating nonlinearly related data)

Make conclusions from the analysis of two variable data (e.g., by using a correlation to suggest a possible cause-and-effect relationship), and judge the reasonableness of the conclusions (e.g., by assessing the strength of the correlation; by considering if there are enough data)

Applying Data Management: By the end of this course, students will:

Recognize and interpret common statistical terms (e.g., percentile, quartile) and expressions (e.g., accurate 19 times out of 20) used in the media (e.g., television, Internet, radio, newspapers)

Describe examples of indices used by the media (e.g., consumer price index, S&P/TSX composite index, new housing price index) and solve problems by interpreting and using indices (e.g., by using the consumer price index to calculate the annual inflation rate)

Interpret statistics presented in the media (e.g., the UN's finding that 2% of the world's population has more than half the world's wealth, whereas half the world's population has only 1% of the world's wealth), and explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view (e.g., by making a general statement based on a weak correlation or an assumed cause and- effect relationship; by starting the vertical scale on a graph at a value other than zero; by making statements using general population statistics without reference to data specific to minority groups)

Assess the validity of conclusions presented in the media by examining sources of data, including Internet sources (i.e., to determine whether they are authoritative, reliable, unbiased, and current), methods of data collection, and possible sources of bias (e.g., sampling bias, non-response bias, a bias in a survey question), and by questioning the analysis of the data (e.g., whether there is any indication of the sample size in the analysis) and conclusions drawn from the data (e.g., whether any assumptions are made about cause and effect)

Gather, interpret, and describe information about applications of data management in occupations, and about college programs that explore these applications (e.g., selling real estate, bookkeeping, managing a restaurant, financial planning, mortgage brokering), and about college programs that explore these applications

Design, justify, and adjust budgets for individuals and families described in case studies, and describe applications of the mathematics of personal finance.

Solving Problems Involving Measurement and Geometry: By the end of this course, students will:

Perform required conversions between the imperial system and the metric system using a variety of tools (e.g., tables, calculators, online conversion tools), as necessary within applications

Solve problems involving the areas of rectangles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications

Solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite figures, in situations arising from real-world applications

Investigating Optimal Dimensions: By the end of this course, students will:

Recognize, through investigation using a variety of tools (e.g., calculators; dynamic geometry software; manipulatives such as tiles, geoboards, toothpicks) and strategies (e.g., modelling; making a table of values; graphing), and explain the significance of optimal perimeter, area, surface area, and volume in various applications (e.g., the minimum amount of packaging material, the relationship between surface area and heat loss)

Determine, through investigation using a variety of tools (e.g., calculators, dynamic geometry software, manipulatives) and strategies (e.g., modelling; making a table of values; graphing), the optimal dimensions of a two-dimensional shape in metric or imperial units for a given constraint (e.g., the dimensions that give the minimum perimeter for a given area)

Solving Problems Involving Trigonometry: By the end of this course, students will:

Solve problems in two dimensions using metric or imperial measurements, including problems that arise from real-world applications (e.g., surveying, navigation, building construction), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios, and of acute triangles using the sine law and the cosine law

Determine the values of the sine, cosine, and tangent of obtuse angles

Gather, interpret, and describe information about applications of trigonometry in occupations, and about college programs that explore these applications

Working With Two-Variable Data: By the end of this course, students will:

Distinguish situations requiring one-variable and two-variable data analysis, describe the associated numerical summaries (e.g., tally charts, summary tables) and graphical summaries (e.g., bar graphs, scatter plots), and recognize questions that each type of analysis addresses (e.g., What is the frequency of a particular trait in a population? What is the mathematical relationship between two variables?)

Describe characteristics of an effective survey (e.g., by giving consideration to ethics, privacy, the need for honest responses, and possible sources of bias, including cultural bias), and design questionnaires (e.g., for determining if there is a relationship between age and hours per week of Internet use, between marks and hours of study, or between income and years of education) or experiments (e.g., growth of plants under different conditions) for gathering two-variable data

Collect two-variable data from primary sources, through experimentation involving observation or measurement, or from secondary sources (e.g., Internet databases, newspapers, magazines), and organize and store the data using a variety of tools (e.g., spreadsheets, dynamic statistical software)

Create a graphical summary of two-variable data using a scatter plot (e.g., by identifying and justifying the dependent and independent variables; by drawing the line of best fit, when appropriate), with and without technology

Determine an algebraic summary of the relationship between two variables that appear to be linearly related (i.e., the equation of the line of best fit of the scatter plot), using a variety of tools (e.g., graphing calculators, graphing software) and strategies (e.g., using systematic trials to determine the slope and y-intercept of the line of best fit; using the regression capabilities of a graphing calculator), and solve related problems (e.g., use the equation of the line of best fit to interpolate or extrapolate from the given data set)

Describe possible interpretations of the line of best fit of a scatter plot (e.g., the variables are linearly related) and reasons for misinterpretations (e.g., using too small a sample; failing to consider the effect of outliers; interpolating from a weak correlation; extrapolating nonlinearly related data)

Determine whether a linear model (i.e., a line of best fit) is appropriate given a set of two-variable data, by assessing the correlation between the two variables (i.e., by describing the type of correlation as positive, negative, or none; by describing the strength as strong or weak; by examining the context to determine whether a linear relationship is reasonable)

Make conclusions from the analysis of two-variable data (e.g., by using a correlation to suggest a possible cause-and-effect relationship), and judge the reasonableness of the conclusions (e.g., by assessing the strength of the correlation; by considering if there are enough data) explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view (e.g., by making a general statement based on a weak correlation or an assumed cause-and-effect relationship; by starting the vertical scale on a graph at a value other than zero; by making statements using general population statistics without reference to data specific to minority groups)

Applying Data Management: By the end of this course, students will:

Recognize and interpret common statistical terms (e.g., percentile, quartile) and expressions (e.g., accurate 19 times out of 20) used in the media (e.g., television, Internet, radio, newspapers)

Describe examples of indices used by the media (e.g., consumer price index, S&P/TSX composite index, new housing price index) and solve problems by interpreting and using indices (e.g., by using the consumer price index to calculate the annual inflation rate)

Interpret statistics presented in the media(e.g., the UN's finding that 2% of the world's population has more than half the world's wealth, whereas half the world's population has only 1% of the world's wealth), and explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view (e.g., by making a general statement based on a weak correlation or an assumed cause-and-effect relationship; by starting the vertical scale on a graph at a value other than zero; by making statements using general population statistics without reference to data specific to minority groups)

Assess the validity of conclusions presented in the media by examining sources of data, including Internet sources (i.e., to determine whether they are authoritative, reliable, unbiased, and current), methods of data collection, and possible sources of bias (e.g., sampling bias, non-response bias, a bias in a survey question), and by questioning the analysis of the data (e.g., whether there is any indication of the sample size in the analysis) and conclusions drawn from the data (e.g., whether any assumptions are made about cause and effect)

Gather, interpret, and describe information about applications of data management in occupations, and about college programs that explore these applications

Solving Exponential Equations Graphically: By the end of this course, students will:

Solve simple exponential equations numerically and graphically, with technology (e.g., use systematic trial with a scientific calculator to determine the solution to the equation 1.05^x = 1,276), and recognize that the solutions may not be exact

Determine, through investigation using graphing technology, the point of intersection of the graphs of two exponential functions (e.g., y = 4^-x and y = 8^x+3), recognize the x-coordinate of this point to be the solution to the corresponding exponential equation (e.g., 4^-x = 8^x=3), and solve exponential equations graphically (e.g., solve 2^x+2 = 2^x + 12 by using the intersection of the graphs of y = 2^x+2 and y = 2^x + 12)

Pose problems based on real-world applications (e.g., compound interest, population growth) that can be modelled with exponential equations, and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation

Solving Exponential Equations Algebraically: By the end of this course, students will:

Simplify algebraic expressions containing integer and rational exponents using the laws of exponents (e.g., x^3 / x^1/2 , square root of x^6 y^12)

Solve exponential equations in one variable by determining a common base (e.g., 2^x = 32, 4^5x-1 =2^2(x+11) , 3^(5x+8) = 27)

Recognize the logarithm of a number to a given base as the exponent to which the base must be raised to get the number, recognize the operation of finding the logarithm to be the inverse operation (i.e., the undoing or reversing) of exponentiation, and evaluate simple logarithmic expressions

Determine, with technology, the approximate logarithm of a number to any base, including base 10 [e.g., by recognizing that log 10(0.372) can be determined using the LOG key on a calculator; by reasoning that logbase 3 of 29 is between 3 and 4 and using systematic trial to determine that log base 3 of 29 is approximately 3.07]

Make connections between related logarithmic and exponential equations (e.g., log base 5 of 125 = 3 can also be expressed as 5^3 = 125), and solve simple exponential equations by rewriting them in logarithmic form (e.g., solving 3^x = 10 by rewriting the equation as log base 3 of 10 = x)

Pose problems based on real-world applications that can be modelled with given exponential equations, and solve these and other such problems algebraically by rewriting them in logarithmic form

Investigating Graphs of Polynomial Functions: By the end of this course, students will:

Recognize a polynomial expression (i.e., a series of terms where each term is the product of a constant and a power of x with a nonnegative integral exponent, such as x^3 - 5x^2 + 2x - 1); recognize the equation of a polynomial function and give reasons why it is a function, and identify linear and quadratic functions as examples of polynomial functions

Compare, through investigation using graphing technology, the graphical and algebraic representations of polynomial (i.e., linear, quadratic, cubic, quartic) functions (e.g., investigate the effect of the degree of a polynomial function on the shape of its graph and the maximum number of x-intercepts; investigate the effect of varying the sign of the leading coefficient on the end behaviour of the function for very large positive or negative x-values)

Describe key features of the graphs of polynomial functions (e.g., the domain and range, the shape of the graphs, the end behaviour of the functions for very large positive or negative x-values)

Distinguish polynomial functions from sinusoidal and exponential functions [e.g., f(x) = sin x, f(x) = 2^x)], and compare and contrast the graphs of various polynomial functions with the graphs of other types of functions

Substitute into and evaluate polynomial functions expressed in function notation, including functions arising from real-world applications

Pose problems based on real-world applications that can be modelled with polynomial functions, and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation

Recognize, using graphs, the limitations of modelling a real-world relationship using a polynomial function, and identify and explain any restrictions on the domain and range (e.g., restrictions on the height and time for a Relationship between height above the ground and time for a falling object)

Connecting Graphs and Equations of Polynomial Functions: By the end of this course, students will:

Factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies (i.e., common factoring, difference of squares, trinomial factoring)

Make connections, through investigation using graphing technology (e.g., dynamic geometry software), between a polynomial function given in factored form [e.g., f(x) = x(x - 1)(x + 1)] and the x-intercepts of its graph, and sketch the graph of a polynomial function given in factored form using its key features (e.g., by determining intercepts and end behaviour; by locating positive and negative regions using test values between and on either side of the x-intercepts)

Determine, through investigation using technology (e.g., graphing calculator, computer algebra systems), and describe the connection between the real roots of a polynomial equation and the x-intercepts of the graph of the corresponding polynomial function [e.g., the real roots of the equation x^4 - 13x^2 + 36 = 0 are the x-intercepts of the graph of f(x) = x^4- 13x^2 + 36]

Solving Problems Involving Polynomial Equations: By the end of this course, students will:

Solve polynomial equations in one variable, of degree no higher than four (e.g., x^2 - 4x = 0, x^4 - 16 = 0, 3x^2 + 5x + 2 = 0), by selecting and applying strategies (i.e., common factoring; difference of squares; trinomial factoring), and verify solutions using technology (e.g., using computer algebra systems to determine the roots of the equation; using graphing technology to determine the x-intercepts of the corresponding polynomial function)

Solve problems algebraically that involve polynomial functions and equations of degree no higher than four, including those arising from real-world applications

Identify and explain the roles of constants and variables in a given formula (e.g., a constant can refer to a known initial value or a known fixed rate; a variable changes with varying conditions)

Expand and simplify polynomial expressions involving more than one variable [e.g., simplify - 2xy(3x^2 y^3 - 5x^3 y^2)], including expressions arising from real-world applications

Solve equations of the form x^n = a using rational exponents (e.g., solve x^3 = 7 by raising both sides to the exponent 1/3)

Determine the value of a variable of degree no higher than three, using a formula drawn from an application, by first substituting known values and then solving for the variable, and by first isolating the variable and then substituting known values

Make connections between formulas and linear, quadratic, and exponential functions [e.g., recognize that the compound interest formula, A = P(1 + i)^n , is an example of an exponential function A(n) when P and i are constant, and of a linear function A(P) when i and n are constant], using a variety of tools and strategies (e.g., comparing the graphs generated with technology when different variables in a formula are set as constants)

Solve multi-step problems requiring formulas arising from real-world applications (e.g., determining the cost of two coats of paint for a large cylindrical tank)

Gather, interpret, and describe information about applications of mathematical modeling in occupations, and about college programs that explore these applications

Applying Trigonometric Ratios: By the end of this course, students will:

Determine the exact values of the sine, cosine, and tangent of the special angles 0 degrees, 30 degrees, 45 degrees, 60 degrees, 90 degrees, and their multiples

Determine the values of the sine, cosine, and tangent of angles from 0 degrees to 360 degrees, through investigation using a variety of tools (e.g., dynamic geometry software, graphing tools) and strategies (e.g., applying the unit circle; examining angles related to the special angles)

Solve multi-step problems in two and three dimensions, including those that arise from real-world applications (e.g., surveying, navigation), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios

Connecting Graphs and Equations of Sinusoidal Functions: By the end of this course, students will:

Make connections between the sine ratio and the sine function and between the cosine ratio and the cosine function by graphing the relationship between angles from 0 degrees to 360 degrees and the corresponding sine ratios or cosine ratios, with or without technology (e.g., by generating a table of values using a calculator; by unwrapping the unit circle), defining this relationship as the function f(x) = sin x or f(x) = cos x, and explaining why the relationship is a function

Sketch the graphs of f(x) = sin x and f(x) = cos x for angle measures expressed in degrees, and determine and describe their key properties (i.e., cycle, domain, range, intercepts, amplitude, period, maximum and minimum values, increasing/decreasing intervals)

Determine, through investigation using technology, the roles of the parameters d and c in functions of the form y = sin (x - d) + c and y = cos (x - d) + c, and describe these roles in terms of transformations on the graphs off(x) = sin x and f(x) = cos x with angles expressed in degrees (i.e., vertical and horizontal translations)

Determine, through investigation using technology, the roles of the parameters a and k in functions of the form y = a sin kx and y = a cos kx, and describe these roles in terms of transformations on the graphs off(x) = sin x and f(x) = cos x with angles expressed in degrees (i.e., reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes)

Determine the amplitude, period, and phase shift of sinusoidal functions whose equations are given in the form f(x) = a sin (k(x - d)) + c or f(x) = a cos (k(x - d)) + c, and sketch graphs of y = a sin (k(x - d)) + c andy = a cos (k(x - d)) + c by applying transformations to the graphs of f(x) = sin x and f(x) = cos x

Solving Problems Involving Sinusoidal Functions: By the end of this course, students will:

Collect data that can be modelled as a sinusoidal function (e.g., voltage in an AC circuit, pressure in sound waves, the height of a tackon a bicycle wheel that is rotating at a fixed speed), through investigation with and without technology, from primary sources, usinga variety of tools (e.g., concrete materials, measurement tools such as motion sensors), or from secondary sources (e.g., websites such as Statistics Canada, E-STAT), and graph the data

Identify periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena, given various representations (i.e., tables of values, graphs, equations), and explain any restrictions that the context places on the domain and range

Pose problems based on applications involving a sinusoidal function, and solve these and other such problems by using a given graph or a graph generated with technology, in degree mode, from a table of values or from its equation

Modelling With Vectors: By the end of this course, students will:

Recognize a vector as a quantity with both magnitude and direction, and identify, gather, and interpret information about real-world applications of vectors (e.g., displacement; forces involved in structural design; simple animation of computer graphics; velocity determined using GPS)

Represent a vector as a directed line segment, with directions expressed in different ways (e.g., 320 degrees; N 40 degrees W), and recognize vectors with the same magnitude and direction but different positions as equal vectors

Resolve a vector represented as a directed line segment into its vertical and horizontal components

Represent a vector as a directed line segment given its vertical and horizontal components(e.g., the displacement of a ship that travels 3 km east and 4 km north can be represented by the vector with a magnitude of 5 km and a direction of N 36.9 degrees E)

Determine, through investigation using a variety of tools (e.g., graph paper, technology) and strategies (i.e., head-to-tail method; parallelogram method; resolving vectors into their vertical and horizontal components), the sum (i.e., resultant) or difference of two vectors

Solve problems involving two-dimensional shapes and three-dimensional figures and arising from real-world applications;

Gather and interpret information about real world applications of geometric shapes and figures in a variety of contexts in technology related fields (e.g., product design, architecture), and explain these applications (e.g., one reason that sewer covers are round is to prevent them from falling into the sewer during removal and replacement)

Perform required conversions between the imperial system and the metric system using a variety of tools (e.g., tables, calculators, online conversion tools), as necessary within applications

Solve problems involving the areas of rectangles, parallelograms, trapezoids, triangles, and circles, and of related composite shapes, in situations arising from real-world applications

Solve problems involving the volumes and surface areas of spheres, right prisms, and cylinders, and of related composite figures, in situations arising from real-world applications

Determine circle properties and solve related problems, including those arising from real-world applications.

Recognize and describe (i.e., using diagrams and words) arcs, tangents, secants, chords, segments, sectors, central angles, and inscribed angles of circles, and some of their real-world applications (e.g., construction of a medicine wheel)

Determine the length of an arc and the area of a sector or segment of a circle, and solve related problems

Determine, through investigation using a variety of tools (e.g., dynamic geometry software), properties of the circle associated with chords, central angles, inscribed angles, and tangents (e.g., equal chords or equal arcs subtend equal central angles and equal inscribed angles; a radius is perpendicular to a tangent at the point of tangency defined by the radius, and to a chord that the radius bisects)

Solve problems involving properties of circles, including problems arising from real-world applications

Investigating Instantaneous Rate of Change at a Point: By the end of this course, students will:

Describe examples of real-world applications of rates of change, represented in a variety of ways (e.g., in words, numerically, graphically, algebraically)

Recognize, through investigation with or without technology, graphical and numerical examples of limits, and explain the reasoning involved (e.g., the value of a function approaching an asymptote, the value of the ratio of successive terms in the Fibonacci sequence)

Make connections, for a function that is smooth over the interval a less than or equal to x less than or equal to a + h, between the average rate of change of the function over this interval and the value of the expression (f(a+h) - f(a))/h, and between the instantaneous rate of change of the function at x = a and the value of the limit as h approaches 0 of (f(a +h) - f(a))/h

Compare, through investigation, the calculation of instantaneous rates of change at a point (a, f(a)) for polynomial functions [e.g., f(x) = x^2 , f(x) = x^3], with and without simplifying the expression f(a+h) - f(a) before substituting values of h that approach zero [e.g., for f(x) = x at x = 3, by determining f(3+1) - f(3).1 = 7, f(3 +0.1) _ f(3)/0.1 = 6.1, f(3 + 0.01) -f(3)/0.01 = 6.01, and f(3 + 0.001) - f (3)/0.001 = 6.001, and by first simplifying f(3 + h) - f (3)/h as (3 + h)^2 - 3^2 /h = 6 + h and then substituting the same values of h to give the same results]

Investigating the Concept of the Derivative Function: By the end of this course, students will:

Determine numerically and graphically the intervals over which the instantaneous rate of change is positive, negative, or zero for a function that is smooth over these intervals (e.g., by using graphing technology to examine the table of values and the slopes of tangents for a function whose equation is given; by examining a given graph), and describe the behaviour of the instantaneous rate of change at and between local maxima and minima

Generate, through investigation using technology, a table of values showing the instantaneous rate of change of a polynomial function, f(x), for various values of x (e.g., construct a tangent to the function, measure its slope, and create a slider or animation to move the point of tangency), graph the ordered pairs, recognize that the graph represents a function called the derivative, f '(x) or dy/dx, and make connections between the graphs of f(x) and f '(x) or y and dy/dx [e.g., when f(x) is linear, f '(x) is constant; when f(x) is quadratic, f '(x) is linear; when f(x) is cubic, f '(x) is quadratic]

Determine the derivatives of polynomial functions by simplifying the algebraic expression (f(x + h) - f(x))/h and then taking the limit of the simplified expression as h approaches zero [i.e., determining limit as h approaches 0 of (f(x + h) - f(x))/h]

Determine, through investigation using technology, the graph of the derivative f '(x) or dy/dx of a given sinusoidal function [i.e., f(x) = sin x, f(x) = cos x] (e.g., by generating a table of values showing the instantaneous rate of change of the function for various values of x and graphing the ordered pairs; by using dynamic geometry software to verify graphically that when f(x) = sin x, f '(x) = cos x, and when f(x) = cos x, f '(x) = - sin x; by using a motion sensor to compare the displacement and velocity of a pendulum)

Determine, through investigation using technology, the graph of the derivative f '(x) or dy/dx of a given exponential function [i.e., f(x) = a^x (a is greater than 0, a does not equal 1)] [e.g., by generating a table of values showing the instantaneous rate of change of the function for various values of x and graphing the ordered pairs; by using dynamic geometry software to verify that when f(x) = a^x , f '(x) = kf(x)], and make connections between the graphs of f(x) and f '(x) or y and dy/dx [e.g., f(x) and f '(x) are both exponential; the ratio f '(x)/f(x) is constant, or f '' (x) = kf(x); f '(x) is a vertical stretch from the x-axis of f(x)]

Determine, through investigation using technology, the exponential function f(x) = a^x (a > 0, a not equal to 1) for which f '(x) = f(x) (e.g., by using graphing technology to create a slider that varies the value of a in order to determine the exponential function whose graph is the same as the graph of its derivative), identify the number e to be the value of a for which f '(x) = f(x) [i.e., given f(x) = e^x , f '(x) = e^x], and recognize that for the exponential function f(x) = e^x the slope of the tangent at any point on the function is equal to the value of the function at that point

Recognize that the natural logarithmic function f(x) = log base e of x, also written as f(x) = ln x, is the inverse of the exponential function f(x) = e^x , and make connections between f(x) = ln x and f(x) = e^x [e.g., f(x) = ln x reverses what f(x) = e^x does; their graphs are reflections of each other in the line y = x; the composition of the two functions, e^lnx or ln e^x , maps x onto itself, that is, e^lnx = x and ln e^x = x]

Verify, using technology (e.g., calculator, graphing technology), that the derivative of the exponential function f(x) = a^x is f'(x) = a^x ln a for various values of a [e.g., verifying numerically for f(x) = 2^x that f'(x) = 2 ln 2 by using a calculator to show that limit as h approaches 0 of (2^h - 1)/h is ln 2 or by graphing f(x) = 2^x , determining the value of the slope and the value of the function for specific x-values, and comparing the ratio f'' (x) /f(x) with ln 2]

Investigating the Properties of Derivatives: By the end of this course, students will:

Verify the power rule for functions of the form f(x) = x^n , where n is a natural number [e.g., by determining the equations of the derivatives of the functions f(x) = x, f(x) = x^2 , f(x) = x^3 , and f(x) = x^4 algebraically using and graphically using slopes of tangents]

Verify the constant, constant multiple, sum, and difference rules graphically and numerically [e.g., by using the function g(x) = kf(x) and comparing the graphs of g'(x) and kf'(x); by using a table of values to verify that f'(x) + g'(x) = (f + g)'(x), given f(x) = x and g(x) = 3x], and read and interpret proofs involving limit as h approaches 0 of (f(x+h) - f(x))/h of the constant, constant multiple, sum, and difference rules (student reproduction of the development of the general case is not required)

Determine algebraically the derivatives of polynomial functions, and use these derivatives to determine the instantaneous rate of change at a point and to determine point(s) at which a given rate of change occurs

Verify that the power rule applies to functions of the form f(x) = x^n , where n is a rational number [e.g., by comparing values of the slopes of tangents to the function f(x) = x^1/2 with values of the derivative function determined using the power rule], and verify algebraically the chain rule using monomial functions [e.g., by determining the same derivative for f(x) = (5x^3)^1/3 by using the chain rule and by differentiating the simplified form, f(x) = 5^1/3 x] and the product rule using polynomial functions [e.g., by determining the same derivative for f(x) = (3x + 2)(2x^2 - 1) by using the product rule and by differentiating the expanded form f(x) = 6x^3 + 4x^2 - 3x - 2]

Solve problems, using the product and chain rules, involving the derivatives of polynomial functions, sinusoidal functions, exponential functions, rational functions [e.g., by expressing f(x) = x^2 +1/x-1as the product f(x) = (x^2 + 1)(x - 1)^-1], radical functions [e.g., by expressing f(x) = squar root of x + 5 as the power f(x) = (x^2 + 5)^ 1/2], and other simple combinations of functions [e.g., f(x) = x sin x, f(x) = sin x/cosx]

Connecting Graphs and Equations of Functions and Their Derivatives: By the end of this course, students will:

Sketch the graph of a derivative function, given the graph of a function that is continuous over an interval, and recognize points of inflection of the given function (i.e., points at which the concavity changes)

Recognize the second derivative as the rate of change of the rate of change (i.e., the rate of change of the slope of the tangent), and sketch the graphs of the first and second derivatives, given the graph of a smooth function

Determine algebraically the equation of the second derivative f ''(x) of a polynomial or simple rational function f(x), and make connections, through investigation using technology, between the key features of the graph of the function (e.g., increasing/ decreasing intervals, local maxima and minima, points of inflection, intervals of concavity)and corresponding features of the graphs of its first and second derivatives (e.g., for an increasing interval of the function, the first derivative is positive; for a point of inflection of the function, the slopes of tangents change their behaviour from increasing to decreasing or from decreasing to increasing, the first derivative has a maximum or minimum, and the second derivative is zero)

Describe key features of a polynomial function, given information about its first and/or second derivatives (e.g., the graph of a derivative, the sign of a derivative over specific intervals, the x-intercepts of a derivative), sketch two or more possible graphs of the function that are consistent with the given information, and explain why an infinite number of graphs is possible

Sketch the graph of a polynomial function, given its equation, by using a variety of strategies (e.g., using the sign of the first derivative; using the sign of the second derivative; identifying even or odd functions) to determine its key features (e.g., increasing/ decreasing intervals, intercepts, local maxima and minima, points of inflection, intervals of concavity), and verify using technology

Solving Problems Using Mathematical Models and Derivatives: By the end of this course, students will:

Make connections between the concept of motion (i.e., displacement, velocity, acceleration) and the concept of the derivative in a variety of ways (e.g., verbally, numerically, graphically, algebraically)

Make connections between the graphical or algebraic representations of derivatives and real-world applications (e.g., population and rates of population change, prices and inflation rates, volume and rates of flow, height and growth rates)

Solve problems, using the derivative, that involve instantaneous rates of change, including problems arising from real-world applications (e.g., population growth, radioactive decay, temperature changes, hours of daylight, heights of tides), given the equation of a function*

Solve optimization problems involving polynomial, simple rational, and exponential functions drawn from a variety of applications, including those arising from real-world situations

Solve problems arising from real-world applications by applying a mathematical model and the concepts and procedures associated with the derivative to determine mathematical results, and interpret and communicate the results

Representing Vectors Geometrically and Algebraically: By the end of this course, students will:

Recognize a vector as a quantity with both magnitude and direction, and identify, gather, and interpret information about real-world applications of vectors (e.g., displacement, forces involved in structural design, simple animation of computer graphics, velocity determined using GPS)

Represent a vector in two-space geometrically as a directed line segment, with directions expressed in different ways (e.g., 320 degrees; N 40 degrees W), and algebraically (e.g., using Cartesian coordinates; using polar coordinates), and recognize vectors with the same magnitude and direction but different positions as equal vectors

Determine, using trigonometric relationships [e.g., x = rcos theta, y = rsin theta, theta=tax^1 (y/x)or tan^-1 (y/x)+180 degrees, r = square root of x^2 + y^2], the Cartesian representation of a vector in two-space given as a directed line segment, or the representation as a directed line segment of a vector in two-space given in Cartesian form [e.g., representing the vector (8, 6) as a directed line segment]

Operating With Vectors: By the end of this course, students will:

Perform the operations of addition, subtraction, and scalar multiplication on vectors represented as directed line segments in two space, and on vectors represented in Cartesian form in two-space and three-space

Determine, through investigation with and without technology, some properties (e.g., commutative, associative, and distributive properties) of the operations of addition, subtraction, and scalar multiplication of vectors

Solve problems involving the addition, subtraction, and scalar multiplication of vectors, including problems arising from real-world applications

Determine, through investigation, properties of the cross product (e.g., investigate whether it is commutative, distributive, or associative; investigate the cross product of collinear vectors)

Describing Lines and Planes Using Linear Equations: By the end of this course, students will:

Recognize that the solution points (x, y) in two-space of a single linear equation in two variables form a line and that the solution points (x, y) in two-space of a system of two linear equations in two variables determine the point of intersection of two lines, if the lines are not coincident or parallel

Determine, through investigation with technology (i.e., 3-D graphing software) and without technology, that the solution points (x, y, z) in three-space of a single linear equation in three variables form a plane and that the solution points (x, y, z) in three-space of a system of two linear equations in three variables form the line of intersection of two planes, if the planes are not coincident or parallel

Determine, through investigation using a variety of tools and strategies (e.g., modeling with cardboard sheets and drinking straws; sketching on isometric graph paper), different geometric configurations of combinations of up to three lines and/or planes in three-space (e.g., two skew lines, three parallel planes, two intersecting planes, an intersecting line and plane); organize the configurations based on whether they intersect and, if so, how they intersect (i.e., in a point, in a line, in a plane)

Describing Lines and Planes Using Scalar, Vector, and Parametric Equations: By the end of this course, students will:

Recognize a scalar equation for a plane in three-space to be an equation of the form Ax + By + Cz + D = 0 whose solution points make up the plane, determine the intersection of three planes represented using scalar equations by solving a system of three linear equations in three unknowns algebraically (e.g., by using elimination or substitution), and make connections between the algebraic solution and the geometric configuration of the three planes

Solve problems relating to lines and planes in three-space that are represented in a variety of ways (e.g., scalar, vector, parametric equations) and involving distances (e.g., between a point and a plane; between two skew lines) or intersections (e.g., of two lines, of a line and a plane), and interpret the result geometrically

Solving Probability Problems Involving Discrete Sample Spaces: By the end of this course, students will:

Recognize and describe how probabilities are used to represent the likelihood of a result of an experiment (e.g., spinning spinners; drawing blocks from a bag that contains different coloured blocks; playing a game with number cubes; playing Aboriginal stick-and-stone games) and the likelihood of a real-world event (e.g., that it will rain tomorrow, that an accident will occur, that a product will be defective)

Determine the theoretical probability, P(i) (i.e., a value from 0 to 1), of each outcome of a discrete sample space (e.g., in situations in which all outcomes are equally likely), recognize that the sum of the probabilities of the outcomes is 1 (i.e., for n outcomes, P(1) + P(2) + P(3) +... + P(n) = 1), recognize that the probabilities P(i) form the probability distribution associated with the sample space, and solve related problems

Determine, through investigation using class-generated data and technology-based simulation models (e.g., using a random-number generator on a spreadsheet or on a graphing calculator; using dynamic statistical software to simulate repeated trials in an experiment), the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases (e.g., ''If I simulate tossing two coins 1000 times using technology, the experimental probability that I calculate for getting two tails on the two tosses is likely to be closer to the theoretical probability of 1/4 than if I simulate tossing the coins only 10 times'')

Recognize and describe an event as a set of outcomes and as a subset of a sample space, determine the complement of an event, determine whether two or more events are mutually exclusive or non-mutually exclusive (e.g., the events of getting an even number or getting an odd number of heads from tossing a coin 5 times are mutually exclusive), and solve related probability problems [e.g., calculate P(not A), P(A and B), P(A or B)] using a variety of strategies (e.g., Venn diagrams, lists, formulas)

Determine whether two events are independent or dependent and whether one event is conditional on another event, and solve related probability problems [e.g., calculate P(A and B), P(A or B), P(A given B)] using a variety of strategies (e.g., tree diagrams, lists, formulas)

Solving Problems Using Counting Principles: By the end of this course, students will:

Recognize the use of permutations and combinations as counting techniques with advantages over other counting techniques (e.g., making a list; using a tree diagram; making a chart; drawing a Venn diagram), distinguish between situations that involve the use of permutations and those that involve the use of combinations (e.g., by considering whether or not order matters), and make connections between, and calculate, permutations and combinations

Solve simple problems using techniques for counting permutations and combinations, where all objects are distinct, and express the solutions using standard combinatorial notation [e.g., n!, P(n, r)]

Solve introductory counting problems involving the additive counting principle (e.g., determining the number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls) and the multiplicative counting principle (e.g., determining the number of ways of selecting 2 boys and 2 girls from a group of 4 boys and 5 girls)

Solve probability problems using counting principles for situations involving equally likely outcomes

Understanding Probability Distributions for Discrete Random Variables: By the end of this course, students will:

Recognize and identify a discrete random variable X (i.e., a variable that assumes a unique value for each outcome of a discrete sample space, such as the value x for the outcome of getting x heads in 10 tosses of a coin), generate a probability distribution [i.e., a function that maps each value x of a random variable X to a corresponding probability, P(X= x)] by calculating the probabilities associated with all values of a random variable, with and without technology, and represent a probability distribution numerically using a table

Calculate the expected value for a given probability distribution [i.e., using E(X)= the summation of xP(X= x)], interpret the expected value in applications, and make connections between the expected value and the weighted mean of the values of the discrete random variable

Represent a probability distribution graphically using a probability histogram (i.e., a histogram on which each rectangle has a base of width 1, centred on the value of the discrete random variable, and a height equal to the probability associated with the value of the random variable), and make connections between the frequency histogram and the probability histogram (e.g., by comparing their shapes)

Recognize conditions (e.g., independent trials) that give rise to a random variable that follows a binomial probability distribution, calculate the probability associated with each value of the random variable, represent the distribution numerically using a table and graphically using a probability histogram, and make connections to the algebraic representation P(X = x) = (n over x)p^x(1-p)^n-x

Recognize conditions (e.g., dependent trials) that give rise to a random variable that follows a hypergeometric probability distribution, calculate the probability associated with each value of the random variable (e.g., by using a tree diagram; by using combinations), and represent the distribution numerically using a table and graphically using a probability histogram

Compare, with technology and using numeric and graphical representations, the probability distributions of discrete random variables (e.g., compare binomial distributions with the same probability of success for increasing numbers of trials; compare the shapes of a hypergeometric distribution and a binomial distribution)

Solve problems involving probability distributions (e.g., uniform, binomial, hypergeometric), including problems arising from real-world applications

Understanding Probability Distributions for Continuous Random Variables: By the end of this course, students will:

Recognize and identify a continuous random variable (i.e., a variable that assumes values from the infinite number of possible outcomes in a continuous sample space), and distinguish between situations that give rise to discrete frequency distributions (e.g., counting the number of outcomes for drawing a card or tossing three coins) and situations that give rise to continuous frequency distributions (e.g., measuring the time taken to complete a task or the maximum distance a ball can be thrown)

Recognize standard deviation as a measure of the spread of a distribution, and determine, with and without technology, the mean and standard deviation of a sample of values of a continuous random variable

Describe challenges associated with determining a continuous frequency distribution (e.g., the inability to capture all values of the variable, resulting in a need to sample; uncertainties in measured values of the variable), and recognize the need for mathematical models to represent continuous frequency distributions

Represent, using intervals, a sample of values of a continuous random variable numerically using a frequency table and graphically using a frequency histogram and a frequency polygon, recognize that the frequency polygon approximates the frequency distribution, and determine, through investigation using technology (e.g., dynamic statistical software, graphing calculator), and compare the effectiveness of the frequency polygon as an approximation of the frequency distribution for different sizes of the intervals

Recognize that theoretical probability for a continuous random variable is determined over a range of values (e.g., the probability that the life of a lightbulb is between 90 hours and 115 hours), that the probability that a continuous random variable takes any single value is zero, and that the probabilities of ranges of values form the probability distribution associated with the random variable

Recognize that the normal distribution is commonly used to model the frequency and probability distributions of continuous random variables, describe some properties of the normal distribution (e.g., the curve has a central peak; the curve is symmetric about the mean; the mean and median are equal; approximately 68% of the data values are within one standard deviation of the mean and approximately 95% of the data values are within two standard deviations of the mean), and recognize and describe situations that can be modelled using the normal distribution (e.g., birth weights of males or of females, household incomes in a neighbourhood, baseball batting averages)

Make connections, through investigation using dynamic statistical software, between the normal distribution and the binomial and hypergeometric distributions for increasing numbers of trials of the discrete distributions (e.g., recognizing that the shape of the hypergeometric distribution of the number of males on a 4-person committee selected from a group of people more closely resembles the shape of a normal distribution as the size of the group from which the committee was drawn increases)

Recognize a z-score as the positive or negative number of standard deviations from the mean to a value of the continuous random variable, and solve probability problems involving normal distributions using a variety of tools and strategies (e.g., calculating a z-score and reading a probability from a table; using technology to determine a probability), including problems arising from real-world applications

Understanding Data Concepts: By the end of this course, students will:

Recognize and describe the role of data in statistical studies (e.g., the use of statistical techniques to extract or mine knowledge of relationships from data), describe examples of applications of statistical studies (e.g., in medical research, political decision making, market research), and recognize that conclusions drawn from statistical studies of the same relationship may differ (e.g., conclusions about the effect of increasing jail sentences on crime rates)

Recognize and explain reasons why variability is inherent in data (e.g., arising from limited accuracy in measurement or from variations in the conditions of an experiment; arising from differences in samples in a survey), and distinguish between situations that involve one variable and situations that involve more than one variable

Distinguish different types of statistical data (i.e., discrete from continuous, qualitative from quantitative, categorical from numerical, nominal from ordinal, primary from secondary, experimental from observational, microdata from aggregate data) and give examples (e.g., distinguish experimental data used to compare the effectiveness of medical treatments from observational data used to examine the relationship between obesity and type 2 diabetes or between ethnicity and type 2 diabetes)

Collecting and Organizing Data: By the end of this course, students will:

Determine and describe principles of primary data collection (e.g., the need for randomization, replication, and control in experimental studies; the need for randomization in sample surveys) and criteria that should be considered in order to collect reliable primary data (e.g., the appropriateness of survey questions; potential sources of bias; sample size)

Explain the distinction between the terms population and sample, describe the characteristics of a good sample, explain why sampling is necessary (e.g., time, cost, or physical constraints), and describe and compare some sampling techniques (e.g., simple random, systematic, stratified, convenience, voluntary)

Describe how the use of random samples with a bias (e.g., response bias, measurement bias, non-response bias, sampling bias) or the use of non-random samples can affect the results of a study

Describe characteristics of an effective survey (e.g., by giving consideration to ethics, privacy, the need for honest responses, and possible sources of bias, including cultural bias), and design questionnaires (e.g., for determining if there is a relationship between a person's age and their hours per week of Internet use, between marks and hours of study, or between income and years of education) or experiments (e.g., growth of plants under different conditions) for gathering data

Collect data from primary sources, through experimentation, or from secondary sources (e.g., by using the Internet to access reliable data from a well-organized database such as E-STAT; by using print sources such as newspapers and magazines), and organize data with one or more attributes (e.g., organize data about a music collection classified by artist, date of recording, and type of music using dynamic statistical software or a spreadsheet) to answer a question or solve a problem

Analysing One-Variable Data: By the end of this course, students will:

Recognize that the analysis of one-variable data involves the frequencies associated with one attribute, and determine, using technology, the relevant numerical summaries (i.e., mean, median, mode, range, interquartile range, variance, and standard deviation)

Determine the positions of individual data points within a one-variable data set using quartiles, percentiles, and z-scores, use the normal distribution to model suitable one variable data sets, and recognize these processes as strategies for one-variable data analysis

Generate, using technology, the relevant graphical summaries of one-variable data (e.g., circle graphs, bar graphs, histograms, stem-and-leaf plots, boxplots) based on the type of data provided (e.g., categorical, ordinal, quantitative)

Interpret, for a normally distributed population, the meaning of a statistic qualified by a statement describing the margin of error and the confidence level (e.g., the meaning of a statistic that is accurate to within 3 percentage points, 19 times out of 20), and make connections, through investigation using technology (e.g., dynamic statistical software), between the sample size, the margin of error, and the confidence level (e.g., larger sample sizes create higher confidence levels for a given margin of error)

Interpret statistical summaries (e.g., graphical, numerical) to describe the characteristics of a one-variable data set and to compare two related one-variable data sets (e.g., compare the lengths of different species of trout; compare annual incomes in Canada and in a third-world country; compare Aboriginal and non-Aboriginal incomes); describe how statistical summaries (e.g., graphs, measures of central tendency) can be used to misrepresent one-variable data; and make inferences, and make and justify conclusions, from statistical summaries of one-variable data orally and in writing, using convincing arguments

Analysing Two-Variable Data: By the end of this course, students will:

Recognize that the analysis of two-variable data involves the relationship between two attributes, recognize the correlation coefficient as a measure of the fit of the data to a linear model, and determine, using technology, the relevant numerical summaries (e.g., summary tables such as contingency tables; correlation coefficients)

Recognize and distinguish different types of relationships between two variables that have a mathematical correlation (e.g., the cause and- effect relationship between the age of a tree and its diameter; the common-cause relationship between ice cream sales and forest fires over the course of a year; the accidental relationship between the consumer price index and the number of known planets in the universe)

Generate, using technology, the relevant graphical summaries of two-variable data (e.g., scatter plots, side-by-side boxplots) based on the type of data provided (e.g., categorical, ordinal, quantitative)

Determine, by performing a linear regression using technology, the equation of a line that models a suitable two-variable data set, determine the fit of an individual data point to the linear model (e.g., by using residuals to identify outliers), and recognize these processes as strategies for two-variable data analysis

Interpret statistical summaries (e.g., scatter plot, equation representing a relationship) to describe the characteristics of a two variable data set and to compare two related two-variable data sets (e.g., compare the relationship between Grade 12 English and mathematics marks with the relationship between Grade 12 science and mathematics marks); describe how statistical summaries (e.g., graphs, linear models) can be used to misrepresent two-variable data; and make inferences, and make and justify conclusions, from statistical summaries of two-variable data orally and in writing, using convincing arguments

Evaluating Validity: By the end of this course, students will:

Interpret statistics presented in the media (e.g., the UN's finding that 2% of the world's population has more than half the world's wealth, whereas half the world's population has only 1% of the world's wealth), and explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view (e.g., by making a general statement based on a weak correlation or an assumed cause-and effect relationship; by starting the vertical scale at a value other than zero; by making statements using general population statistics without reference to data specific to minority groups)

Assess the validity of conclusions presented in the media by examining sources of data, including Internet sources (i.e., to determine whether they are authoritative, reliable, unbiased, and current), methods of data collection, and possible sources of bias (e.g., sampling bias, non-response bias, cultural bias in a survey question), and by questioning the analysis of the data (e.g., whether there is any indication of the sample size in the analysis) and conclusions drawn from the data (e.g., whether any assumptions are made about cause and effect)

Gather, interpret, and describe information about applications of data management in occupations (e.g., actuary, statistician, business analyst, sociologist, medical doctor, psychologist, teacher, community planner), and about university programs that explore these applications

Designing and Carrying Out a Culminating Investigation: By the end of this course, students will:

Design a plan to study the problem (e.g., identify the variables and the population; develop an ethical survey; establish the procedures for gathering, summarizing, and analysing the primary or secondary data; consider the sample size and possible sources of bias)

Gather data related to the study of the problem (e.g., by using a survey; by using the Internet; by using a simulation) and organize the data (e.g., by setting up a database; by establishing intervals), with or without technology

Interpret, analyse, and summarize data related to the study of the problem (e.g., generate and interpret numerical and graphical statistical summaries; recognize and apply a probability distribution model; calculate the expected value of a probability distribution), with or without technology

Draw conclusions from the analysis of the data (e.g., determine whether the analysis solves the problem), evaluate the strength of the evidence (e.g., by considering factors such as sample size or bias, or the number of times a game is played), specify any limitations of the conclusions, and suggest follow-up problems or investigations

Presenting and Critiquing the Culminating Investigation: By the end of this course, students will:

Answer questions about the culminating investigation and respond to critiques (e.g., by elaborating on the procedures; by justifying mathematical reasoning)

Interpreting and Displaying Data: By the end of this course, students will:

Read and interpret graphs (e.g., bar graph, broken-line graph, histogram) obtained from various sources (e.g., newspapers, magazines, Statistics Canada website)

Explain the distinction between the terms population and sample, describe the characteristics of a good sample, and explain why sampling is necessary (e.g., time, cost, or physical constraints)

Collect categorical data from primary sources, through experimentation involving observation (e.g., by tracking food orders in restaurants offering healthy food options) or measurement, or from secondary sources (e.g., Internet databases, newspapers, magazines), and organize and store the data using a variety of tools (e.g., spreadsheets, dynamic statistical software)

Represent categorical data by constructing graphs (e.g., bar graph, broken-line graph, circle graph) using a variety of tools (e.g., dynamic statistical software, graphing calculator, spreadsheet)

Make inferences based on the graphical representation of data (e.g., an inference about a sample from the graphical representation of a population), and justify conclusions orally or in writing using convincing arguments (e.g., by showing that it is reasonable to assume that a sample is representative of a population)

Make and justify conclusions about a topic of personal interest by collecting, organizing (e.g., using spreadsheets), representing (e.g., using graphs), and making inferences from categorical data from primary sources (i.e., collected through measurement or observation) or secondary sources (e.g., electronic data from databases such as E-STAT, data from newspapers or magazines)

Explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view (e.g., by making general statements based on small samples; by making statements using general population statistics without reference to data specific to minority groups)

Gather, interpret, and describe information about applications of data management in the workplace and in everyday life

Investigating Probability: By the end of this course, students will:

Determine the theoretical probability of an event (i.e., the ratio of the number of favourable outcomes to the total number of possible outcomes, where all outcomes are equally likely), and represent the probability in a variety of ways (e.g., as a fraction, as a percent, as a decimal in the range 0 to 1)

Identify examples of the use of probability in the media (e.g., the probability of rain, of winning a lottery, of wait times for a service exceeding specified amounts) and various ways in which probability is represented (e.g., as a fraction, as a percent, as a decimal in the range 0 to 1)

Perform simple probability experiments (e.g., rolling number cubes, spinning spinners, flipping coins, playing Aboriginal stick-and-stone games), record the results, and determine the experimental probability of an event

Compare, through investigation, the theoretical probability of an event with the experimental probability, and describe how uncertainty explains why they might differ (e.g., ''I know that the theoretical probability of getting tails is 0.5, but that does not mean that I will always obtain 3 tails when I toss the coin 6 times''; ''If a lottery has a 1 in 9 chance of winning, am I certain to win if I buy 9 tickets?'')

Determine, through investigation using class generated data and technology-based simulation models (e.g., using a random-number generator on a spreadsheet or on a graphing calculator), the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases (e.g., ''If I simulate tossing a coin 1000 times using technology, the experimental probability that I calculate for getting tails in any one toss is likely to be closer to the theoretical probability than if I simulate tossing the coin only 10 times'')

Interpret information involving the use of probability and statistics in the media, and describe how probability and statistics can help in making informed decisions in a variety of situations (e.g., weighing the risk of injury when considering different occupations; using a weather forecast to plan outdoor activities; using sales data to stock a clothing store with appropriate styles and sizes)

Renting or Owning Accommodation: By the end of this course, students will:

Identify the financial implications (e.g., responsibility for paying the cost of accommodation and furnishings; greater responsibility for financial decision making) and the nonfinancial implications (e.g., greater freedom to make decisions; the demands of time management or of adapting to a new environment; the possibility of loneliness or of the need to share responsibilities) associated with living independently

Designing Budgets: By the end of this course, students will:

Categorize personal expenses as nondiscretionary (e.g., rent, groceries, utilities, loan payments) or discretionary (e.g., entertainment, vacations)

Categorize personal non-discretionary expenses as fixed (e.g., rent, cable, car insurance) or variable (e.g., groceries, clothing, vehicle maintenance)

Read and interpret prepared individual or family budgets, identify and describe the key components of a budget, and describe how budgets can reflect personal values (e.g., as they relate to shopping, saving for a long-term goal, recreational activities, family, community)

Design, with technology (e.g., using spreadsheet templates, budgeting software, online tools) and without technology (e.g., using budget templates), explain, and justify a monthly budget suitable for an individual or family described in a given case study that provides the specifics of the situation (e.g., income; personal responsibilities; expenses such as utilities, food, rent/mortgage, entertainment, transportation, charitable contributions; long-term savings goals)

Make adjustments to a budget to accommodate changes in circumstances (e.g., loss of hours at work, change of job, change in personal responsibilities, move to new accommodation, achievement of a long-term goal, major purchase), with technology (e.g., spreadsheet template, budgeting software)

Filing Income Tax: By the end of this course, students will:

Explain why most Canadians are expected to file a personal income tax return each year, and identify and describe the major parts of a personal income tax return (i.e., identification, total income, net income, taxable income, refund or balance owing)

Gather, interpret, and describe the information and documents required for filing a personal income tax return (e.g., CRA guides, forms, and schedules; T4 slips; receipts for charitable donations), and explain why they are required

Gather, interpret, and compare information about common tax credits (e.g., tuition fees, medical expenses, charitable donations) and tax deductions (e.g., moving expenses, child care expenses, union dues)

Complete a simple personal income tax return (i.e., forms and schedules), with or without tax preparation software

Gather, interpret, and describe some additional information that a self-employed individual should provide when filing a personal income tax return (e.g., a statement of business activities that includes business expenses such as insurance, advertising, and motor-vehicle expenses)

Gather, interpret, and describe information about services that will complete a personal income tax return (e.g., tax preparation service, chartered accountant, voluntary service in the community) and resources that will help with completing a personal income tax return (e.g., forms and publications available on the Canada Revenue Agency website, tax preparation software for which rebates are available), and compare the services and resources on the basis of the assistance they provide and their cost

Gather, interpret, and describe information about applications of the mathematics of personal finance in the workplace (e.g., selling real estate, bookkeeping, managing a restaurant)

Measuring and Estimating: By the end of this course, students will:

Measure, using a variety of tools (e.g., measuring tape, metre or yard stick, measuring cups, graduated cylinders), the lengths of common objects and the capacities of common containers, using the metric system and the imperial system

Convert measures within systems (e.g., centimeters and metres, kilograms and grams, litres and millilitres, feet and inches, ounces and pounds), as required within applications that arise from familiar contexts

Convert measures between systems (e.g., centimeters and inches, pounds and kilograms, square feet and square metres, litres and U.S. gallons, kilometres and miles, cups and millilitres, millilitres and teaspoons, degrees Celsius and degrees Fahrenheit), as required within applications that arise from familiar contexts

Applying Measurement and Design: By the end of this course, students will:

Construct accurate right angles in practical contexts (e.g., by using the 3-4-5 triplet to construct a region with right-angled corners on a floor), and explain connections to the Pythagorean theorem

Apply the concept of perimeter in familiar contexts (e.g., baseboard, fencing, door and window trim)

Estimate the areas and volumes of irregular shapes and figures, using a variety of strategies (e.g., counting grid squares; displacing water)

Solve problems involving the areas of rectangles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications

Solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite figures, in situations arising from real-world applications

Construct a two-dimensional scale drawing of a familiar setting (e.g., classroom, flower bed, playground) on grid paper or using design or drawing software

Construct, with reasonable accuracy, a three dimensional scale model of an object or environment of personal interest (e.g., appliance, room, building, garden, bridge)

Investigate, plan, design, and prepare a budget for a household improvement (e.g., landscaping a property; renovating a room), using appropriate technologies (e.g., design or decorating websites, design or drawing software, spreadsheet)

Identify and describe situations that involve proportional relationships and the possible consequences of errors in proportional reasoning, and solve problems involving proportional reasoning, arising in applications from work and everyday life.

Identify and describe applications of ratio and rate, and recognize and represent equivalent ratios (e.g., show that 4:6 represents the same ratio as 2:3 by showing that a ramp with a height of 4 m and a base of 6 m and a ramp with a height of 2 m and a base of 3 m are equally steep) and equivalent rates (e.g., recognize that paying $1.25 for 250 mL of tomato sauce is equivalent to paying $3.75 for 750 Ml of the same sauce), using a variety of tools (e.g., concrete materials, diagrams, dynamic geometry software)

Identify situations in which it is useful to make comparisons using unit rates, and solve problems that involve comparisons of unit rates

Identify and describe real-world applications of proportional reasoning (e.g., mixing concrete; calculating dosages; converting units; painting walls; calculating fuel consumption; calculating pay; enlarging patterns), distinguish between a situation involving a proportional relationship (e.g., recipes, where doubling the quantity of each ingredient doubles the number of servings; long-distance phone calls billed at a fixed cost per minute, where talking for half as many minutes costs half as much) and a situation involving a non-proportional relationship (e.g., cellular phone packages, where doubling the minutes purchased does not double the cost of the package; food purchases, where it can be less expensive to buy the same quantity of a product in one large package than in two or more small packages; hydro bills, where doubling consumption does not double the cost) in a personal and/or workplace context, and explain their reasoning

Solve problems involving proportional reasoning in everyday life (e.g., applying fertilizers; mixing gasoline and oil for use in small engines; mixing cement; buying plants for flower beds; using pool or laundry chemicals; doubling recipes; estimating cooking time from the time needed per pound; determining the fibre content of different sizes of food servings)

Solve problems involving proportional reasoning in work-related situations (e.g., calculating overtime pay; calculating pay for piecework; mixing concrete for small or large jobs)

Evaluating Logarithmic Expressions By the end of this course, students will:

Recognize the logarithm of a number to a given base as the exponent to which the base must be raised to get the number, recognize the operation of finding the logarithm to be the inverse operation (i.e., the undoing or reversing) of exponentiation, and evaluate simple logarithmic expressions

Determine, with technology, the approximate logarithm of a number to any base, including base 10 (e.g., by reasoning that log base 3 of 29 is between 3 and 4 and using systematic trial to determine that logbase 3 of 29 is approximately 3.07)

Make connections between related logarithmic and exponential equations (e.g., log base 5 of 125 = 3 can also be expressed as 5^3 = 125), and solve simple exponential equations by rewriting them in logarithmic form (e.g., solving 3^x = 10 by rewriting the equation as log base 3 of 10 = x

Make connections between the laws of exponents and the laws of logarithms [e.g., use the statement 10^a+b = 10^a 10^b to deduce that log base 10 of x + log base 10 of y = logbase 10 of (xy)], verify the laws of logarithms with or without technology (e.g., use patterning to verify the quotient law for logarithms by evaluating expressions such as log base 10 of 1000 - log base 10 of 100 and then rewriting the answer as a logarithmic term to the same base), and use the laws of logarithms to simplify and evaluate numerical expressions

Connecting Graphs and Equations of Logarithmic Functions: By the end of this course, students will:

Determine, through investigation with technology (e.g., graphing calculator, spreadsheet) and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, increasing/decreasing behaviour) of the graphs of logarithmic functions of the form f(x) = log base b of x, and make connections between the algebraic and graphical representations of these logarithmic functions

Recognize the relationship between an exponential function and the corresponding logarithmic function to be that of a function and its inverse, deduce that the graph of a logarithmic function is the reflection of the graph of the corresponding exponential function in the line y = x, and verify the deduction using technology

Pose problems based on real-world applications of exponential and logarithmic functions (e.g., exponential growth and decay, the Richter scale, the pH scale, the decibel scale), and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation

Solving Exponential and Logarithmic Equations: By the end of this course, students will:

Recognize equivalent algebraic expressions involving logarithms and exponents, and simplify expressions of these types

Solve exponential equations in one variable by determining a common base (e.g., solve 4^x = 8^(x+3) by expressing each side as a power of 2) and by using logarithms (e.g., solve 4^x = 8^(x+3) by taking the logarithm base 2 of both sides), recognizing that logarithms base 10 are commonly used (e.g., solving 3^x = 7 by taking the logarithm base 10 of both sides)

Solve simple logarithmic equations in one variable algebraically [e.g., log base 3 of (5x + 6) = 2, log base 10 of (x + 1) = 1]

Solve problems involving exponential and logarithmic equations algebraically, including problems arising from real-world applications

Understanding and Applying Radian Measure: By the end of this course, students will:

Recognize the radian as an alternative unit to the degree for angle measurement, define the radian measure of an angle as the length of the arc that subtends this angle at the centre of a unit circle, and develop and apply the relationship between radian and degree measure

Represent radian measure in terms of pi (e.g., pi/3 radians, pi radians) and as a rational number (e.g., 1.05 radians, 6.28 radians)

Determine, with technology, the primary trigonometric ratios (i.e., sine, cosine, tangent) and the reciprocal trigonometric ratios (i.e., cosecant, secant, cotangent) of angles expressed in radian measure

Determine, without technology, the exact values of the primary trigonometric ratios and the reciprocal trigonometric ratios for the special angles 0,pi/6,pi/4,pi/3,pi/2, and their multiples less than or equal to 2pi

Connecting Graphs and Equations of Trigonometric Functions: By the end of this course, students will:

Sketch the graphs of f(x) = sin x and f(x) = cos x for angle measures expressed in radians, and determine and describe some key properties (e.g., period of 2pi, amplitude of 1) in terms of radians

Make connections between the tangent ratio and the tangent function by using technology to graph the relationship between angles in radians and their tangent ratios and defining this relationship as the function f(x) = tan x, and describe key properties of the tangent function

Graph, with technology and using the primary trigonometric functions, the reciprocal trigonometric functions (i.e., cosecant, secant, cotangent) for angle measures expressed in radians, determine and describe key properties of the reciprocal functions (e.g., state the domain, range, and period, and identify and explain the occurrence of asymptotes), and recognize notations used to represent the reciprocal functions [e.g., the reciprocal of f(x) = sin x can be represented using csc x, 1/f(x), or 1/sin x, but not using f^-1(x) or sin^-1 x, which represent the inverse function]

Determine the amplitude, period, and phase shift of sinusoidal functions whose equations are given in the form f(x) = a sin (k(x - d)) + c or f(x) = a cos(k(x - d)) + c, with angles expressed in radians

Sketch graphs of y = a sin (k(x - d)) + c and y = a cos(k(x - d)) + c by applying transformations to the graphs of f(x) = sin x and f(x) = cos x with angles expressed in radians, and state the period, amplitude, and phase shift of the transformed functions

Pose problems based on applications involving a trigonometric function with domain expressed in radians (e.g., seasonal changes in temperature, heights of tides, hours of daylight, displacements for oscillating springs), and solve these and other such problems by using a given graph or a graph generated with or without technology from a table of clues or from its equation

Solving Trigonometric Equations: By the end of this course, students will:

Explore the algebraic development of the compound angle formulas (e.g., verify the formulas in numerical examples, using technology; follow a demonstration of the algebraic development [student reproduction of the development of the general case is not required]), and use the formulas to determine exact values of trigonometric ratios [e.g., determining the exact value of sin ( pi/12)by first rewriting it in terms of special angles as sin ( pi/4 - pi/6)]

Recognize that trigonometric identities are equations that are true for every value in the domain (i.e., a counter-example can be used to show that an equation is not an identity), prove trigonometric identities through the application of reasoning skills, using a variety of relationships (e.g., tan x = sin x/cos x; sin^2 x + cos^2 x = 1; the reciprocal identities; the compound angle formulas), and verify identities using technology

Solve linear and quadratic trigonometric equations, with and without graphing technology, for the domain of real values from 0 to 2 pi, and solve related problems

Connecting Graphs and Equations of Polynomial Functions: By the end of this course, students will:

Recognize a polynomial expression (i.e., a series of terms where each term is the product of a constant and a power of x with a nonnegative integral exponent, such as x^3 - 5x^2 + 2x - 1); recognize the equation of a polynomial function, give reasons why it is a function, and identify linear and quadratic functions as examples of polynomial functions

Compare, through investigation using graphing technology, the numeric, graphical, and algebraic representations of polynomial (i.e., linear, quadratic, cubic, quartic) functions (e.g., compare finite differences in tables of values; investigate the effect of the degree of a polynomial function on the shape of its graph and the maximum number of x-intercepts; investigate the effect of varying the sign of the leading coefficient on the end behaviour of the function for very large positive or negative x-values)

Describe key features of the graphs of polynomial functions (e.g., the domain and range, the shape of the graphs, the end behaviour of the functions for very large positive or negative x-values)

Distinguish polynomial functions from sinusoidal and exponential functions [e.g., f(x) = sin x, g(x) = 2^x], and compare and contrast the graphs of various polynomial functions with the graphs of other types of functions

Make connections, through investigation using graphing technology (e.g., dynamic geometry software), between a polynomial function given in factored form [e.g., f(x) = 2(x - 3)(x + 2)(x - 1)] and the x-intercepts of its graph, and sketch the graph of a polynomial function given in factored form using its key features (e.g., by determining intercepts and end behaviour; by locating positive and negative regions using test values between and on either side of the x-intercepts)

Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af (k(x - d)) + c, and describe these roles in terms of transformations on the graphs of f(x) = x^3 and f(x) = x^4 (i.e., vertical and horizontal translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes)

Determine an equation of a polynomial function that satisfies a given set of conditions (e.g., degree of the polynomial, intercepts, points on the function), using methods appropriate to the situation (e.g., using the x-intercepts of the function; using a trial-and-error process with a graphing calculator or graphing software; using finite differences), and recognize that there may be more than one polynomial function that can satisfy a given set of conditions (e.g., an infinite number of polynomial functions satisfy the condition that they have three given x-intercepts)

Connecting Graphs and Equations of Rational Functions: By the end of this course, students will:

Determine, through investigation with and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals) of the graphs of rational functions that are the reciprocals of linear and quadratic functions, and make connections between the algebraic and graphical representations of these rational functions [e.g., make connections between f(x) = 1/(x^2 -4)and its graph by using graphing technology and by reasoning that there are vertical asymptotes at x = 2 and x = -2 and a horizontal asymptote at y = 0 and that the function maintains the same sign as f(x) = 1/ (x^2 - 4)]

Determine, through investigation with and without technology, key features (i.e., vertical and horizontal asymptotes, domain and range, intercepts, positive/negative intervals, increasing/decreasing intervals) of the graphs of rational functions that have linear expressions in the numerator and denominator [e.g., f(x) = 2x/(x-3), h(x) = x-2/(3x + 4)], and make connections between the algebraic and graphical representations of these rational functions

Sketch the graph of a simple rational function using its key features, given the algebraic representation of the function

Solving Polynomial and Rational Equations: By the end of this course, students will:

Make connections, through investigation using technology (e.g., computer algebra systems), between the polynomial function f(x), the divisor x - a, the remainder from the division f(x)/x-a, and f(a) to verify the remainder theorem and the factor theorem

Factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies (i.e., common factoring, difference of squares, trinomial factoring, factoring by grouping, remainder theorem, factor theorem)

Determine, through investigation using technology (e.g., graphing calculator, computer algebra systems), the connection between the real roots of a polynomial equation and the x-intercepts of the graph of the corresponding polynomial function, and describe this connection [e.g., the real roots of the equation x^4 - 13x^2 + 36 = 0 are the x-intercepts of the graph of f(x) = x^4 - 13x^2 + 36]

Solve polynomial equations in one variable, of degree no higher than four (e.g., 2x^3 - 3x^2 + 8x - 12 = 0), by selecting and applying strategies (i.e., common factoring, difference of squares, trinomial factoring, factoring by grouping, remainder theorem, factor theorem), and verify solutions using technology (e.g., using computer algebra systems to determine the roots; using graphing technology to determine the x-intercepts of the graph of the corresponding polynomial function)

Determine, through investigation using technology (e.g., graphing calculator, computer algebra systems), the connection between the real roots of a rational equation and the x-intercepts of the graph of the corresponding rational function, and describe this connection [e.g., the real root of the equation (x-2)/(x-3) = 0 is 2, which is the x-intercept of the function f(x) = (x-2)/(x-3); the equation 1/(x-3)= 0 has no not intersect the x-axis]

Solve simple rational equations in one variable algebraically, and verify solutions using technology (e.g., using computer algebra systems to determine the roots; using graphing technology to determine the x-intercepts of the graph of the corresponding rational function)

Solve problems involving applications of polynomial and simple rational functions and equations [e.g., problems involving the factor theorem or remainder theorem, such as determining the values of k for which the function f(x) = x^3 + 6x^2 + kx - 4 gives the same remainder when divided by x - 1 and x + 2]

Solving Inequalities: By the end of this course, students will:

Determine solutions to polynomial inequalities in one variable [e.g., solve f(x) greater than 0, where f(x) = x^3 - x^2 + 3x - 9] and to simple rational inequalities in one variable by graphing the corresponding functions, using graphing technology, and identifying intervals for which x satisfies the inequalities

Solve linear inequalities and factorable polynomial inequalities in one variable (e.g., x^3 + x^2 > 0) in a variety of ways (e.g., by determining intervals using x-intercepts and evaluating the corresponding function for a single x-value within each interval; by factoring the polynomial and identifying the conditions for which the product satisfies the inequality), and represent the solutions on a number line or algebraically (e.g., for the inequality x^4 - 5x^2 + 4 less than 0, the solution represented algebraically is -2 < x < -1 or 1 < x < 2)

Understanding Rates of Change: By the end of this course, students will:

Gather, interpret, and describe information about real-world applications of rates of change, and recognize different ways of representing rates of change (e.g., in words, numerically, graphically, algebraically)

Recognize that the rate of change for a function is a comparison of changes in the dependent variable to changes in the independent variable, and distinguish situations in which the rate of change is zero, constant, or changing by examining applications, including those arising from real-world situations (e.g., rate of change of the area of a circle as the radius increases, inflation rates, the rising trend in graduation rates among Aboriginal youth, speed of a cruising aircraft, speed of a cyclist climbing a hill, infection rates)

Sketch a graph that represents a relationship involving rate of change, as described in words, and verify with technology (e.g., motion sensor) when possible

Calculate and interpret average rates of change of functions (e.g., linear, quadratic, exponential, sinusoidal) arising from real-world applications (e.g., in the natural, physical, and social sciences), given various representations of the functions (e.g., tables of values, graphs, equations)

Recognize examples of instantaneous rates of change arising from real-world situations, and make connections between instantaneous rates of change and average rates of change (e.g., an average rate of change can be used to approximate an instantaneous rate of change)

Determine, through investigation using a variety of tools and strategies (e.g., using a table of values to calculate slopes of secants or graphing secants and measuring their slopes with technology), the approximate slope of the tangent to a given point on the graph of a function (e.g., quadratic, exponential, sinusoidal) by using the slopes of secants through the given point (e.g., investigating the slopes of secants that approach the tangent at that point more and more closely), and make connections to average and instantaneous rates of change

Solve problems involving average and instantaneous rates of change, including problems arising from real-world applications, by using numerical and graphical methods (e.g., by using graphing technology to graph a tangent and measure its slope)

Combining Functions: By the end of this course, students will:

Determine, through investigation, and explain some properties (i.e., odd, even, or neither; increasing/decreasing behaviours) of functions formed by adding, subtracting, multiplying, and dividing general functions [e.g., f(x) + g(x), f(x)g(x)]

Determine the composition of two functions [i.e., f(g(x))] numerically (i.e., by using a table of values) and graphically, with technology, for functions represented in a variety of ways (e.g., function machines, graphs, equations), and interpret the composition of two functions in real-world applications

Determine algebraically the composition of two functions [i.e., f(g(x))], verify that f(g(x)) is not always equal to g( f(x)) [e.g., by determining f(g(x)) and g( f(x)), given f(x) = x + 1 and g(x) = 2x], and state the domain [i.e., by defining f(g(x)) for those x-values for which g(x) is defined and for which it is included in the domain of f(x)] and the range of the composition of two functions

Solve problems involving the composition of two functions, including problems arising from real-world applications

Demonstrate, by giving examples for functions represented in a variety of ways (e.g., function machines, graphs, equations), the property that the composition of a function and its inverse function maps a number onto itself [i.e., f^-1( f(x)) = x and f( f^-1 (x)) = x demonstrate that the inverse function is the reverse process of the original function and that it undoes what the function does]

Using Function Models to Solve Problems: By the end of this course, students will:

Compare, through investigation using a variety of tools and strategies (e.g., graphing with technology; comparing algebraic representations; comparing finite differences in tables of values) the characteristics (e.g., key features of the graphs, forms of the equations) of various functions (i.e., polynomial, rational, trigonometric, exponential, logarithmic)

Solve graphically and numerically equations and inequalities whose solutions are not accessible by standard algebraic techniques

Solve problems, using a variety of tools and strategies, including problems arising from real-world applications, by reasoning with functions and by applying concepts and procedures involving functions (e.g., by constructing a function model from data, using the model to determine mathematical results, and interpreting and communicating the results within the context of the problem)

Scientific Investigation Skills: Throughout this course, students will:

Initiating and Planning [IP]: Formulate relevant scientific questions about observed relationships, ideas, problems, or issues, make informed predictions, and/or formulate educated hypotheses to focus inquiries or research

Analysing and Interpreting [AI]: Draw conclusions based on inquiry results and research findings, and justify their conclusions with reference to scientific knowledge

Communicating [C]: Communicate ideas, plans, procedures, results, and conclusions orally, in writing, and/or in electronic presentations, using appropriate language and a variety of formats (e.g., data tables, laboratory reports, presentations, debates, simulations, models)

Communicating [C]: Use appropriate numeric, symbolic, and graphic modes of representation (e.g., biological diagrams, three-dimensional molecular models), and appropriate units of measurement (e.g., SI and imperial units)

Communicating [C]: Express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figures

Initiating and Planning [IP]: Select appropriate instruments (e.g., dialysis tubing, glassware, sphygmomanometer) and materials (e.g., DNA models, plants, plant cuttings, molecular models), and identify appropriate methods, techniques, and procedures, for each inquiry

Initiating and Planning [IP]: Identify and locate a variety of print and electronic sources that enable them to address research topics fully and appropriately

Initiating and Planning [IP]: Apply knowledge and understanding of safe laboratory practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHMIS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory and biological materials (e.g., plants and invertebrates); and by using appropriate personal protection

Performing and Recording [PR]: Conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and data

Performing and Recording [PR]: Compile accurate data from laboratory and other sources, and organize and record the data, using appropriate formats, including tables, flow charts, graphs, and/or diagrams

Performing and Recording [PR]: Select, organize, and record relevant information on research topics from a variety of appropriate sources, including electronic, print, and/or human sources, using suitable formats and an accepted form of academic documentation

Analysing and Interpreting [AI]: Synthesize, analyse, interpret, and evaluate qualitative and/or quantitative data to determine whether the evidence supports or refutes the initial prediction or hypothesis and whether it is consistent with scientific theory; identify sources of bias and/or error; and suggest improvements to the inquiry to reduce the likelihood of error

Analysing and Interpreting [AI]: Analyse the information gathered from research sources for logic, accuracy, reliability, adequacy, and bias

Identify and describe a variety of careers related to the fields of science under study (e.g., scientific journalist, fisheries and wildlife officer, physician, infectious disease researcher, geneticist) and the education and training necessary for these careers

Describe the contributions of scientists, including Canadians (e.g., Evelyn Roden Nelson, Maude Menten, Albert Juan Aguayo, Kimberley J. Fernie, Michael Archer), to the fields under study

Relating Science to Technology, Society, and the Environment: By the end of this course, students will:

Analyse technological applications related to enzyme activity in the food and pharmaceutical industries (e.g., the production of dairy products; breadmaking; the use of enzymes to control reaction rates in pharmaceuticals) [AI, C]

Evaluate, on the basis of research, some advances in cellular biology and related technological applications (e.g., new treatments for cancer, HIV/AIDS, and hepatitis C; radioisotopic labelling to study the function of internal organs; fluorescence to study genetic material within cells; forensic biological techniques to aid in crime resolution) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to biochemistry, including, but not limited to: active and passive transport, covalent and ionic bond, allosteric site, substrate, substrate-enzyme complex, and inhibition [C]

Plan and conduct an investigation to demonstrate the movement of substances across a membrane (e.g., the effects of salt water and distilled water on a potato) [IP, PR]

Construct and draw three-dimensional molecular models of important biochemical compounds, including carbohydrates, proteins, lipids, and nucleic acids [PR, C]

Conduct biological tests to identify biochemical compounds found in various food samples (e.g., use Benedict's solution to test for carbohydrates in food samples), and compare the biochemical compounds found in each food to those found in the others [PR, AI, C]

Plan and conduct an investigation related to a cellular process (e.g., factors that affect enzyme activity; factors that affect transport of substances across cell membranes), using appropriate laboratory equipment and techniques, and report the results in an appropriate format [IP, PR, C]

Understanding Basic Concepts: By the end of this course, students will:

Explain the roles of various organelles, such as lysosomes, vacuoles, mitochondria, internal cell membranes, ribosomes, smooth and rough endoplasmic reticulum, and Golgi bodies, in cellular processes

Describe the structure of important biochemical compounds, including carbohydrates, proteins, lipids, and nucleic acids, and explain their function within cells

Identify common functional groups within biological molecules (e.g., hydroxyl, carbonyl, carboxyl, amino, phosphate), and explain how they contribute to the function of each molecule

Describe the chemical structures and mechanisms of various enzymes

Identify and describe the four main types of biochemical reactions (oxidation-reduction [redox], hydrolysis, condensation, and neutralization)

Describe the structure of cell membranes according to the fluid mosaic model, and explain the dynamics of passive transport, facilitated diffusion, and the movement of large particles across the cell membrane by the processes of endocytosis and exocytosis

Relating Science to Technology, Society, and the Environment: By the end of this course, students will:

Analyse the role of metabolic processes in the functioning of and interactions between biotic and abiotic systems (e.g., specialized microbes and enzymes in biotechnological applications to treat wastewater in the pulp and paper industry; microbes and enzymes in bioremediation, such as in the cleanup of oil spills; energy transfer from producers to consumers) [AI, C]

Assess the relevance, to their personal lives and to the community, of an understanding of cell biology and related technologies (e.g., knowledge of metabolic processes is relevant to personal choices about exercise, diet, and the use of pharmacological substances; knowledge of cellular processes aids in our understanding and treatment of mitochondrial diseases [a group of neuromuscular diseases]) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to metabolism, including, but not limited to: energy carriers, glycolysis, Krebs cycle, electron transport chain, ATP synthase, oxidative phosphorylation, chemiosmosis, proton pump, photolysis, Calvin cycle, light and dark reactions, and cyclic and noncyclic phosphorylation [C]

Conduct a laboratory investigation into the process of cellular respiration to identify the products of the process, interpret the qualitative observations, and display them in an appropriate format [PR, AI, C

Conduct a laboratory investigation of the process of photosynthesis to identify the products of the process, interpret the qualitative observations, and display them in an appropriate format [PR, AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Explain the chemical changes and energy conversions associated with the processes of aerobic and anaerobic cellular respiration (e.g., in aerobic cellular respiration, glucose and oxygen react to produce carbon dioxide, water, and energy in the form of heat and ATP; in anaerobic cellular respiration, yeast reacts with glucose in the absence of oxygen to produce carbon dioxide and ethanol)

Explain the chemical changes and energy conversions associated with the process of photosynthesis (e.g., carbon dioxide and water react with sunlight to produce oxygen and glucose)

Use the laws of thermodynamics to explain energy transfer in the cell during the processes of cellular respiration and photosynthesis

Describe, compare, and illustrate (e.g., using flow charts) the matter and energy transformations that occur during the processes of cellular respiration (aerobic and anaerobic) and photosynthesis, including the roles of oxygen and organelles such as mitochondria and chloroplasts

Relating Science to Technology, Society, and the Environment: By the end of this course, students will:

Analyse, on the basis of research, some of the social, ethical, and legal implications of biotechnology (e.g., the bioengineering of animal species, especially those intended for human consumption; the cultivation of transgenic crops; the patenting of life forms; cloning) [IP, PR, AI, C]

Analyse, on the basis of research, some key aspects of Canadian regulations pertaining to biotechnology (e.g., current or potential legislation for mandatory DNA fingerprinting, human cloning, ownership of a genome, patenting of genetically modified organisms), and compare them to regulations from another jurisdiction [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to molecular genetics, including, but not limited to: polymerase I, II, and III, DNA ligase, helicase, Okazaki fragment, mRNA, rRNA, tRNA, codon, anticodon, translation, transcription, and ribosome subunits [C]

Analyse a simulated strand of DNA to determine the genetic code and base pairing of DNA (e.g., determine base sequences of DNA for a protein; analyse base sequences in DNA to recognize an anomaly) [AI]

Conduct an investigation to extract DNA from a specimen of plant or animal protein [PR]

Investigate and analyse the cell components involved in the process of protein synthesis, using appropriate laboratory equipment and techniques, or a computer simulation [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Explain the current model of DNA replication, and describe the different repair mechanisms that can correct mistakes in DNA sequencing

Compare the structures and functions of RNA and DNA, and explain their roles in the process of protein synthesis

Explain the steps involved in the process of protein synthesis and how genetic expression is controlled in prokaryotes and eukaryotes by regulatory proteins (e.g., the role of operons in prokaryotic cells; the mechanism of gene expression in eukaryotic cells)

Explain how mutagens, such as radiation and chemicals, can cause mutations by changing the genetic material in cells (e.g., the mechanisms and effects of point mutations and frameshift mutations)

Describe some examples of genetic modification, and explain how it is applied in industry and agriculture (e.g., the processes involved in cloning, or in the sequencing of DNA bases; the processes involved in the manipulation of genetic material and protein synthesis; the development and mechanisms of the polymerization chain reaction)

Describe the functions of some of the cell components used in biotechnology (e.g., the roles of plasmids, restriction enzymes, recombinant DNA, and vectors in genetic engineering)

Describe, on the basis of research, some of the historical scientific contributions that have advanced our understanding of molecular genetics (e.g., discoveries made by Frederick Griffith, Watson and Crick, Hershey and Chase)

Assess, on the basis of findings from a case study, the effects on the human body of taking chemical substances to enhance performance or improve health (e.g., the risks and benefits of taking large quantities of vitamins or amino acids; the effects on the human body of substances that people use to cope with stress) [PR, AI, C]

Evaluate, on the basis of research, some of the human health issues that arise from the impact of human activities on the environment (e.g., the effects of synthetic estrogen compounds released into our water systems; the effects of leaching of compounds from plastic products into soil and water) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to homeostasis, including, but not limited to: insulin, testosterone, estrogen, nephron, dialysis, pituitary, synapse, and acetylcholine [C]

Plan and construct a model to illustrate the essential components of the homeostatic process (e.g., create a flow chart that illustrates representative feedback mechanisms in living things) [IP, AI, C]

Plan and conduct an investigation to study a feedback system (e.g., stimulus response loop) [IP, PR, AI]

Plan and conduct an investigation to study the response mechanism of an invertebrate to external stimuli (e.g., the instinctive behaviour of an invertebrate in response to a stimulus such as light), using appropriate laboratory equipment and techniques [IP, PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Describe the anatomy and physiology of the endocrine, excretory, and nervous systems, and explain how these systems interact to maintain homeostasis

Explain how reproductive hormones act in human feedback mechanisms to maintain homeostasis (e.g., the actions of male and female reproductive hormones on their respective body systems)

Describe the homeostatic processes involved in maintaining water, ionic, thermal, and acid-base equilibrium, and explain how these processes help body systems respond to both a change in environment and the effects of medical treatments (e.g., the role of feedback mechanisms in water balance or thermoregulation; how the buffering system of blood maintains the body's pH balance; the effect of medical treatments on the endocrine system; the effects of chemotherapy on homeostasis)

Analyse the effects of human population growth, personal consumption, and technological development on our ecological footprint (e.g., the deforestation resulting from expanding development and demand for wood products causes the destruction of habitats that support biological diversity; the acidification of lakes associated with some industrial processes causes a decrease in fish populations) [AI, C]

Assess, on the basis of research, the effectiveness of some Canadian technologies and projects intended to nourish expanding populations (e.g., the risks and benefits of growing genetically modified canola; some of the sustainable development projects funded by the Canadian International Development Agency [CIDA]) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to population dynamics, including, but not limited to: carrying capacity, population growth, population cycle, fecundity, and mortality [C]

Use conceptual and mathematical population growth models to calculate the growth of populations of various species in an ecosystem (e.g., use the concepts of exponential, sigmoid, and sinusoidal growth to estimate the sizes of various populations) [PR, AI, C]

Determine, through laboratory inquiry or using computer simulations, the characteristics of population growth of two different populations (e.g., the different population cycles of a predator and its prey; the population cycles of two populations that compete for food; the increase of Aboriginal compared to non-Aboriginal populations and the significant difference in average age between the two groups) [PR, AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Explain the concepts of interaction (e.g., competition, predation, defense mechanism, symbiotic relationship, parasitic relationship) between different species

Describe the characteristics of a given population, such as its growth, density (e.g., fecundity, mortality), distribution, and minimum viable size

Explain factors such as carrying capacity, fecundity, density, and predation that cause fluctuation in populations, and analyse the fluctuation in the population of a species of plant, wild animal, or microorganism

Explain the concept of energy transfer in a human population in terms of the flow of food energy in the production, distribution, and use of food resources

Explain how a change in one population in an aquatic or terrestrial ecosystem can affect the entire hierarchy of living things in that system (e.g., how the disappearance of crayfish from a lake causes a decrease in the bass population of the lake; how the disappearance of beaver from an ecosystem causes a decrease in the wolf population in that ecosystem)

Scientific Investigation Skills: Throughout this course, students will:

Analysing and Interpreting [AI]: Draw conclusions based on inquiry results and research findings, and justify their conclusions with reference to scientific knowledge

Communicating [C]: Communicate ideas, plans, procedures, results, and conclusions orally, in writing, and/or in electronic presentations, using appropriate language and a variety of formats (e.g., data tables, laboratory reports, presentations, debates, simulations, models)

Communicating [C]: Use appropriate numeric, symbolic, and graphic modes of representation (e.g., represent ionic and molecular compounds by their accepted formulae and names), and appropriate units of measurement (e.g., SI and imperial units)

Initiating and Planning [IP]: Select appropriate instruments (e.g., spectroscope, centrifuge, burettes, meters) and materials (e.g., acid/base indicators, solubility tables, galvanic cells), and identify appropriate methods, techniques, and procedures, for each inquiry

Initiating and Planning [IP]: Apply knowledge and understanding of safe laboratory practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHMIS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory materials (e.g., safely disposing of organic solutions); and by using appropriate personal protection (e.g., wearing safety goggles)

Performing and Recording [PR]: Conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and data

Performing and Recording [PR]: Compile accurate data from laboratory and other sources, and organize and record the data, using appropriate formats, including tables, flow charts, graphs, and/or diagrams

Analysing and Interpreting [AI]: Synthesize, analyse, interpret, and evaluate qualitative and/or quantitative data; solve problems involving quantitative data; determine whether the evidence supports or refutes the initial prediction or hypothesis and whether it is consistent with scientific theory; identify sources of bias and/or error; and suggest improvements to the inquiry to reduce the likelihood of error

Identify and describe a variety of careers related to the fields of science under study (e.g., environmental technologist, pharmacy technician, electroplating technician, green building or renewable energy technician, veterinary technician, biochemical technologist) and the education and training necessary for these careers

Describe the contributions of scientists, including Canadians (e.g., Jed Harrison, Louis Slotin, Paul Kebarle, James Robert Bolton, Brian Evans Conway, Lee Wilson), to the fields under Study

Evaluate the risks and benefits to the environment of some commonly used chemical substances (e.g., substances used in fireworks, fire extinguishers, ''green'' cleaning products) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to qualitative analysis of matter, including, but not limited to: double displacement, precipitate, and energy level [C]

Investigate precipitation reactions and flame tests, using qualitative analysis instruments, equipment, and techniques (e.g., gas discharge tubes, high-voltage electrical sources, spectroscope, centrifuge) [PR, AI]

Conduct qualitative analyses of an unknown sample (e.g., a household or workplace chemical), using a flow chart and experimental procedures, including flame tests and precipitation reactions, to determine the presence of metal ions [PR, AI]

Identify an unknown gas sample (e.g., hydrogen, helium, neon) by observing its emission spectrum and comparing it to the spectra of known gases [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Explain the relationship between the atomic number and the mass number of an element, and the difference between isotopes and radioisotopes of an element

Describe various types of chemical reactions, including synthesis, decomposition, single displacement, and double displacement reactions

Explain basic procedures used in qualitative analysis of elements and compounds, including flame tests, precipitation reactions, and the observation of emission spectra

Relate observations from investigations using flame tests and emission spectra to the concept of quanta of energy proposed by Neils Bohr

Identify various materials and products used in everyday life that are made from organic compounds (e.g., synthetic fabrics, drugs, pesticides, cosmetics, organic solvents, car parts, artificial hearts), and assess the benefits of those products for society, as well as the health hazards they pose [AI, C]

Research a useful product made from one or more organic substances (e.g., CDs, made from crude oil), and assess the environmental impact of the production, use, and disposal of the product [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to organic chemistry, including, but not limited to: electronegativity, covalent bond, and functional group [C]

Draw Lewis structures to represent the covalent bonds in some simple organic molecules (e.g., CH4) [AI, C]

Build molecular models of, and create structural formulae for, some simple organic molecules (e.g., methane, butane, ethyne) [PR, AI, C]

Conduct an inquiry to determine the physical and chemical properties of some common organic compounds (e.g., solubility [in polar and non-polar solvents], conductivity, odour, combustibility) [PR, AI]

Conduct an inquiry to demonstrate separation of a mixture of liquids by distillation [PR]

Conduct an inquiry to identify some of the products of the combustion of a hydrocarbon and an alcohol [PR, AI]

Conduct an inquiry to synthesize a common organic compound (e.g., produce an ester, make soap) [PR]

Predict the nature of a bond (e.g., non-polar covalent or polar covalent), using the electronegativity values of atoms (e.g., H2, Cl2, O2, H2O, CH4, CH3OH) [AI]

Understanding Basic Concepts: By the end of this course, students will:

Describe the unique characteristics of the carbon atom in terms of covalent bonding

Identify functional group structures that define common classes of organic compounds (e.g., alkenes, alkanes, alkynes, alcohols, aldehydes, ketones, carboxylic acids, esters, amines)

Explain the general properties (e.g., polarity, solubility in water) of molecules that contain oxygen or nitrogen

Use structural formulae to describe some simple organic chemical reactions (e.g., addition, substitution, combustion)

Explain how the physical properties of a substance affect the processes used to separate organic chemical substances (e.g., distillation of crude oil, distillation of alcohols)

Identify the first ten hydrocarbons of the alkanes, the alkenes, and the alkynes by their names and structural formulae, using International Union of Pure and Applied Chemistry (IUPAC) nomenclature for alkanes, alkenes, and alkynes

Explain the dangers associated with the use of organic solvents (e.g., dry-cleaning compounds, paint thinners, glue solvents, nail polish remover), and some general precautions related to their use

Analyse, on the basis of research, a technological application that is based on the oxidation-reduction (redox) reaction that occurs in galvanic cells (e.g., in cardiac pacemakers, batteries, electroplating) [IP, PR, AI, C]

Analyse, on the basis of research, the causes of metal corrosion, and assess the environmental impact of some techniques used to protect metals from corrosion (e.g., rustproofing, painting, cathodic protection, galvanization) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to electrochemistry, including, but not limited to: oxidation, anode, and electrolyte [C]

Analyse the processes in galvanic cells, and draw labelled diagrams of these cells to show the oxidation or reduction reaction that occurs in each of the half-cells, the direction of electron flow, the location of the electrodes, and the direction of ion movement [AI, C]

Design and conduct an inquiry to determine the factors that affect rate of corrosion of a metal (e.g., stress on the metal, contact between two metals, surface oxide, the nature of the electrolyte, the nature of the metal) [IP, PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Explain the concepts of oxidation and reduction in terms of the chemical changes that occur during redox reactions

Describe the components of a galvanic cell, and explain how each component functions in a redox reaction

Describe the chemical reaction that results in the corrosion of metal

Analyse processes in the home, the workplace, or the environmental sector that require an understanding of accurate chemical calculations (e.g., baking according to a recipe; manufacturing items such as fertilizer, paint, pharmaceuticals; testing water quality in a public pool) [AI, C]

Assess, on the basis of research, the importance of quantitative accuracy in the concentration of solutions used for medical purposes or personal care (e.g., cough syrup, intravenous solutions, sunscreen) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to stoichiometry, including, but not limited to: molar mass, molar concentration, percentage yield, and Avogadro's number [C]

Calculate the molar mass of simple compounds with the aid of the periodic table [AI]

Convert the quantity of chemicals in simple chemical reactions from number of particles to number of moles and mass, using the mole concept [AI]

Solve problems involving relationships between the following variables in a chemical reaction: quantity in moles, number of particles, atomic mass, concentration of solution, and volume of solution [AI]

Solve problems involving stoichiometric relationships in balanced chemical equations [AI]

Use qualitative observations of a chemical reaction to identify the chemical changes, presence of limiting reagents, and the products occurring in a chemical reaction (e.g., aluminum reacting with copper(II) chloride solution, steel wool reacting with oxygen) [PR, AI]

Prepare aqueous solutions of given concentrations (e.g., concentrations expressed in grams per litre or moles per litre) by dissolving a solid solute in a solvent or by diluting a concentrated solution (e.g., a stock solution) [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Describe the relationships between Avogadro's number, the mole concept, and the molar mass of any given substance

Explain the relationships between the mole concept, the values of coefficients, the number of particles, and the mass of substances in balanced chemical equations

Explain the concept of molar concentration of a solution, using appropriate units of measure

Explain the concept of a limiting reagent in a chemical reaction, using examples of chemical processes from everyday life (e.g., synthesis of aspirin, synthesis of ammonia)

Evaluate, on the basis of research, the effectiveness of government initiatives or regulations (e.g., the Great Lakes Action Plan), and the actions of individuals (e.g., use of public transportation), intended to improve air and water quality, and propose a personal action plan to support these efforts [IP, PR, AI, C]

Evaluate the importance of quantitative chemical analysis in assessing air and water quality (e.g., the use of Environment Canada's Air Quality Index to determine when smog advisories need to be issued; systems to monitor the quality of drinking water), and explain how these analyses contribute to environmental awareness and responsibility [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to chemical analysis and chemistry in the environment, including, but not limited to: ozone, hard water, titration, pH, ppm, and ppb [C]

Write balanced chemical equations to represent the chemical reactions involved in the neutralization of acids and bases [AI, C]

Conduct an acid-base titration to determine the concentration of an acid or a base (e.g., the concentration of acetic acid in vinegar) [PR, AI]

Conduct an inquiry, using available technology (e.g., probewear) or chemical tests, to detect the presence of inorganic substances in various samples of water [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Identify major and minor chemical components of Earth's atmosphere

Identify gases and particulates that are commonly found in the atmosphere, and explain how they affect air quality (e.g., greenhouse gases, tropospheric and stratospheric ozone, carbon monoxide, chlorofluorocarbons, soot)

State and explain the Arrhenius definition of acids and bases

Explain the difference between strong and weak acids, and between strong and weak bases, in terms of degree of ionization

Identify the gas emissions that are the major contributors to acid precipitation, and explain the steps in the formation of acid rain

Explain the difference between the concepts of strength and concentration when referring to solutions of acids and bases

Identify inorganic substances that can be found dissolved in water as a result of natural processes and human activities (e.g., hard water contains metal ions)

Scientific Investigation Skills: Throughout this course, students will:

Analysing and Interpreting [AI]: Draw conclusions based on inquiry results and research findings, and justify their conclusions with reference to scientific knowledge

Communicating [C]: Communicate ideas, plans, procedures, results, and conclusions orally, in writing, and/or in electronic presentations, using appropriate language and a variety of formats (e.g., data tables, laboratory reports, presentations, debates, simulations, models)

Communicating [C]: Use appropriate numeric, symbolic, and graphic modes of representation, and appropriate units of measurement (e.g., SI units, imperial units)

Initiating and Planning [IP]: Select appropriate instruments (e.g., glassware, calorimeter, thermometer) and materials (e.g., chemical compounds and solutions), and identify appropriate methods, techniques, and procedures, for each inquiry

Initiating and Planning [IP]: Apply knowledge and understanding of safe laboratory practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHMIS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory materials; and by using appropriate personal protection (e.g., wearing safety goggles)

Performing and Recording [PR]: Conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and data

Performing and Recording [PR]: Compile accurate data from laboratory and other sources, and organize and record the data, using appropriate formats, including tables, flow charts, graphs, and/or diagrams

Analysing and Interpreting [AI]: Synthesize, analyse, interpret, and evaluate qualitative and/or quantitative data; solve problems involving quantitative data; determine whether the evidence supports or refutes the initial prediction or hypothesis and whether it is consistent with scientific theory; identify sources of bias and error; and suggest improvements to the inquiry to reduce the likelihood of error

Identify and describe a variety of careers related to the fields of science under study (e.g., food and drug analyst, chemical safety officer, nurse practitioner, consumer protection specialist, metallurgy technologist, environmental and waste management technician, geochemist) and the education and training necessary for these careers

Describe the contributions of scientists, including Canadians (e.g., Robert G. Ackman, Alice Wilson, Carol Ann Budd, Norman L. Bowen, Brian Evans Conway), to the fields under study

Assess the impact on human health, society, and the environment of organic compounds used in everyday life (e.g., polymers, nutritional supplements, food additives, pharmaceuticals, pesticides) [AI, C]

Propose a personal course of action to reduce the use of compounds that are harmful to human health and the environment (e.g., weed lawns by hand rather than using herbicides, use cloth bags for shopping to reduce the number of plastic bags in landfill sites, choose fuel-efficient or hybrid vehicles to reduce fossil fuel emissions) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to organic chemistry, including, but not limited to: organic compound, functional group, saturated hydrocarbon, unsaturated hydrocarbon, structural isomer, stereoisomer, and polymer [C]

Use International Union of Pure and Applied Chemistry (IUPAC) nomenclature conventions to identify names, write chemical formulae, and create structural formulae for the different classes of organic compounds, including hydrocarbons, alcohols, aldehydes, ketones, carboxylic acids, esters, ethers, amines, amides, and simple aromatic compounds [AI, C]

Analyse, on the basis of inquiry, various organic chemical reactions (e.g., production of esters, polymerization, oxidation of alcohols, multiple bonds in an organic compound, combustion reactions, addition reactions) [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Compare the different classes of organic compounds, including hydrocarbons, alcohols, aldehydes, ketones, carboxylic acids, esters, ethers, amines, and amides, by describing the similarities and differences in names and structural formulae of the compounds within each class

Describe the similarities and differences in physical properties (e.g., solubility in different solvents, odour, melting point, boiling point) within each class of organic compounds

Explain the chemical changes that occur during various types of organic chemical reactions, including substitution, addition, elimination, oxidation, esterification, and hydrolysis

Explain the difference between an addition reaction and a condensation polymerization reaction

Explain the concept of isomerism in organic compounds, and how variations in the properties of isomers relate to their structural and molecular formulae

Assess the benefits to society of technologies that are based on the principles of atomic and molecular structures (e.g., magnetic resonance imaging [MRI], infrared spectroscopy, X-ray crystallography, nuclear energy, medical applications of spectroscopy and mass spectrometry) [AI, C]

Evaluate the benefits to society, and the impact on the environment, of specialized materials that have been created on the basis of scientific research into the structure of matter and chemical bonding (e.g., bulletproof fabric, nanotechnologies, superconductors, instant adhesives) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to structure and properties of matter, including, but not limited to: orbital, emission spectrum, energy level, photon, and dipole [C]

Use the Pauli exclusion principle, Hund's rule, and the aufbau principle to write electron configurations for a variety of elements in the periodic table [AI, C]

Predict the shapes of simple molecules and ions (e.g., CH4, SO3, O2, H2O, NH4 +), using the valence shell electron pair repulsion (VSEPR) model, and draw diagrams to represent their molecular shapes [AI, C]

Predict the polarity of various chemical compounds, based on their molecular shapes and the difference in the electronegativity values of the atoms [AI]

Predict the type of solid (ionic, molecular, covalent network, metallic) formed by a given substance in a chemical reaction, and describe the properties of that solid [AI]

Conduct an inquiry to observe and analyse the physical properties of various substances (e.g., salts, metals) and to determine the type of chemical bonding present in each substance [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Explain how experimental observations and inferences made by Ernest Rutherford and Niels Bohr contributed to the development of the planetary model of the hydrogen atom

Describe the electron configurations of a variety of elements in the periodic table, using the concept of energy levels in shells and subshells, as well as the Pauli exclusion principle, Hund's rule, and the aufbau principle

Identify the characteristic properties of elements in each of the s, p, and d blocks of the periodic table, and explain the relationship between the position of an element in the periodic table, its properties, and its electron configuration

Explain how the physical properties of a solid or liquid (e.g., solubility, boiling point, melting point, melting point suppression, hardness, electrical conductivity, surface tension) depend on the particles present and the types of intermolecular and intramolecular forces (e.g., covalent bonding, ionic bonding, Van der Waals forces, hydrogen bonding, metallic bonding)

Describe a Canadian contribution to the field of atomic and molecular theory (e.g., the work of Richard F.W. Bader of McMaster University on electronic density in small molecules; the work of Robert J. LeRoy of the University of Waterloo on the mathematical technique to determine the atomic radius of molecules known as the LeRoy Radius; the work of Ronald J. Gillespie of McMaster University on the VSEPR model)

Analyse some conventional and alternative energy technologies (e.g., fossil fuel-burning power plants, hydro-powered generators, solar panels, wind turbines, fuel cells), and evaluate them in terms of their efficiency and impact on the environment [AI, C]

Analyse the conditions (e.g., temperature, pressure, presence of a catalyst) required to maximize the efficiency of some common natural or industrial chemical reactions (e.g., decomposition, combustion, neutralization), and explain how the improved efficiency of the reaction contributes to environmental sustainability [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to energy changes and rates of reaction, including, but not limited to: enthalpy, activation energy, endothermic, exothermic, potential energy, and specific heat capacity [C]

Write thermochemical equations, expressing the energy change as a change in H value or as a heat term in the equation [AI, C]

Solve problems involving analysis of heat transfer in a chemical reaction, using the equation Q = mc(change in T) (e.g., calculate the energy released in the combustion of an organic compound, and express the results in energy per mole of fuel [J/mol]) [AI, C]

Plan and conduct an inquiry to determine how various factors (e.g., change in temperature, addition of a catalyst, increase in surface area of a solid reactant) affect the rate of a chemical reaction [IP, PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Compare the energy changes resulting from physical change (e.g., boiling water), chemical reactions (e.g., bleaching a stain), and nuclear reactions (e.g., fission, fusion), in terms of whether energy is released or absorbed

Compare the energy change from a reaction in which bonds are formed to one in which bonds are broken, and explain these changes in terms of endothermic and exothermic reactions

Explain how mass, heat capacity, and change in temperature of a substance determine the amount of heat gained or lost by the substance

Explain, using collision theory and potential energy diagrams, how factors such as temperature, the surface area of the reactants, the nature of the reactants, the addition of catalysts, and the concentration of the solution control the rate of a chemical reaction

Describe simple potential energy diagrams of chemical reactions (e.g., the relationships between the relative energies of reactants and products and the activation energy of the reaction)

Explain, with reference to a simple chemical reaction (e.g., combustion), how the rate of a reaction is determined by the series of elementary steps that make up the overall reaction mechanism

Analyse the optimal conditions for a specific chemical process related to the principles of equilibrium that takes place in nature or is used in industry (e.g., the production of sulfuric acid, electrolyte balance in the human body, sedimentation in water systems) [AI, C]

Assess the impact of chemical equilibrium processes on various biological, biochemical, and technological systems (e.g., remediation in areas of heavy metal contamination, development of gallstones, use of buffering in medications, use of barium sulfate in medical diagnosis) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to chemical systems and equilibrium, including, but not limited to: homogeneous, closed system, reversible reaction, equilibrium constant, equilibrium concentration, molar solubility, and buffer [C]

Predict, applying Le Chatelier's principle or the reaction quotient for a given reaction, how various factors (e.g., changes in volume, temperature, or concentration of reactants or products in a solution) would affect a chemical system at equilibrium, and conduct an inquiry to test those predictions [PR, AI]

Conduct an inquiry to determine the value of an equilibrium constant for a chemical reaction (e.g., Keq for iron(III) thiocyanate, Ksp for calcium hydroxide, Ka for acetic acid) [PR, AI]

Solve problems related to equilibrium by performing calculations involving concentrations of reactants and products (e.g., Keq, Ksp, Ka, pH, pOH, Kp, Kb) [AI]

Solve problems related to acid-base equilibrium, using acid-base titration data and the pH at the equivalence point [AI]

Understanding Basic Concepts: By the end of this course, students will:

Explain the concept of dynamic equilibrium, using examples of physical and chemical equilibrium systems (e.g., liquid-vapour equilibrium, weak electrolytes in solution, reversible chemical reactions)

Explain the concept of chemical equilibrium and how it applies to the concentration of reactants and products in a chemical reaction at equilibrium

Explain Le Chatelier's principle and how it applies to changes to a chemical reaction at equilibrium

Identify common equilibrium constants, including Keq, Ksp, Kw, Ka, Kb, and Kp, and write the expressions for each

Compare the properties of strong and weak acids, and strong and weak bases, using the concept of dynamic equilibrium

Assess, on the basis of research, the viability of using electrochemical technologies as alternative sources of energy (e.g., fuel cells for emergency power generation or as power sources in remote locations), and explain their potential impact on society and the environment [IP, PR, AI, C]

Analyse health and safety issues involving electrochemistry (e.g., corrosion of metal pipes in drinking water systems) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to electrochemistry, including, but not limited to: half-reaction, electrochemical cell, reducing agent, oxidizing agent, redox reaction, and oxidation number [C]

Conduct an inquiry to analyse, in qualitative terms, an oxidation-reduction (redox) reaction [PR, AI, C]

Write balanced chemical equations for oxidation-reduction reactions, using various methods including oxidation numbers of atoms and the half-reaction method of balancing [AI, C]

Build a galvanic cell and measure its cell potential [PR, AI]

Analyse the processes in galvanic cells, and draw labelled diagrams of these cells to show the oxidation or reduction reaction that occurs in each of the half-cells, the direction of electron flow, the electrode polarity (anode and cathode), the cell potential, and the direction of ion movement [AI, C]

Predict the spontaneity of redox reactions, based on overall cell potential as determined using a table of standard reduction potentials for redox half-reactions [AI]

Understanding Basic Concepts: By the end of this course, students will:

Explain redox reactions in terms of the loss and gain of electrons and the associated change in oxidation number

Identify the components of a galvanic cell, and explain how each component functions in a redox reaction

Describe galvanic cells in terms of oxidation and reduction half-cells whose voltages can be used to determine overall cell potential

Explain how the hydrogen half-cell is used as a standard reference to determine the voltages of another half-cell

Explain some applications of electrochemistry in common industrial processes (e.g., in refining metals such as aluminum and zinc; in the production of hydrogen)

Explain the corrosion of metals in terms of an electrochemical process, and describe some common corrosion-inhibiting techniques (e.g., painting, galvanizing, cathodic protection)

Scientific Investigation Skills: Throughout this course, students will:

Initiating and Planning [IP]: Formulate relevant scientific questions about observed relationships, ideas, problems, or issues, make informed predictions, and/or formulate educated hypotheses to focus inquiries or research

Communicating [C]: Use appropriate numeric (e.g., SI and imperial units), symbolic, and graphic modes of representation (e.g., use appropriate time scales when representing geological time, or appropriate units to represent astronomical distances)

Communicating [C]: Express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figures

Initiating and Planning [IP]: Select appropriate instruments (e.g., hand lens, spectrographs, rock hammers) and materials (e.g., star charts, geological maps, mineral identification kits), and identify appropriate methods, techniques, and procedures, for each inquiry

Initiating and Planning [IP]: Identify and locate a variety of print and electronic sources that enable them to address research topics fully and appropriately

Initiating and Planning [IP]: Apply knowledge and understanding of safe laboratory and field work practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHMIS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory materials (e.g., following safety procedures when collecting samples; using materials safely when identifying minerals and rocks); and by using appropriate personal protection (e.g., wearing safety goggles when testing rock or mineral samples; using proper protective eyewear when observing the sun)

Performing and Recording [PR]: Conduct inquiries, controlling relevant variables, and adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and data

Performing and Recording [PR]: Compile accurate observations and data from laboratory and other sources (e.g., field work), and organize and record the data, using appropriate formats, including tables, flow charts, graphs, and/or diagrams

Performing and Recording [PR]: Select, organize, and record relevant information on research topics from a variety of appropriate sources, including electronic, print, and/or human sources (e.g., personal communication), using suitable formats and an accepted form of academic documentation

Analysing and Interpreting [AI]: Synthesize, analyse, interpret, and evaluate qualitative and/or quantitative data to determine whether the evidence supports or refutes the initial prediction or hypothesis and whether it is consistent with scientific theory; identify sources of bias and/or error; and suggest improvements to the inquiry to reduce the likelihood of error

Analysing and Interpreting [AI]: Analyse the information gathered from research sources for logic, accuracy, reliability, adequacy, and bias

Identify and describe a variety of careers related to the field of science under study (e.g., astronomer, paleontologist, astrophysicist, geologist, professor, planetarium curator) and the education and training necessary for these careers

Describe the contributions of scientists, including Canadian scientists (e.g., Alice Wilson, George M. Dawson, Thomas Edvard Krogh, William E. Logan, Richard Bond, Helen Sawyer Hogg, Joseph B. Tyrrell), to the fields under study

Analyse a major milestone in astronomical knowledge or theory (e.g., the discovery of the red shift in the spectra of galaxies; the knowledge gathered from the particle accelerator experiments at CERN in Switzerland), and explain how it revolutionized thinking in the scientific community [AI, C]

Analyse why and how a particular technology related to astronomical research was developed and how it has been improved over time (e.g., the evolution from optical to radio telescopes and to the Hubble telescope) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to astronomy, including, but not limited to: Doppler effect, electromagnetic radiation, protostar, celestial equator, ecliptic, altitude and azimuth, and right ascension and declination [C]

Locate observable features of the night sky using star charts, computer models, or direct observation, and record the location of these features using astronomical terms (e.g., celestial equator, ecliptic) and systems (e.g., altitude and azimuth, right ascension and declination) [PR, C]

Analyse spectroscopic data mathematically or graphically to determine various properties of stars (e.g., determine surface temperature from peak wavelength using Wein's law; predict chemical composition from spectral absorption lines; determine motion using the Doppler effect) [AI, C]

Use the Hertzsprung-Russell diagram to determine the interrelationships between the properties of stars (e.g., between mass and luminosity, between colour and luminosity) and to investigate their evolutionary pathways [PR, AI]

Investigate, in quantitative terms, properties of stars, including their distance from Earth (using the parallax method), surface temperature, absolute magnitude, and luminosity [PR, AI]

Investigate, using photographs or diagrams, the basic features of different types of galaxies (e.g., elliptical, spiral, barred spiral, irregular, peculiar), including the Milky Way [PR]

Understanding Basic Concepts: By the end of this course, students will:

Describe the theoretical and evidential underpinnings of the big bang theory (e.g., the theory that cosmic microwave background radiation is an echo of the big bang; physical evidence of the mass of the universe, and the relationship between mass and gravity) and their implications for the evolution of the universe

Explain the scale of distances between celestial bodies (e.g., with reference to astronomical units, light years, and parsecs) and the methods astronomers use to determine these distances (e.g., stellar parallax, cepheid variables)

Describe the characteristics of electromagnetic radiation (e.g., the relationship between wavelength, frequency, and energy) and the ways in which each region of the electromagnetic spectrum is used in making astronomical observations (e.g., X-rays in the search for black holes; infrared radiation to see through interstellar dust)

Explain how stars are classified on the basis of their surface temperature, luminosity, and chemical composition

Explain, with reference to a specific star (e.g., Rigel, Sirius, Arcturus), how astronomers use techniques to determine the properties of stars (e.g., mass, diameter, magnitude, temperature, luminosity)

Describe the sequence of events in the life cycle of a star, from its formation to the main sequence phase and beyond, with specific reference to energy sources and forces involved

Explain the relationship between the type of death of a star and the star's initial mass (e.g., a star with a low mass will form a planetary nebula and a white dwarf)

Analyse political considerations related to, and economic and environmental consequences (actual and/or potential) of, exploration of the solar system (e.g., political pressures underlying the original Space Race; the ability to monitor environmental conditions from space) [AI, C]

Analyse, on the basis of research, a specific technology that is used in space exploration and that has applications in other areas of research or in the environmental sector (e.g., Canadian satellites and robotics, spacecraft technologies, ground base and orbital telescopes, devices to mitigate the effects of the space environment on living organisms), and communicate their findings [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to planetary science, including, but not limited to: solar system, geocentric, heliocentric, geodesy, geosynchronous, eccentricity, apogee, aphelion, perigee, and perihelion [C]

Identify geological features and processes that are common to Earth and other bodies in the solar system (e.g., craters, faults, volcanic eruptions), and create a model or illustration to show these features, using data and images from satellites and space probes [PR, AI, C]

Use an inquiry or research process to investigate the effects of various forms of radiation and high-energy particles on bodies, organisms, and devices within the solar system (e.g., the effects of cosmic rays on atmospheric phenomena, of ultraviolet light on human and animal eyes and skin, of solar wind on radio communications) [IP, PR]

Investigate the ways in which interactions between solid bodies have helped to shape the solar system, including Earth (e.g., the accretion of minor bodies, the formation of moons, the formation of planetary rings) [PR]

Investigate the properties of Earth that protect life from hazards such as radiation and collision with other bodies (e.g., Earth's orbital position helps protect it from asteroids, some of which are deflected by the Jovian planets; Earth's magnetic field protects the planet from solar wind; atmospheric ozone minimizes incoming ultraviolet radiation) [PR]

Investigate techniques used to study and understand objects in the solar system (e.g., the measurement of gravitational pull on space probes to determine the mass of an object, the use of spectroscopy to study atmospheric compositions, the use of the global positioning system to track plate movement and tectonic activity from space) [PR]

Understanding Basic Concepts: By the end of this course, students will:

Explain the composition of the solar system (e.g., the sun, terrestrial inner planets, the asteroid belt, gas giant outer planets, the Kuiper belt, the scattered disc, the heliopause, the Oort cloud), and describe the characteristics of each component

Identify and explain the classes of objects orbiting the sun (e.g., planets, dwarf planets, small solar system bodies [SSSBs])

Explain the formation of the solar system with reference to the fundamental forces and processes involved (e.g., how gravitational force led to the contraction of the original solar nebula)

Identify the factors that determined the properties of bodies in the solar system (e.g., differences in distance from the sun result in temperature variations that determine whether substances on a planet, moon, or other body are solid or gaseous)

Identify and explain the properties of celestial bodies within or beyond the solar system, other than Earth, that might support the existence of life (e.g., the possible existence of liquid water on Europa; the proximity of a body to its host star)

Compare Earth with other objects in the solar system with respect to properties such as mass, size, composition, rotation, magnetic field, and gravitational field

Identify Kepler's laws, and use them to describe planetary motions (e.g., the shape of their orbits; differences in their orbital velocity)

Identify Newton's laws, and use them to explain planetary motion

Describe the major external processes and phenomena that affect Earth (e.g., radiation and particles from the ''quiet'' and ''active'' sun; cosmic rays; gravity of the sun and moon; asteroidal and cometary debris, including their force, energy, and matter)

Analyse the relationship between climate and geology, and, using geological records, assess the impact of long-term climate change on life on Earth [AI, C]

Evaluate the significance of contributions, including Canadian contributions, to our understanding of geological time and of changes in Earth systems over time (e.g., the contributions of Raymond A. Price; the Canadian contribution to the development of Landsat) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to Earth and its geological history, including, but not limited to: Milankovitch cycles, era, epoch, period, parent isotope, hot spot, paleomagnetism, and index fossil [C]

Use a research process to investigate the geological history of an area in Ontario (e.g., use a sequence diagram, geological maps showing main geological units or associated rock types, and/or surficial/bedrock geology maps to investigate the Oak Ridges Moraine or Niagara Escarpment) [IP, PR]

Investigate various types of preserved geological evidence of major changes that have taken place in Earth history (e.g., fossil evidence of mass extinctions, topographic evidence of past glaciations, evidence of plate movement in igneous rocks with magnetic reversals) [PR]

Produce a model or diagram to illustrate how geological time scales compare to human time scales (e.g., major events in Earth's geological history or the geological history of their region compared to major events in human history or students' own lifespans) [PR, C]

Produce diagrams to illustrate the development of various types of unconformities preserved in a sequence of strata (e.g., angular unconformity, disconformity, nonconformity) [PR, C]

Design and build a model to represent radioactive decay and the concept of half-life determination [IP, PR]

Investigate interactions over time between physical, chemical, and biological processes, and explain how they have affected environmental conditions throughout Earth's geological history (e.g., the impact of increasing amounts of atmospheric oxygen on stromatolites; the impact of increasing amounts of atmospheric carbon dioxide on global warming; the influence of plants on the water cycle, other life forms, the atmosphere, weathering, and erosion) [PR, AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Describe evidence for the evolution of life through the Proterozoic, Paleozoic, Mesozoic, and Cenozoic eras, using important groups of fossils that date from each era (e.g., stromatolites, trilobites, brachiopods, crinoids, fish, angiosperms, gymnosperms, dinosaurs, mammals)

Describe various kinds of evidence that life forms, climate, continental positions, and Earth's crust have changed over time (e.g., evidence of mass extinction, of past glaciations, of the existence of Pangaea and Gondwanaland)

Describe some processes by which fossils are produced and/or preserved (e.g., original preservation, carbonization, replacement, permineralization, mould and cast formations)

Compare and contrast relative and absolute dating principles and techniques as they apply to natural systems (e.g., the law of superposition; the law of cross-cutting relationships; varve counts; carbon-14 or uranium-lead dating)

Identify and describe the various methods of isotopic age determination, giving for each the name of the isotope, its half-life, its effective dating range, and some of the materials that it can be used to date (e.g., uranium-lead dating of rocks; carbon dating of organic materials)

Explain the influence of paradigm shifts (e.g., from uniformitarianism to catastrophism) in the development of geological thinking

Explain the different types of evidence used to determine the age of Earth (e.g., index fossils; evidence provided by radiometric dating of geological materials or lithostratigraphy) and how this evidence has influenced our understanding of the age of the planet

Assess the direct and indirect impact on local, provincial/regional, or national economies of the exploration for and extraction and refinement/processing of Earth materials (e.g., gold, uranium, sand, gravel, dimension stone, fossil fuels) [AI, C]

Analyse technologies and techniques used to explore for and extract natural resources, and assess their actual or potential environmental repercussions [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to Earth materials, including, but not limited to: geothermal vents, porosity, permeability, cleavage, fracture, cementation, evaporite, and foliation [C]

Investigate the properties of various Earth materials (e.g., density, conductivity, porosity; whether they are magnetic or radioactive), and explain how these properties affect how the materials are used and what technologies and techniques are used to explore for or extract them (e.g., radiometric instruments, electromagnetic or gravity surveys) [PR, AI, C]

Conduct a series of tests (e.g., hardness, streak, density) to identify and classify common minerals (e.g., quartz, calcite, potassium feldspar, plagioclase feldspar, muscovite, biotite, talc, graphite, hornblende) [PR, AI]

Investigate common igneous rocks (e.g., granite, obsidian, andesite, basalt, gabbro), using a hand lens, classify them on the basis of their texture (e.g., porphyritic, phaneritic, aphanitic) and composition (e.g., acid, intermediate, basic), and use this information to determine their origins (i.e., extrusive or intrusive) [PR, AI]

Investigate sedimentary rocks (e.g., conglomerate, breccia, sandstone, shale, limestone, dolostone, chert, gypsum, rock salt, coal), using a hand lens, classify them on the basis of their texture (e.g., coarse- or fine-grained, detrital) and composition (e.g., clastic, chemical, fossil inclusions), and use this information to determine their origin (e.g., clastic, chemical) [PR, AI]

Investigate metamorphic rocks (e.g., slate, phyllite, schist, gneiss, quartzite, marble), using a hand lens, and classify them on the basis of their characteristics (e.g., foliation, crystallinity) in order to identify their parent rock and the temperature, pressure, and chemical conditions at their formation [PR, AI]

Investigate a geological setting in their local area (e.g., a river/stream bed or lakeshore; a rock outcrop), and identify and classify rock samples collected from that area [PR, AI]

Plan and conduct an inquiry to investigate the factors that determine the size and form of mineral crystals (e.g., the temperature of the solution, the type of salt, the level of saturation, the temperature of slides containing melted salol) [IP, PR]

Understanding Basic Concepts: By the end of this course, students will:

Identify the physical and chemical properties of selected minerals, and describe the tests used to determine these properties

Describe the formation (i.e., intrusive or extrusive) and identify the distinguishing characteristics of igneous rocks (e.g., composition and eruption type; mineralogical content indicating the type of volcano in which a rock was formed)

Describe the formation of clastic and chemical sediments, and the characteristics of the corresponding sedimentary rocks (e.g., shape and size of particles, nature of their deposition)

Describe the different ways in which metamorphic rocks are formed (i.e., through changes in temperature, pressure, and chemical conditions) and the factors that contribute to their variety (e.g., variation in parent rock; regional or contact metamorphism)

Describe the role of Earth materials in the safe disposal of industrial and urban waste and toxic materials (e.g., the low permeability of clays makes them suitable material for barriers in waste disposal sites)

Evaluate the accuracy and reliability of technological methods of monitoring and predicting earthquakes, tsunamis, and volcanic eruptions [AI, C]

Analyse developments in technology (e.g., sonar, seismology, magnetometers) or Earth science endeavours (e.g., Lithoprobe, Geosat, Ocean Drilling Program) that have contributed to our understanding of Earth's interior, crust, and surface [AI, C]

Analyse the relationship between human activities and various geological structures and processes (e.g., the relationship between the location of deposits and the extraction/use of resources; the relationship between urban development and/or building codes and the probability of earthquakes or volcanic activity), and propose ways in which the relationships can be effectively or sustainably managed [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to geological processes, including, but not limited to: shear forces, compression forces, liquifaction, Benioff zone, aquifer, internal plastic flow, basal slip, midoceanic ridge, bedding, cross-cutting, isostasy, and lithification [C]

Investigate the difference between weathering and erosion (e.g., weathering occurs when the edge of a riverbank disintegrates from the force of the water; erosion occurs when the water transports the soil downstream), and construct models of the processes of physical, chemical, and biological weathering (e.g., tap water dripping on a bar of soap; vinegar dripping on a marble chip; dried beans soaking in a sealed plastic jar) [PR]

Produce a model showing simple sedimentary sequences (e.g., successive layering, sorted sequences), using block diagrams or three-dimensional models (e.g., layering as sand settles in an aquarium) [PR, C]

Investigate, through laboratory inquiry or computer simulation, the main types of seismic waves, and produce a model (e.g., using 3D block diagrams or springs and ropes) to illustrate for each the nature of its propagation, the transfer of energy, and its movement through rocks [PR, C]

Locate the epicentre of an earthquake, given the appropriate seismographic data (e.g., the travel-time curves to three recording stations for a single event) [AI]

Produce a scale model (e.g., a 3D block diagram) of the interior of Earth, differentiating between the layers and their characteristics (e.g., label cross-sections with the dimensions of the crust, mantle, and inner and outer core, and add travel-time curves for various seismic waves to provide data on the characteristics of the individual layers) [PR, C]

Design and test models that show the types (i.e., falls, slides, or flows) and causes (e.g., effect of gravity [angle of repose], water content, earthquakes) of mass wasting [IP, PR, AI]

Analyse information from a plan view (e.g., topographic map, air photo, geologic map) and sectional view (e.g., cross section, block diagram) in order to deduce the geologic history of an area [AI]

Understanding Basic Concepts: By the end of this course, students will:

Describe the types of boundaries (convergent, divergent, transform) between lithospheric plates, and explain the types of internal Earth processes occurring at each (e.g., subduction, divergence, convergence, hot spot activity, folding, faulting)

Describe the characteristics of the main types of seismic waves (i.e., P- and S-waves; R- and L-waves), and explain the different modes of travel, travel times, and types of motion associated with each

Compare qualitative and quantitative methods used to measure earthquake intensity and magnitude (e.g., the Mercalli Scale, the Richter Scale)

Explain how different erosional processes contribute to changing landscapes (e.g., channel erosion, mass-wasting events)

Identify and describe types of sediment transport (e.g., water, wind, glacial) and the types of load (i.e., dissolved load, suspended load, bed load) as sediment is moved by each type of transport

Describe the landforms produced by water, wind, or ice erosion

Describe the sedimentary structures formed by wind, water, or ice deposition

Identify major areas of tectonic activity in the world by plotting the location of major recorded earthquakes and active volcanoes on a map, and distinguish the areas by type of tectonic activity (e.g., Japan - convergent boundary; Iceland - divergent boundary; California - transform boundary)

Explain the processes of continuous recycling of major rock types (i.e., the rock cycle) throughout Earth history

Scientific Investigation Skills: Throughout this course, students will:

Initiating and Planning [IP]: Formulate relevant scientific questions about observed relationships, ideas, problems, or issues, make informed predictions, and/or formulate educated hypotheses to focus inquiries or research

Communicating [C]: Use appropriate numeric, symbolic, and graphic modes of representation, and appropriate units of measurement (e.g., SI and imperial units)

Communicating [C]: Express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figures

Initiating and Planning [IP]: Select appropriate instruments (e.g., a decibel meter, spot plates, glassware, thermometers) and materials (e.g., a heat lamp, agar plates, circuit boards), and identify appropriate methods, techniques, and procedures, for each inquiry

Initiating and Planning [IP]: Identify and locate a variety of print and electronic sources that enable them to address research topics fully and appropriately

Initiating and Planning [IP]: Apply knowledge and understanding of safe laboratory practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHMIS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory materials; and by using appropriate personal protection

Performing and Recording [PR]: Select, organize, and record relevant information on research topics from a variety of appropriate sources, including electronic, print, and/or human sources, using suitable formats and an accepted form of academic documentation

Analysing and Interpreting [AI]: Synthesize, analyse, interpret, and evaluate qualitative and/or quantitative data to determine whether the evidence supports or refutes the initial prediction or hypothesis and whether it is consistent with scientific theory; identify sources of bias and/or error; and suggest improvements to the inquiry to reduce the likelihood of error

Analysing and Interpreting [AI]: Analyse the information gathered from research sources for logic, accuracy, reliability, adequacy, and bias

Identify and describe a variety of careers related to the fields of science under study (e.g., chemical technician, baker, blood laboratory assistant, custodian, public works employee, cosmetologist) and the education and training necessary for these careers

Describe the contributions of scientists, including Canadians (e.g., Lorne Trottier, David Butler-Jones, Francine Decary, Robert G.E. Murray, Susan Barr), to the fields under study

Assess a workplace setting, either real or simulated, with respect to hazards that could affect workers or the environment, using appropriate criteria (e.g., a checklist for a health and safety audit) [AI, C]

Analyse and summarize the requirements of selected sections of workplace safety and/or environmental protection legislation related to a career of personal interest (e.g., regulations applying to mining in the Occupational Health and Safety Act; regulations applying to waste management in the Ontario Environmental Protection Act) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to hazards in the workplace, including, but not limited to: occupational exposure limits (OEL), designated substance regulation (DSR), personal protective equipment (PPE), route of entry, controlled product, infectious material, inhalation, absorption, ingestion, injection, and exposure values [C]

Plan and conduct an inquiry to determine what factors affect rates of chemical reactions (e.g., the concentration of an acid affects its rate of reaction with metals) [IP, PR, AI]

Investigate the effectiveness of methods used to reduce the impact of noise in the workplace (e.g., use a decibel meter to measure noise level before and after the installation of sound insulation; measure the effectiveness of earplugs at different sound levels) [PR]

Investigate the effects of workers' exposure to heat or cold (e.g., the effects of industrial heat sources such as molten materials on workers in foundries and factories; the effects of seasonal heat and cold, including exposure to solar radiation, on outdoor workers in construction, landscaping, agriculture, or hydro line repair; the effects of cold on workers in refrigerated warehouses) [PR]

Use a research process to investigate procedures for the safe handling of biohazardous and/or infectious materials in the workplace, and communicate their findings (e.g., create a webpage on the universal precautions for handling biological hazards; create a poster illustrating the steps for proper hand washing) [IP, PR, C]

Understanding Basic Concepts: By the end of this course, students will:

Describe the ways in which hazardous materials enter the body (i.e., ingestion, inhalation, absorption, and injection), and explain the importance of using personal protective equipment (e.g., gloves, appropriate eye wear, aprons, self-contained breathing apparatus) to avoid contamination

Identify common physical hazards in the workplace (e.g., hazards posed by noise; cutting tools; electrical power lines; extreme heat and cold), and describe potentially harmful situations and practices (e.g., work at heights on unstable equipment) as well as best safety practices (e.g., properly securing ladders and scaffolding) relating to these hazards

Identify common biological hazards in the workplace (e.g., bacteria, viruses, fungi), and describe potentially harmful situations and practices (e.g., improper disposal of syringes) as well as best safety practices (e.g., use of PPE such as gloves and masks) relating to these hazards

Identify common chemical hazards in the workplace (e.g., oxidizers, acid and base solutions), and describe potentially harmful situations and practices (e.g., inadequate venting of fine dust particles in flour mills) as well as best safety practices (e.g., wearing goggles and a self-contained breathing apparatus when working near substances that can irritate the eyes or lungs) relating to these hazards

Describe ways in which workers can address safety issues in the workplace (e.g., by reporting an unsafe condition to a supervisor; by refusing unsafe work)

Explain qualitatively how factors such as temperature, concentration, and the size of the opening of a container affect storage and disposal of chemicals in the workplace

Analyse, on the basis of research, a chemical product used in a particular profession or in the home (e.g., pool chemicals, chlorine bleach, hair dye), and prepare guidelines for safe and responsible use of the product [IP, PR, AI, C]

Assess the environmental consequences of improper disposal of chemical products commonly used in the home (e.g., pouring paint down the drain; dumping batteries in garbage destined for landfill sites) [AI, C]

Evaluate the appropriateness of current disposal practices in their home, at school, or in the community, with particular reference to the disposal of chemical waste [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology relating to chemical reactions and chemical products, including, but not limited to: synthesis, decomposition, neutralization, polymerization, combustion, single and double displacement, pH, solvent, organic, inorganic, and dilution [C]

Use an inquiry process to determine how various conditions affect a chemical reaction, by altering the conditions under which a reaction occurs (e.g., temperature, length of time, amount of reactants, pH of a solution), observing the effects of the alterations, and comparing the outcome and final product of each reaction (e.g., make borax slime, then alter the proportion of the ingredients and measure the impact on properties of the product) [IP, PR, AI]

Prepare dilutions using concentrated solutions, and observe or measure the changes in properties (e.g., pH, colour, viscosity, density) [PR]

Safely conduct a chemical reaction in order to produce a common household or consumer product (e.g., taffy, shampoo, toothpaste, nylon, lip balm) [PR]

Classify various household products on the pH scale, using pH paper, indicator solutions, and/or a pH meter [PR, AI]

Investigate a variety of consumer products within a given category (e.g., shampoo, window cleaner, disinfectant), focusing on products claiming to be environmentally friendly, and analyse them with respect to selected factors (e.g., cost, effectiveness, impact on the environment) [PR, AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Describe the types of chemical reactions (e.g., synthesis, single displacement, double displacement, decomposition, combustion, polymerization, neutralization) and the signs of chemical change in each

Explain, in qualitative terms, why some chemical substances mix and others do not (e.g., ethanol and vinegar are both polar and therefore miscible)

Explain the function of the pH scale and how pH test results are interpreted

Identify organic and inorganic compounds commonly used in the home and workplace (organic: fats, oils, fuels, common solvents; inorganic: acids and bases, mineral solvents, ammonia, baking soda), and compare their properties

Evaluate the effectiveness of a public policy measure or technological advance intended to control the spread of disease (e.g., mandatory immunization, screening for tuberculosis, quarantine) [AI, C]

Evaluate the impact, current and/or potential, of an individual's choice not to participate in a public health strategy intended to reduce the spread of disease (e.g., a hospital worker who does not follow recommendations regarding hand washing; a worker in a retirement home who does not get a flu shot) [AI, C]

Analyse, on the basis of research, the advantages and disadvantages of selected technologies used to try to control disease (e.g., the effectiveness of pharmaceuticals at combating disease; the side effects of a variety of drugs) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to the prevention of disease, including, but not limited to: communicable, non-communicable, microorganism, pathogen, disease, epidemiology, vector, immunization record, quarantine, pandemic, vaccine, antiseptic, sterilization, disinfection, and pasteurization [C]

Conduct an investigation, using safe practices and aseptic techniques, to compare the characteristics and growth of different types of non-pathogenic bacteria [PR, AI]

Investigate the effects of various drug therapies (e.g., different antibiotic discs) on the growth of bacteria [PR, AI]

Use a simulation (e.g., phenolphthalein and sodium hydroxide; a computer simulation) to demonstrate how diseases can spread through a community, and analyse the results [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Describe modes of transmission of some communicable diseases, including those that are insect-borne (e.g., malaria, encephalitis), airborne (e.g., influenza, tuberculosis), waterborne (e.g., cholera, poliomyelitis), sexually transmitted (e.g., HIV/AIDS), and food-borne (e.g., mad cow disease, trichinosis, salmonella)

Identify the causes and symptoms of various diseases (e.g., AIDS, influenza, salmonella, West Nile virus), and describe measures intended to prevent their spread

Describe the reasons for immunization against specific diseases, the function of records of immunization in Ontario, and the importance of maintaining a personal immunization schedule

Describe the use of vaccines, antibiotics, antiseptics, and other medical measures, both conventional and alternative, intended to control disease

Explain the differences between bacteria and viruses in terms of their size, structure, and reproduction, and the methods used to control their spread

Explain the importance of the proper use, storage, and disposal of medications (e.g., the importance of taking the full course of antibiotics, following directions, keeping medications away from children, monitoring side effects, returning expired medication to a pharmacy for disposal)

Assess the social and environmental impact of electrical technologies, including the impact associated with the manufacture and disposal of electronic devices (e.g., the impact of electrical devices used in the health care field, such as pacemakers or respirators; the impact of energy generation needed to power electrical devices and appliances) [AI, C]

Assess electrical hazards that can be found at home and in the workplace (e.g., electrical outlets close to areas where spills might occur; overloaded circuits), and propose practical courses of action to address the problems [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to electricity, including, but not limited to: energy, power, kilowatt-hour, potential difference, current, conductor, short circuit, circuit breaker, fuse, and resistance [C]

Draw energy flow diagrams and/or write energy transformation equations that illustrate the energy transformation occurring in household devices, including the production of waste energy (e.g., energy transformations in a digital music player: electrical energy yields kinetic energy + sound energy + light + waste heat energy) [C]

Build a simple electrical device or circuit (e.g., a loudspeaker, an electric motor, a D-cell, a circuit containing a 40W lightbulb and a dimmer switch), following a clear set of instructions and diagrams, and using appropriate tools safely [PR]

Calculate the electrical energy consumption of two similar appliances (e.g., an old and a new refrigerator), using the power ratings that appear on the appliance, and compare the financial and environmental costs (e.g., carbon dioxide emissions) of running the two appliances [AI]

Analyse changes in household energy consumption over a given time period (e.g., throughout the course of a day; between a week in January and a week in May), and give reasons for the changes [AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Describe basic electric circuit components, including those that regulate the flow of electricity or are used as safety mechanisms (e.g., switches, bimetallic strips, resistors, ground fault interrupters [GFIs], surge protectors), and explain their layout in an electric circuit

Describe forms of energy (e.g., electrical, mechanical, sound, light, thermal) and the energy transformations that occur in common electrical devices, including production of waste energy (e.g., heat)

Identify situations in which direct current (DC) and alternating current (AC) are used (e.g., DC is used in a portable appliance such as a flashlight; AC is used in a household appliance such as a kettle)

Explain the difference in voltage requirements, and identify some household appliances that require 110 V AC (e.g., microwave oven, blender) and some that require 220 V AC to operate (e.g., conventional oven, clothes dryer)

Describe safety procedures to be followed when using electric systems at home or at work (e.g., ensuring that tools and appliances are properly grounded; unplugging appliances by pulling the plug, not the cord), and explain how dangerous situations can occur (e.g., an overloaded circuit can overheat and cause a fire; digging through buried electrical cable can cause a severe shock)

Assess the environmental implications of food choices available in a variety of situations (e.g., in the school cafeteria, a fast-food restaurant, a supermarket, a local farmers' market, an organic meat shop), and propose ways to minimize the environmental impact of their food choices [AI, C]

Evaluate the nutritional content of a menu (e.g., from the school cafeteria, a fast-food restaurant, a coffee shop, a retirement home, a hospital), and propose ways to improve it, using information from Eating Well with Canada's Food Guide or Eating Well with Canada's Food Guide: First Nations, Inuit, and Metis [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate vocabulary related to nutritional science, including, but not limited to: nutrient, lipid, carbohydrate, protein, vitamin, mineral, qualitative test, serving size, food additive, trans fat, cholesterol, kilojoule, calorie, saturated, unsaturated, hydrogenated, essential amino acid, and preservative [C]

Conduct an investigation to compare commercial food products and home-made foods (e.g., commercial and home-made cookies or cake; a shake from a fast-food restaurant and a home-made milk shake; commercial orange drink and freshly squeezed orange juice), with reference to qualitative and quantitative differences such as the number of ingredients, types of nutrients, non-nutrient additives, texture, and colour [PR, AI]

Conduct an investigation to test for the presence of various nutrients in foods (e.g., use iodine to test for starch; use Benedict's solution to test for simple sugar) [PR]

Plan and conduct an investigation into the effectiveness of food preservatives (e.g., use lemon juice to reduce oxidation of apple slices; compare mould growth on commercial and home-made bread) [IP, PR]

Modify a recipe or menu to meet a dietary restriction (e.g., reduce the cholesterol content by replacing whole eggs with egg whites; reduce the sodium content by cutting salt; replace milk with soy milk; replace meat with tofu or legumes), and explain the reasons for the changes (e.g., sodium can contribute to high blood pressure; dairy products can cause digestive problems for people who are lactose intolerant; non-animal sources of protein are necessary for vegans, who do not eat any animal products) [PR, C]

Understanding Basic Concepts: By the end of this course, students will:

Identify sources of the principal food nutrients (e.g., carbohydrates, lipids, proteins, vitamins, minerals, fibre), with reference to Canada's Food Guide, and describe the function of these nutrients in the body

Identify the type of information commonly found on a food label, and describe how the information is organized (e.g., serving size, percentage of daily values, amount of each component)

Explain the meaning of a variety of descriptors found on food labels (e.g., ''fat free'', ''low fat'', ''lite'', ''pure'', ''organic'', ''lean'', ''diet'')

Describe the function of non-nutrient food additives (e.g., lecithin; monosodium glutamate [MSG]; artificial colour, flavour, and sweetener; preservatives), and explain their effects on human health

Scientific Investigation Skills: Throughout this course, students will:

Communicating [C]: Use appropriate numeric, symbolic, and graphic modes of representation, and appropriate units of measurement (e.g., SI and imperial units)

Initiating and Planning [IP]: Select appropriate instruments (e.g., respirometer, titration apparatus) and materials (e.g., prepared slides, Petri dishes, food samples), and identify appropriate methods, techniques, and procedures, for each inquiry

Initiating and Planning [IP]: Apply knowledge and understanding of safe laboratory practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHMIS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory materials, including biological waste (e.g., techniques to prevent contamination of specimens); and by using appropriate personal protection (e.g., wearing gloves when handling biological specimens)

Performing and Recording [PR]: Select, organize, and record relevant information on research topics from a variety of appropriate sources, including electronic, print, and/or human sources, using suitable formats and an accepted form of academic documentation

Identify and describe a variety of careers related to the fields of science under study (e.g., nuclear medicine technician, nurse practitioner, hematologist, dietitian, geneticist) and the education and training necessary for these careers

Describe the contributions of scientists, including Canadians (e.g., Frederick Banting, John A. Hopps, Louis Siminovitch, Jean Cuthand Goodwill, Nancy Olivieri), to the field under study

Assess the costs and benefits of a conventional medical technology, therapy, or device that is used to diagnose or treat a human health condition (e.g., diagnostic technologies such as X-rays and ultrasound; surgical procedures such as laser removal of tumours; biomedical devices such as prosthetics) [AI, C]

Identify a variety of alternative technologies and therapies used to diagnose or treat human health conditions (e.g., biofeedback, acupuncture, homeopathy, chiropractic, Aboriginal healing practices), and assess the effectiveness of one such therapy [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to medical technologies, including, but not limited to: aseptic techniques, feedback loop, biochemical, and biomechanical [C]

Use a variety of medical technologies to collect data related to blood pressure, heart rate, lung capacity, and body mass, and analyse the data (e.g., use a stethoscope to determine heart rate under various conditions; use a respirometer to measure lung capacity) [PR, AI]

Use a microscope to investigate prepared slides of human blood, identifying blood cells by type, size, and number, and determine the ratios between different cells in the samples [PR, AI]

Interpret information generated by a variety of imaging technologies (e.g., X-rays, ultrasound), and communicate their findings [AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Explain the four primary vital signs in humans (i.e., body temperature, heart rate, blood pressure, respiration rate)

Describe the normal range for various physiological and biochemical indicators (e.g., heart rate, lung capacity, blood pressure, blood sugar)

Explain the function and use of a variety of medical devices and technologies for diagnostic and treatment purposes (e.g., sphygmomanometer, stethoscope, ultrasound, X-ray, computerized axial tomography [CAT] scan, pacemaker, chemotherapy)

Describe the function and use of technologies, devices, and techniques for biomedical repair (e.g., prosthetics, artificial organs, plastic surgery)

Describe a recent technological development or advance in diagnosis or treatment in the health care field (e.g., artificial skin for burn victims, artificial and transgenic organ transplants, smart drugs, nanotechnologies, biophotonics)

Analyse, on the basis of research, the impact, both positive and negative, of scientific and technological advances intended to prevent the spread of illness and disease [IP, PR, AI, C]

Evaluate the impact of individual choices (e.g., with respect to vaccination, the proper use of antibiotics or mosquito repellent) on the control of pathogens and the prevention of disease [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to pathogens and diseases, including, but not limited to: parasite, epidemiology, pathogenesis, and vector [C]

Analyse, on the basis of inquiry, the effects of various treatments on pathogenesis (e.g., the effect of mouthwash or penicillin on the growth of bacteria) [PR, AI]

Analyse, using prepared slides or computer simulations, the characteristics, properties, and virulence of various bacteria [PR, AI]

Use an inquiry process to demonstrate the effect of the use of sterile techniques (e.g., pasteurization, use of an autoclave) on pathogenesis [IP, PR]

Understanding Basic Concepts: By the end of this course, students will:

Describe the characteristics and life cycles, including reproductive cycles, of representative pathogens (e.g., lysogenic cycle; lytic cycle; infectious cycle of malaria)

Describe the mode of transmission of various diseases, including those that are insect-borne (e.g., malaria, encephalitis), airborne (e.g., influenza, tuberculosis), water-borne (e.g., cholera, poliomyelitis), sexually transmitted (e.g., HIV/AIDS), and food-borne (e.g., mad cow disease, trichinosis, salmonella)

Explain how the human immune response acts as a natural defence against infection

Describe the role of vaccines, antibiotics, antiretrovirals, and other drug therapies and antiseptics in the control of pathogenesis

Describe non-medical ways to protect oneself from contracting pathogenic disease in a variety of situations (e.g., aseptic techniques such as wearing sterile gloves; proper personal hygiene such as frequent and thorough hand washing; the use of insect repellent)

Describe some of the means used by international non-governmental organizations (e.g., Medecins sans Frontieres, Oxfam, Ryan's Well Foundation, UN agencies, the Stephen Lewis Foundation) to control the spread of disease (e.g., distribution of vaccines, medication, malaria nets; installing wells so people have access to clean water; public education on strategies for transmission prevention)

Describe aseptic techniques used in the workplace, and explain their importance in preventing the spread of pathogens (e.g., cooking meat to a safe temperature and refrigerating leftovers quickly to avoid growth of bacteria in restaurant food; frequent hand sanitizing and use of sterile gloves in hospitals to prevent the spread of pathogens to vulnerable populations)

Analyse the social and economic costs and benefits of the use of non-nutrient food additives in food preservation and food enhancement techniques (e.g., sulfites in dried fruit; food colouring; MSG) [AI, C]

Evaluate the impact of some personal and societal factors (e.g., allergies, disease, body image, cultural preferences) on eating behaviours (e.g., the relationship between societal ideals of beauty and interest in ''fad'' diets) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to nutritional science, including, but not limited to: macromolecules, protein, starch, vitamin, carbohydrate, fats, lipids, pepsin, and amylase [C]

Plan and conduct chemical tests on a variety of foods to determine their chemical components (e.g., protein, starch, fats, lipids, carbohydrates, vitamins) [IP, PR, AI]

Investigate how enzymes break down macromolecules (e.g., amylase digests starch; pepsin and hydrochloric acid digest protein), and test the products of different types of digestion (e.g., use Benedict's solution to test for the presence of simple sugars produced by the digestion of carbohydrates) [PR]

Investigate the process of emulsification in fats and lipids (e.g., using commercially obtained bile and cooking oil) [PR]

Conduct titrations to determine the effects of various antacids on hydrochloric acid [PR, AI]

Plan and conduct an inquiry to determine the nutrient or energy content in selected food samples (e.g., hamburger, bread) [IP, PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Describe the basic chemical components of proteins, carbohydrates, fats and lipids, and vitamins and minerals, and explain their functions in the body

Explain how laboratory methods are used to determine the relative energy content of food (e.g., use of a calorimeter)

Describe requirements for a balanced diet based on the biochemical and energy needs of the average body, and explain how these requirements might vary among people with different lifestyles (e.g., young children, the elderly, a person with diabetes, an athlete)

Describe the structure and function of the components of the digestive system (e.g., mouth, tongue, epiglottis, esophagus, stomach, intestines, liver, gall bladder, pancreas, appendix, rectum, anus, salivary glands, saliva, bile) with respect to physical and chemical digestion

Describe optimum conditions for the effective functioning of some digestive enzymes found within the human body (e.g., amylase, pepsin)

Assess the impact of scientific research and technological advances on public health around the world (e.g., widespread immunization for diseases such as polio, telemedicine for people in remote areas, new drug therapies to combat disease) [AI, C]

Assess, on the basis of research, the effectiveness of a municipal, provincial, or federal government initiative intended to protect the public health of Canadians (e.g., immunization programs, smoking bans, Health Canada advisories) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to public health issues, including, but not limited to: pandemic, contamination, infectious disease, quarantine, and vaccination [C]

Analyse and interpret, using a case study or research data, scientific evidence regarding the effectiveness of a public health program intended to reduce disease transmission (e.g., distribution of bed nets to fight malaria; safe injection sites for intravenous drug users; programs to encourage hand washing in hospitals to stop the spread of C.Difficile) [AI, C]

Use a research process to investigate public health strategies developed to combat a potential pandemic (e.g., SARS, C. Difficile, avian flu) [IP, PR]

Use a research process to locate a media report on a public health issue (e.g., the handling of SARS, the banning of bisphenol-A in plastic bottles), summarize its arguments, and assess them from a scientific perspective [IP, PR, AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Describe the characteristics according to which a pandemic is classified (e.g., the strain of a virus, its mode of transmission)

Explain how pandemics have affected humanity throughout history (e.g., the bubonic plague of 1347-1352 in Europe, the cholera pandemic of 1817-1823 in Asia, the global Spanish influenza pandemic of 1918-1920, the contemporary AIDS pandemic)

Explain the impact of various threats to public health, including infectious diseases (e.g., hepatitis, HIV/AIDS, tuberculosis, malaria, sexually transmitted diseases), chronic diseases (e.g., cardiovascular disease, diabetes, asthma), and environmental factors (e.g., climate change, air pollution, chemical pollutants, radiation)

Explain a variety of social factors that can promote the rapid spread of infectious diseases (e.g., global population growth, international travel, poor sanitation, lack of clean drinking water)

Describe public health measures, including legislation, that are used for the protection of the public (e.g., quarantines, vaccinations, water chlorination, regulations on what items travellers can bring into a country)

Explain why some populations are particularly susceptible to specific health problems (e.g., the risk of diabetes among First Nations populations; the risk of thalassemia among Mediterranean populations; the risk of pneumonia and tuberculosis among people with HIV/AIDS)

Analyse social issues related to an application of biotechnology in the health, agricultural, or environmental sector (e.g., issues related to the uses of genetically modified organisms or to the uses and availability of in vitro fertilization) [AI, C]

Analyse, on the basis of research, ethical and legal issues related to an application of biotechnology in the health, agricultural, or environmental sector (e.g., ethical questions related to xenotransplantation; legal issues related to access to an individual's genetic information) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to biotechnology, including, but not limited to: selective breeding, hybridization, replication, mutation, genomics, and gene therapy [C]

Plan and conduct an inquiry into various traditional biotechnological techniques used in the food industry (e.g., the use of fermentation to produce bread, cheese, yogurt) [IP, PR]

Investigate, through laboratory inquiry or computer simulation, a recently developed biotechnological method used in the health sector (e.g., the process of electrophoresis to degrade DNA) [PR]

Investigate, through laboratory inquiry or computer simulation, a recently developed biotechnological method used in the field of agriculture (e.g., bioremediation of a chemical fertilizer spill; the cloning of corn; the use of synthetic hormones to promote growth in livestock) [PR]

Understanding Basic Concepts: By the end of this course, students will:

Explain various methods used, over time, in the field of biotechnology (e.g., use of living organisms to make or modify products, selective breeding to create particular breeds of animals, manipulation of genes to develop organisms with particular traits)

Explain the structure and functions of macromolecules (e.g., DNA, RNA) and the synthesis of proteins (e.g., transcription, translation, gene expression)

Describe applications of biotechnology in the health (e.g., genomics, gene therapy, xenotransplantation, in vitro fertilization), agricultural (e.g., genetically modified crops, biopesticides, cloning), and environmental sectors (e.g., bioremediation, phytoremediation)

Scientific Investigation Skills: Throughout this course, students will:

Communicating [C]: Use appropriate numeric (e.g., SI and imperial units), symbolic, and graphic modes of representation (e.g., free-body diagrams, algebraic equations)

Initiating and Planning [IP]: Select appropriate instruments (e.g., electronic probes, pendulums, cylinders) and materials (e.g., motion carts, magnets, simple machines), and identify appropriate methods, techniques, and procedures, for each inquiry

Initiating and Planning [IP]: Apply knowledge and understanding of safe laboratory practices and procedures when planning investigations by correctly interpreting Workplace Hazardous Materials Information System (WHMIS) symbols; by using appropriate techniques for handling and storing laboratory equipment and materials and disposing of laboratory materials; and by using appropriate personal protection (e.g., personal protective equipment when carrying out fluids experiments)

Analysing and Interpreting [AI]: Synthesize, analyse, interpret, and evaluate qualitative and/or quantitative data; solve problems using quantitative data; determine whether the evidence supports or refutes the initial prediction or hypothesis and whether it is consistent with scientific theory; identify sources of bias and/or error; and suggest improvements to the inquiry to reduce the likelihood of error

Identify and describe a variety of careers related to the fields of science under study (e.g., alternative energy advocate, sustainable energy technician, electrician, mechanic) and the education and training necessary for these careers

Describe the contributions of scientists, including Canadians (e.g., Elijah McCoy, Jaisel Vadgama, Gerald Vincent Bull, Elizabeth Cannon, Richard Marceau, Normand C. Beaulieu), to the fields under study

Analyse the design and uses of a transportation technology (e.g., snowmobiles, automobiles, motorized personal water craft), and evaluate its social and environmental impact, including the impact on risk behaviour and accident rates [AI, C]

Analyse how technologies are used to track the motion of objects, and outline various kinds of scientific knowledge gained through the use of such technologies (e.g., data on animal populations and migrations, on changes in ocean currents related to global warming, on the behaviour of celestial objects) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to motion, including, but not limited to: distance, displacement, position, speed, acceleration, instantaneous, force, and net force [C]

Conduct an inquiry to measure gravitational acceleration, and calculate the percentage error of the experimental value [PR, AI, C]

Plan and conduct investigations to measure distance and speed for objects moving in one dimension in uniform motion [IP, PR]

Plan and conduct investigations to measure constant acceleration for objects moving in one dimension [IP, PR]

Draw distance-time graphs, and use the graphs to calculate average speed and instantaneous speed of objects moving in one dimension [PR, AI, C]

Draw speed-time graphs, and use the graphs to calculate average acceleration and distance of objects moving in one dimension [PR, AI, C]

Solve simple problems involving one-dimensional average speed, distance, and elapsed time, using the algebraic equation v average = change in d / change in t [AI]

Solve simple problems involving one-dimensional average acceleration, change in speed, and elapsed time using the algebraic equation a average = change in v / change in t [AI]

Plan and conduct an inquiry to determine the relationship between the net force acting on an object and its acceleration in one dimension [IP, PR, AI]

Analyse, in quantitative terms, the forces acting on an object, and use free-body diagrams to determine net force and acceleration of the object in one dimension [AI, C]

Understanding Basic Concepts: By the end of this course, students will:

Distinguish between constant, instantaneous, and average speed, and give examples of each involving uniform and non-uniform motion

Describe the relationship between one-dimensional average speed, distance, and elapsed time

Describe, in quantitative terms, the relationship between one-dimensional average acceleration, change in speed, and elapsed time

State Newton's laws, and apply them qualitatively and quantitatively to explain the motion of an object in one dimension

Explain the relationship between the acceleration of an object and the net unbalanced force acting on that object

Analyse advantages and disadvantages of friction within mechanical systems in real-world situations, as well as methods used to increase or reduce friction in these systems (e.g., advantages of, and methods for increasing, friction on the surface of car tires and the soles of hiking boots; disadvantages of, and methods for reducing, friction between moving parts of artificial joints) [AI, C]

Evaluate, on the basis of research, the effectiveness of a common mechanical system in addressing a social or environmental challenge (e.g., prosthetic devices, bathtub lifts, high-efficiency heating and cooling systems) [IP, PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to mechanical systems, including, but not limited to: coefficients of friction, torque, mechanical advantage, work input, and work output [C]

Analyse, in qualitative and quantitative terms, the forces (e.g., gravitational, frictional, and normal forces; tension) acting on an object in one dimension, and describe the resulting motion of the object [AI, C]

Use an inquiry process to determine the factors affecting static and kinetic friction, and to determine the corresponding coefficient of friction between an everyday object and the surface with which it is in contact [PR, AI]

Use an inquiry process to determine the relationships between force, distance, and torque for the load arm and effort arm of levers [IP, PR, AI]

Solve problems involving torque, force, loadarm length, and effort-arm length as they relate to the three classes of levers [AI]

Investigate, in quantitative terms, common machines (e.g., a bicycle, a can opener, a piano) with respect to input and output forces and mechanical advantage [PR]

Construct a simple or compound machine, and determine its mechanical advantage (e.g., a pulley, a mobile, a can crusher, a trebuchet) [PR, AI]

Understanding Basic Concepts: By the end of this course, students will:

Identify and describe, in quantitative and qualitative terms, applications of various types of simple machines (e.g., wedges, screws, levers, pulleys, gears, wheels and axles)

Explain the operation and mechanical advantage of compound machines and biomechanical systems (e.g., block-and-tackle, winch, chain-and- sprocket systems; the human leg, arm)

Explain, with reference to force and displacement, the conditions necessary for work to be done

Evaluate, on the basis of research, the impact on society and the environment of the evolution of an electrical technology (e.g., electric cars or buses, electric appliances) [IP, PR, AI, C]

Assess the impact of an electromagnetic technology that is used for the benefit of society or the environment (e.g., devices for diagnosing and treating diseases, technologies for treating seeds to increase the rate of germination) [AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to electricity and magnetism, including, but not limited to: direct current, alternating current, electrical potential difference, resistance, power, energy, permanent magnet, electromagnet, magnetic field, motor principle, and electric motor [C]

Construct real and simulated mixed direct current (DC) circuits (i.e., parallel, series, and mixed circuits), and analyse them in quantitative terms to test Kirchhoff's laws [PR, AI]

Analyse, in quantitative terms, real or simulated DC circuits and circuit diagrams, using Ohm's law and Kirchhoff's laws [AI]

Conduct an inquiry to determine the magnetic fields produced by a permanent magnet, a straight current-carrying conductor, and a solenoid, and illustrate their findings [PR, AI, C]

Conduct an inquiry to determine the direction of the magnetic field of a straight current-carrying conductor or solenoid [PR, AI]

Conduct an inquiry to determine the direction of the forces on a straight current-carrying conductor that is placed in a uniform magnetic field [PR, AI]

Construct, or deconstruct and explain the components of, a basic electric device (e.g., a DC motor, a water-level detector) [PR, C]

Understanding Basic Concepts: By the end of this course, students will:

Compare and contrast the behaviour and functions of series, parallel, and mixed DC circuits

Compare and contrast direct current and alternating current (AC) in qualitative terms (e.g., the difference between DC and AC motors), and describe situations in which each is used

State Kirchhoff's laws and Ohm's law, and use them to explain, in quantitative terms, direct current, potential difference, and resistance in mixed circuit diagrams

Identify and explain safety precautions related to electrical circuits in the school, home, and workplace (e.g., the importance of turning off the current before performing electrical repairs; the reasons for grounding circuits; how to safely replace spent fuses; the use of double insulated tools and appliance circuit breakers)

Describe, with the aid of an illustration, the magnetic field produced by permanent magnets (bar and U-shaped) and electromagnets (straight conductor and solenoid)

Distinguish between conventional current and electron flow

State Oersted's principle, and apply the right-hand rule to explain the direction of the magnetic field produced when electric current flows through a long, straight conductor and through a solenoid

State the motor principle, and use the right-hand rule to explain the direction of the force experienced by a conductor

Explain, using diagrams, the components and operation of a DC electric motor

Analyse an energy-transformation technology (e.g., wind turbines, refrigerators, telephones, steam engines, coal-fired electrical plants), and evaluate its impact on society and the environment [AI, C]

Propose a course of practical action to improve the sustainability of an energy-transformation technology (e.g., solar panels, internal combustion engines, fuel cells, air conditioners) [PR, AI, C]

Developing Skills of Investigation and Communication: By the end of this course, students will:

Use appropriate terminology related to energy and energy transformations, including, but not limited to: work, gravitational potential energy, kinetic energy, chemical energy, energy transformations, and efficiency [C]

Use the law of conservation of energy to solve problems involving gravitational potential energy, kinetic energy, and thermal energy [AI]

Construct a simple device that makes use of energy transformations (e.g., a pendulum, a roller coaster), and use it to investigate transformations between gravitational potential energy and kinetic energy [PR]

Design and construct a complex device that integrates energy transformations (e.g., a mousetrap vehicle, an ''egg-drop'' container, a wind turbine), and analyse its operation in qualitative and quantitative terms [IP, PR, AI]

Investigate a simple energy transformation (e.g., the use of an elastic band to propel a miniature car), explain the power and output, and calculate the energy [PR, AI, C]

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