Ontario Curriculum
A.1.1: determine, through investigation (e.g., by expanding terms and patterning), the exponent laws for multiplying and dividing algebraic expressions involving exponents [e.g., (x³)(x²), x³ ÷ (x to the 5th power)] and the exponent law for simplifying algebraic expressions involving a power of a power [e.g. (x to the 6th power times y³)²]
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
A.1.2: simplify algebraic expressions containing integer exponents using the laws of exponents
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
A.1.6: 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) to the n power), where h represents the height of a bouncing ball and n represents the number of bounces]
Cosine Function
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
A.2.1: 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
Cosine Function
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Sine Function
Tangent Function
A.2.2: describe trends based on given graphs, and use the trends to make predictions or justify decisions (e.g., given a graph of the men's 100-m world record versus the year, predict the world record in the year 2050 and state your assumptions; given a graph showing the rising trend in graduation rates among Aboriginal youth, make predictions about future rates)
Arithmetic Sequences
Arithmetic and Geometric Sequences
Correlation
Geometric Sequences
Solving Using Trend Lines
A.2.5: compare, through investigation with technology, the graphs of pairs of relations (i.e., linear, quadratic, exponential) by describing the initial conditions and the behaviour of the rates of change (e.g., compare the graphs of amount versus time for equal initial deposits in simple interest and compound interest accounts)
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Simple and Compound Interest
A.2.6: 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
Exponential Growth and Decay - Activity B
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
A.3.3: make connections between formulas and linear, quadratic, and exponential functions [e.g., recognize that the compound interest formula, A = P((1 + i) to the n power), 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)
Exponential Functions - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Simple and Compound Interest
A.3.5: gather, interpret, and describe information about applications of mathematical modelling in occupations, and about college programs that explore these applications
Exponential Growth and Decay - Activity B
B.1.2: determine, through investigation using technology (e.g., the TVM Solver on a graphing calculator; online tools), the effects of changing the conditions (i.e., the payments, the frequency of the payments, the interest rate, the compounding period) of an ordinary simple annuity (i.e., an annuity in which payments are made at the end of each period, and compounding and payment periods are the same) (e.g., long-term savings plans, loans)
B.1.5: gather and interpret information about mortgages, describe features associated with mortgages (e.g., mortgages are annuities for which the present value is the amount borrowed to purchase a home; the interest on a mortgage is compounded semi-annually but often paid monthly), and compare different types of mortgages (e.g., open mortgage, closed mortgage, variable-rate mortgage)
B.1.7: generate an amortization table for a mortgage, using a variety of tools and strategies (e.g., input data into an online mortgage calculator; determine the payments using the TVM Solver on a graphing calculator and generate the amortization table using a spreadsheet), calculate the total interest paid over the life of a mortgage, and compare the total interest with the original principal of the mortgage
B.1.8: determine, through investigation using technology (e.g., TVM Solver, online tools, financial software), the effects of varying payment periods, regular payments, and interest rates on the length of time needed to pay off a mortgage and on the total interest paid
C.1.2: solve problems involving the areas of rectangles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications
Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
C.1.3: 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
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
C.2.1: 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)
C.2.2: 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)
C.2.3: determine, through investigation using a variety of tools and strategies (e.g., modelling with manipulatives; making a table of values; graphing), the optimal dimensions of a right rectangular prism, a right triangular prism, and a right cylinder in metric or imperial units for a given constraint (e.g., the dimensions that give the maximum volume for a given surface area)
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
C.3.1: 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
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
C.3.2: make connections between primary trigonometric ratios (i.e., sine, cosine, tangent) of obtuse angles and of acute angles, through investigation using a variety of tools and strategies (e.g., using dynamic geometry software to identify an obtuse angle with the same sine as a given acute angle; using a circular geoboard to compare congruent triangles; using a scientific calculator to compare trigonometric ratios for supplementary angles)
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
C.3.3: determine the values of the sine, cosine, and tangent of obtuse angles
Classifying Triangles
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
D.1.1: 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?)
D.1.4: 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
Correlation
Lines of Best Fit Using Least Squares - Activity A
Scatter Plots - Activity A
Solving Using Trend Lines
D.1.6: 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)
Correlation
Lines of Best Fit Using Least Squares - Activity A
Solving Using Trend Lines
D.1.8: make conclusions from the analysis of twovariable 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)
Correlation
Solving Using Trend Lines
D.2.1: 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)
Correlation last revised: 8/18/2015