A: Mathematical Models

A.1: make connections between the numeric, graphical, and algebraic representations of quadratic relations, and use the connections to solve problems;

A.1.1: construct tables of values and graph quadratic relations arising from real-world applications (e.g., dropping a ball from a given height; varying the edge length of a cube and observing the effect on the surface area of the cube)

Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A.1.2: determine and interpret meaningful values of the variables, given a graph of a quadratic relation arising from a real-world application

Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A.1.3: determine, through investigation using technology, the roles of a, h, and k in quadratic relations of the form y = a(x - h)² + k, and describe these roles in terms of transformations on the graph of y = x² (i.e., translations; reflections in the x-axis; vertical stretches and compressions to and from the x-axis)

Quadratics in Factored Form
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

A.1.4: sketch graphs of quadratic relations represented by the equation y = a(x - h)² + k (e.g., using the vertex and at least one point on each side of the vertex; applying one or more transformations to the graph of y = x²)

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

A.1.6: express the equation of a quadratic relation in the standard form y = ax² + bx + c, given the vertex form y = a(x - h)² + k, and verify, using graphing technology, that these forms are equivalent representations

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic

A.1.7: factor trinomials of the form ax² + bx + c , where a = 1 or where a is the common factor, by various methods

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A.1.8: determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts of the graph of the corresponding quadratic relation

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Quadratics in Factored Form
Roots of a Quadratic

A.1.9: solve problems, using an appropriate strategy (i.e., factoring, graphing), given equations of quadratic relations, including those that arise from real-world applications (e.g., break-even point)

Quadratics in Factored Form
Roots of a Quadratic

A.2: demonstrate an understanding of exponents, and make connections between the numeric, graphical, and algebraic representations of exponential relations;

A.2.1: determine, through investigation using a variety of tools and strategies (e.g., graphing with technology; looking for patterns in tables of values), and describe the meaning of negative exponents and of zero as an exponent

Dividing Exponential Expressions

A.2.2: evaluate, with and without technology, numeric expressions containing integer exponents and rational bases (e.g., 2 to the -3rd power, 6³, 3456 to the 0 power, 1.03 to the 10th power)

Exponents and Power Rules
Fractions with Unlike Denominators

A.2.3: determine, through investigation (e.g., by patterning with and without a calculator), the exponent rules for multiplying and dividing numerical expressions involving exponents [e.g., (½)³ x (½)²], and the exponent rule for simplifying numerical expressions involving a power of a power [e.g.,(5³)²]

Multiplying Exponential Expressions

A.2.5: make and describe connections between representations of an exponential relation (i.e., numeric in a table of values; graphical; algebraic)

Exponential Functions - Activity A

A.2.6: distinguish exponential relations from linear and quadratic relations by making comparisons in a variety of ways (e.g., comparing rates of change using finite differences in tables of values; inspecting graphs; comparing equations), within the same context when possible (e.g., simple interest and compound interest, population growth)

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Quadratics in Factored Form
Roots of a Quadratic
Simple and Compound Interest

A.3: describe and represent exponential relations, and solve problems involving exponential relations arising from real-world applications.

A.3.1: collect data that can be modelled as an exponential relation, through investigation with and without technology, from primary sources, using a variety of tools (e.g., concrete materials such as number cubes, coins; measurement tools such as electronic probes), or from secondary sources (e.g.,websites such as Statistics Canada, E-STAT), and graph the data

Exponential Functions - Activity A

A.3.2: describe some characteristics of exponential relations arising from real-world applications (e.g., bacterial growth, drug absorption) by using tables of values (e.g., to show a constant ratio, or multiplicative growth or decay) and graphs (e.g., to show, with technology, that there is no maximum or minimum value)

Exponential Functions - Activity A

A.3.3: pose problems involving exponential relations arising from a variety of real-world applications (e.g., population growth, radioactive decay, compound interest), and solve these and other such problems by using a given graph or a graph generated with technology from a given table of values or a given equation

Exponential Functions - Activity A
Simple and Compound Interest

A.3.4: solve problems using given equations of exponential relations arising from a variety of real-world applications (e.g., radioactive decay, population growth, height of a bouncing ball, compound interest) by substituting values for the exponent into the equations

Simple and Compound Interest

B: Personal Finance

B.1: compare simple and compound interest, relate compound interest to exponential growth, and solve problems involving compound interest;

B.1.1: determine, through investigation using technology, the compound interest for a given investment, using repeated calculations of simple interest, and compare, using a table of values and graphs, the simple and compound interest earned for a given principal (i.e., investment) and a fixed interest rate over time

Simple and Compound Interest

B.1.2: determine, through investigation (e.g., using spreadsheets and graphs), and describe the relationship between compound interest and exponential growth

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Simple and Compound Interest

B.1.3: solve problems, using a scientific calculator, that involve the calculation of the amount, A (also referred to as future value, FV), and the principal, P (also referred to as present value, PV), using the compound interest formula in the form A = P((1 + i) to the n power) [or FV = PV((1 + i)to the n power)]

Simple and Compound Interest

B.1.5: solve problems, using a TVM Solver on a graphing calculator or on a website, that involve the calculation of the interest rate per compounding period, i, or the number of compounding periods, n, in the compound interest formula A = P((1 + i) to the n power) [or FV = PV((1 + i) to the n power)]

Simple and Compound Interest

B.1.6: determine, through investigation using technology (e.g., a TVM Solver on a graphing calculator or on a website), the effect on the future value of a compound interest investment or loan of changing the total length of time, the interest rate, or the compounding period

Simple and Compound Interest

C: Geometry and Trigonometry

C.1: represent, in a variety of ways, two-dimensional shapes and three-dimensional figures arising from real-world applications, and solve design problems;

C.1.1: recognize and describe real-world applications of geometric shapes and figures, through investigation (e.g., by importing digital photos into dynamic geometry software), in a variety of contexts (e.g., product design, architecture, fashion), 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)

Classifying Quadrilaterals - Activity B

C.1.2: represent three-dimensional objects, using concrete materials and design or drawing software, in a variety of ways (e.g., orthographic projections [i.e., front, side, and top views], perspective isometric drawings, scale models)

3D and Orthographic Views - Activity A

C.1.3: create nets, plans, and patterns from physical models arising from a variety of real-world applications (e.g., fashion design, interior decorating, building construction), by applying the metric and imperial systems and using design or drawing software

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

C.2: solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications.

C.2.1: solve problems, 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

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

D: Data Management

D.1: solve problems involving one-variable data by collecting, organizing, analysing, and evaluating data;

D.1.3: 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)

Polling: City
Polling: Neighborhood

D.1.4: describe and compare sampling techniques (e.g., random, stratified, clustered, convenience, voluntary); collect one-variable data from primary sources, using appropriate sampling techniques in a variety of real-world situations; and organize and store the data

Polling: Neighborhood

D.1.5: identify different types of one-variable data (i.e., categorical, discrete, continuous), and represent the data, with and without technology, in appropriate graphical forms (e.g., histograms, bar graphs, circle graphs, pictographs)

Histograms

D.1.7: calculate, using formulas and/or technology (e.g., dynamic statistical software, spreadsheet, graphing calculator), and interpret measures of central tendency (i.e., mean, median, mode) and measures of spread (i.e., range, standard deviation)

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

D.1.8: explain the appropriate use of measures of central tendency (i.e., mean, median, mode) and measures of spread (i.e., range, standard deviation)

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

D.1.9: compare two or more sets of one-variable data, using measures of central tendency and measures of spread

Describing Data Using Statistics
Line Plots
Populations and Samples

D.2: determine and represent probability, and identify and interpret its applications.

D.2.2: 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)

Geometric Probability - Activity A
Probability Simulations
Theoretical and Experimental Probability

D.2.3: perform a probability experiment (e.g., tossing a coin several times), represent the results using a frequency distribution, and use the distribution to determine the experimental probability of an event

Geometric Probability - Activity A
Line Plots
Populations and Samples
Probability Simulations
Theoretical and Experimental Probability

D.2.4: compare, through investigation, the theoretical probability of an event with the experimental probability, and explain why they might differ

Probability Simulations
Theoretical and Experimental Probability

D.2.5: determine, through investigation using classgenerated 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 tossing tails is likely to be closer to the theoretical probability than if I simulate tossing the coin only 10 times")

Geometric Probability - Activity A
Polling: City
Probability Simulations
Solving Using Trend Lines
Theoretical and Experimental Probability