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)

Addition and Subtraction of Functions
Quadratics in Polynomial Form

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)

Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translations
Zap It! Game

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)

Quadratics in Vertex Form
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

Quadratics in Vertex Form

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 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

Polynomials and Linear Factors
Quadratics in Factored Form

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 Polynomial Form

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
Exponents and Power Rules
Multiplying Exponential Expressions

A.2.4: graph simple exponential relations, using paper and pencil, given their equations [e.g., y = 2 to the x power, y = 10 to the x power, y = (½) to the x power]

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

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

Introduction to Exponential Functions

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

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)

Introduction to Exponential Functions

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

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

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

Compound Interest
Exponential Growth and Decay

B.1.4: calculate the total interest earned on an investment or paid on a loan by determining the difference between the amount and the principal [e.g., using I = A – P (or I = FV – PV)]

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

Compound Interest

B.2: compare services available from financial institutions, and solve problems involving the cost of making purchases on credit;

B.2.4: gather, interpret, and compare information about current credit card interest rates and regulations, and determine, through investigation using technology, the effects of delayed payments on a credit card balance

Compound Interest

B.2.5: solve problems involving applications of the compound interest formula to determine the cost of making a purchase on credit

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.1.2: 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

C.1.4: solve design problems that satisfy given constraints (e.g., design a rectangular berm that would contain all the oil that could leak from a cylindrical storage tank of a given height and radius), using physical models (e.g., built from popsicle sticks, cardboard, duct tape) or drawings (e.g., made using design or drawing software), and state any assumptions made

Segment and Angle Bisectors

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, Cosine, and Tangent Ratios

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
Populations and Samples

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
Stem-and-Leaf Plots

D.1.6: identify and describe properties associated with common distributions of data (e.g., normal, bimodal, skewed)

Mean, Median, and Mode
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

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)

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

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)

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

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

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Real-Time Histogram

D.1.10: solve problems by interpreting and analysing one-variable data collected from secondary sources

Describing Data Using Statistics

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

D.2.1: identify examples of the use of probability in the media 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)

Probability Simulations
Theoretical and Experimental Probability

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)

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
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

Binomial Probabilities
Polling: City
Probability Simulations

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

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

D.2.5: 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 tossing tails is likely to be closer to the theoretical probability than if I simulate tossing the coin only 10 times”)

Geometric Probability