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Skills available for Ontario grade 11 math curriculum

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11.A Mathematical Models

11.B Personal Finance

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

    • 11.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

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

    • 11.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)]

    • 11.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)]

    • 11.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)]

    • 11.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

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

    • 11.B.2.1 gather, interpret, and compare information about the various savings alternatives commonly available from financial institutions (e.g., savings and chequing accounts, term investments), the related costs (e.g., cost of cheques, monthly statement fees, early withdrawal penalties), and possible ways of reducing the costs (e.g., maintaining a minimum balance in a savings account; paying a monthly flat fee for a package of services)

    • 11.B.2.2 gather and interpret information about investment alternatives (e.g., stocks, mutual funds, real estate, GICs, savings accounts), and compare the alternatives by considering the risk and the rate of return

    • 11.B.2.3 gather, interpret, and compare information about the costs (e.g., user fees, annual fees, service charges, interest charges on overdue balances) and incentives (e.g., loyalty rewards; philanthropic incentives, such as support for Olympic athletes or a Red Cross disaster relief fund) associated with various credit cards and debit cards

    • 11.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

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

  • 11.B.3 interpret information about owning and operating a vehicle, and solve problems involving the associated costs.

    • 11.B.3.1 gather and interpret information about the procedures and costs involved in insuring a vehicle (e.g., car, motorcycle, snowmobile) and the factors affecting insurance rates (e.g., gender, age, driving record, model of vehicle, use of vehicle), and compare the insurance costs for different categories of drivers and for different vehicles

    • 11.B.3.2 gather, interpret, and compare information about the procedures and costs (e.g., monthly payments, insurance, depreciation, maintenance, miscellaneous expenses) involved in buying or leasing a new vehicle or buying a used vehicle

    • 11.B.3.3 solve problems, using technology (e.g., calculator, spreadsheet), that involve the fixed costs (e.g., licence fee, insurance) and variable costs (e.g., maintenance, fuel) of owning and operating a vehicle

11.C Geometry and Trigonometry

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

    • 11.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)

    • 11.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)

    • 11.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

    • 11.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

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

11.D Data Management

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

    • 11.D.1.1 identify situations involving one-variable data (i.e., data about the frequency of a given occurrence), and design questionnaires (e.g., for a store to determine which CDs to stock, for a radio station to choose which music to play) or experiments (e.g., counting, taking measurements) for gathering one-variable data, giving consideration to ethics, privacy, the need for honest responses, and possible sources of bias

    • 11.D.1.2 collect one-variable data from secondary sources (e.g., Internet databases), and organize and store the data using a variety of tools (e.g., spreadsheets, dynamic statistical software)

    • 11.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)

    • 11.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

    • 11.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)

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

    • 11.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)

    • 11.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)

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

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

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

    • 11.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)

    • 11.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)

    • 11.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

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

    • 11.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")

    • 11.D.2.6 interpret information involving the use of probability and statistics in the media, and make connections between probability and statistics (e.g., statistics can be used to generate probabilities)