Course Outline for Grade 12 College Foundations MAP4C

Transcription

1 Course Outline for Grade 12 College Foundations MAP4C UNIT 1 TRIGONOMETRY Pearson Pg # , Introduction to Trigonometry, Primary Trig Ratios C3.1 solve problems in two dimensions using metric measurements, including problems that arise from real-world. Pg #6-8 Primary Trig. Ratios - Angles C3.1 solve problems in two dimensions using metric or imperial measurements, including problems that arise from realworld applications. Pg. 19, #5,6 Pg. 23, 3,7,8,11,13 Pg #3,5,13 Pg #4ac,7ac,8b Pg. 33 # Pg. 39 # , 1.3 Obtuse Angles C3.3 determine the values of the sine, cosine, and tangent of obtuse angles. 1.4 Sine Law C3.1 solve problems in two dimensions using metric measurements, including problems that arise from real-world. 1.5 Cosine Law C3.1 solve problems in two dimensions using metric measurements, including problems that arise from real-world Solving Trig Word Problems C3.2 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. Pg #6,7,10,12,13,16 Pg #2,6-8,10,12,15 Pg. 57 TBA 1.6 Word Problems C3.4 solve problems involving oblique triangles, including those that arise from real-world applications, using the sine law (in nonambiguous cases only) and the cosine law, and using metric units. C3.5 gather, interpret, and describe information about applications of trigonometry in occupations, and about college programs that explore these applications. Review study guide on pg. 53 Summative Quiz Take-up Summative and more review (Practise Test)

2 UNIT 2 - MEASUREMENT AND GEOMETRY Pearson Pg Do all checks Activate Prior Knowledge Measurement Conversion C1.1 perform required conversions between the imperial system and the metric system using a variety of tools. Pg #4,5,6,9,10, 12 Pg #2,8a,11,12, 15 Pg #4, 7c, 8bc,16,18 Pg #1,4,5,6,7,8, 13 Pg #2,3,9,10,11, Area of Composite Shapes C1.2 solve problems involving the areas of rectangles, triangles, and circles, and of related composite shapes. C1.3 solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite 2.2 Volume C1.3 solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite 2.2 Surface Area C1.3 solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related composite 2.3 Maximum Area for a Given Perimeter include triangles and trigonometry 2.3 Minimum Perimeter for a Given Area area, and volume in various applications C2.2 determine, through investigation using a dimensions of a two dimensional shape in metric or imperial units for a given constraint. area, and volume in various applications C2.2 determine, through investigation using a dimensions of a two dimensional shape in metric or imperial units for a given constraint Pg #4,6 2.6 Maximum Volume for a Given Surface Area

3 UNIT 3 Two Variable Data Pg #9, Minimum Surface Area for a Given Volume area, and volume in various applications. C2.3 determine, through investigation using a dimensions of a right rectangular prism, a right triangular prism, and a right cylinder in metric or imperial units for a given constraint. area, and volume in various applications. C2.3 determine, through investigation using a dimensions of a right rectangular prism, a right triangular prism, and a right cylinder in metric or imperial units for a given constraint. Pg #1-10,15 Pg. 123 #1-6 Performance Task Review Day 1 Summative Quiz Review Day 2 C1. solve problems involving measurement and geometry and arising from real-world applications; C2. explain the significance of optimal dimensions in real-world applications, and determine optimal dimensions of twodimensional shapes and three-dimensional Pearson Pg. 133 #1, 2, 4, 5, 7, One and Two Variable Data A2.1 interpret graphs to describe a relationship using language and units appropriate to the context A2.2 describe trends based on given graphs, and use the trends to make predictions or justify decisions Sample problem: Given the following graph, describe the trend in Canadian greenhouse gas emissions over the time period shown. Describe some factors that may have influenced these emissions over time. Predict the emissions today, explain your prediction using the graph and possible factors, and verify using current data. D1.3 collect two-variable data from primary sources, through experimentation involving observation or measurement, or from secondary sources and organize and store the data using a variety of tools Sample problem: Download census data from Statistics Canada on age and average income, store the data using dynamic statistics

4 Pg. 142 #1,2,3,5,7b,8,10,12 Pg. 153 #2,3,4,6,7,8,9 Pg.159 # Scatter Plots to Identify Relationships 3.3 Line of Best Fit 3.4 Line of Best Fit Using Technology software, and organize the data in a summary table. D1.4 create a graphical summary of two-variable data using a scatter plot with and without technology A1.1 distinguish situations requiring onevariable and two-variable data analysis, describe the associated numerical summaries and graphical summaries and recognize questions that each type of analysis addresses Sample problem: Given a table showing shoe size and height for several people, pose a question that would require one-variable analysis and a question that would require two-variable analysis of the data. A1.5 determine an algebraic summary of the relationship between two variables that appear to be linearly related (using a variety of tools and strategies and solve related problems A1.8 make conclusions from the analysis of twovariable data and judge the reasonableness of the conclusions explain how the media, the advertising industry, and others use and misuse statistics to promote a certain point of view D1.7 determine whether a linear model is appropriate given a set of two-variable data, by assessing the correlation between the two variables. D1.6 describe possible interpretations of the line of best fit of a scatter plot and reasons for misinterpretations Pg #1-9 Pg. 186 #1-10, 13 Pg. 189 # Conducting an Experiment to collect Two-Variable Data Day 2: Experiment...replace the summative quiz Review Day 1 Return and Take-up Summative Quiz Review Day 2: Practice Test D1. collect, analyse, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data; D2. demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations D1.2 describe characteristics of an effective survey and design questionnaires or experiments for gathering two-variable data UNIT 4 Statistical Literacy Pearson Pg.192 #1-3 Pg. 193 # 1, 2 Pg. 194 # 1, 2 Pg. 200 #1, 2, 4, 7, 8, 9, 11 4 Activate Prior Knowledge 4.1 Interpreting Statistics 2.1 recognize and interpret common statistical terms 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,

5 With a partner: Complete Inquire on page 206 Pg. 229 #1 5, 8, 12 Pg. 237 #1 5, 7, 11 Inquire on pg. 246 In class assignment Pg #1 4, 9 12, Statistics in the Media 4.5 Use and Misuse of Statistics 4.6 Understanding Indices 4.8 Statistical Literacy and Occupations Summative Assessment Review newspapers) 2.3 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) 2.4 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) Sample problem: The headline that accompanies the following graph says "Big Increase in Profits". Suggest reasons why this head-line may or may not be true. (omitted graph from page 145) 2.2 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) Sample problem: Use the new housing price index on E-STAT to track the cost of purchasing a new home over the past 10 years in the Toronto area, and compare with the cost in Calgary, Charlottetown, and Vancouver over the same period. Predict how much a new home that today costs $ in each of these cities will cost in 5 years 2.5 gather, interpret, and describe information about applications of data management in occupations, and about college programs that explore these applications 2.5 gather, interpret, and describe information about applications of data management in occupations, and about college programs that explore these applications

6 UNIT 5 Graphical Models and Algebraic Models Pearson Pg. 293 #1-7, 9, 10 Pg. 303 #1-7, 10 Pg. 315 #1-8, 11, 14 Pg #1a, 2b, 4, 5a, 6c, 7, 8, 9, 11, Day Day Day3 Graphing Functions (Linear, Quadratic, and Exponential) Graphing calculator needed. This will take 2 3 days. There will be a minisummative after these lessons. A2.1 interpret graphs to describe a relationship using language and units appropriate to the context A2.2 describe trends based on given graphs, and use the trends to make predictions or justify decisions A2.3 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 A2.4 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 A2.5 compare, through investigation with technology, the graphs of pairs of relations by describing the initial conditions and the behaviour of the rates of A2.6 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 and strategies and solve related problems. 6.2 Rearranging Formulas A3.2 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 Pg #1-6, 7b, 8c, 9,10, 12, 14 Pg #1-6, 10, 12 Pg #1-7, Exponent Laws (integer exponents) 6.5 Powers with Rational Exponents (x m/n ) 6.6 Solving Exponential Equations A1.1 determine, through investigation the exponent laws for multiplying and dividing algebraic expressions involving exponents and the exponent law for simplifying algebraic expressions involving a power of a power. A1.2 simplify algebraic expressions containing integer exponents using the laws of exponents. A1.3 determine, through investigation using a variety of tools (and strategies, the value of a power with a rational exponent A1.4 evaluate, with or without technology, numerical expressions involving rational exponents and rational bases. A1.5 solve simple exponential equations numerically and graphically, with technology and recognize that the solutions may not be exact. A3.4 solve multi-step problems requiring formulas arising from real-world applications. A1.7 solve exponential equations in one variable by determining a common base. A3.1 solve equations of the form x n = a using rational exponents.

7 Pg #1-5, 8, 13 Pg. 399 Pg #5-25 Practice Test Pg. 403 # Solving Applications for Exponential Equations x n = a Graphic calculators needed. Study Guide & Chapter Review Review Summative Quiz Take-up Quiz and review A1.6 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 A3.3 make connections between formulas and linear, quadratic, and exponential functions, using a variety of tools and strategies A3.5 gather, interpret, and describe information about applications of mathematical modelling in occupations, and about college programs that explore these applications. UNIT 6 Budgets Pearson