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Eastern School District Math 521E Curriculum Outcomes Checklist ESD Curriculum Delivery Math 521E Curriculum Outcomes Checklist Unit 1: Geometry Geometry (G) GCO: Develop spatial sense. SCO-G1: Demonstrate an understanding of basic geometric concepts, including Points; Lines; Line segments; Planes; Angles; Two-dimensional figures. Students who have achieved this outcome should be able to: A. Identify, model and interpret drawings involving points, lines, planes and angles. B. Identify intersecting lines and planes. C. Measure the length of a line segment. D. Identify congruent line segments. E. Find the distance between two points on a number line and on a coordinate plane. F. Find the midpoint of a line segment on a number line and on a coordinate plane. G. Determine the coordinates of an endpoint of a line segment. H. Name, measure and classify angles. I. Identify and use congruent angles and the bisector of an angle. J. Identify and use special pairs of angles. K. Find measures of line segments and angles, by performing calculations and by using algebraic reasoning. L. Identify and name polygons. M. Find the perimeter, circumference and/or area of two-dimensional figures. SCO-G2: Demonstrate an understanding of parallel and perpendicular lines. Students who have achieved this outcome should be able to: A. Identify the relationships between two lines or two planes. B. Identify transversals and classify angle pairs formed by parallel lines and transversals. C. Use theorems about parallel lines to determine the relationships between specific pairs of angles. D. Use algebra to find angle measurements. E. Prove that two lines are parallel using angle relationships. SCO-G3: Demonstrate an understanding of triangles. Students who have achieved this outcome should be able to: A. Identify and classify triangles by angle and side measures. B. Apply the Triangle Angle Sum Theorem to solve a problem. C. Apply the Exterior Angle Theorem to solve a problem. D. Find the missing side and angle values in a triangle. SCO-G4: Demonstrate an understanding of congruent triangles. Students who have achieved this outcome should be able to: A. Identify and use the corresponding parts of two congruent polygons. B. Use the Third Angles Theorem to solve a problem. C. Prove that two triangles are congruent using the definition of congruence. D. Use the SSS, SAS, ASA and AAS postulates to prove that two triangles are congruent. E. Apply triangle congruence in a real-world situation. F. Use the properties of isosceles and equilateral triangles to find missing measures in a triangle. G. Use the properties of isosceles and equilateral triangles within proofs. Math 521E Curriculum Outcomes Checklist Unit 2: Logical Reasoning Logical Reasoning (LR) GCO: Develop logical reasoning. SCO-LR1: Analyse and prove conjectures, using inductive reasoning, to solve problems. Students who have achieved this outcome should be able to: A. Make a conjecture based on inductive reasoning, and use the conjecture to make predictions. B. Find a counterexample to show that a conjecture is false. C. Determine the truth values of negations, conjunctions and disjunctions, and represent them using Venn diagrams. SCO-LR2: Demonstrate an understanding of logical reasoning. Students who have achieved this outcome should be able to: A. Use a Venn diagram to determine whether a conclusion is valid. B. Determine the truth values of negations, conjunctions and disjunctions, and represent them using Venn diagrams. C. Write a compound statement for a given conjunction or disjunction. D. Construct a truth table for a given situation. E. Analyse a statement in “if-then” form by identifying the hypothesis and conclusion. F. Write a conditional statement in “if-then” form. G. Determine the truth value of a conditional statement. H. Write the converse, inverse and contrapositive of an “if-then” statement. SCO-LR3: Analyse and prove conjectures, using deductive reasoning, to solve problems. Students who have achieved this outcome should be able to: A. Determine whether a conclusion is based on inductive or deductive reasoning. B. Use the Law of Detachment to determine whether a conclusion is valid. C. Use the Law of Syllogism to determine whether a conclusion is valid. D. Apply the laws of deductive reasoning to draw a valid conclusion from given statements. SCO-LR4: Use logical reasoning to write geometric and algebraic proofs. Students who have achieved this outcome should be able to: A. Identify, analyse and use the basic postulates about points, lines and planes. B. Justify each step when solving an equation. C. Use algebra to write a two-column proof. D. Use the properties of equality to write a two-column geometric proof. E. Write proofs involving Segment addition and angle addition; Segment congruence and angle congruence; Supplementary and complementary angles; Congruent and right angles; Vertical angles. SCO-LR5: Analyse and prove conjectures, using indirect proof. Students who have achieved this outcome should be able to: A. State the assumption for starting an indirect proof. B. Write indirect algebraic and geometric proofs. Math 521E Curriculum Outcomes Checklist Unit 3: Probability Probability (P) GCO: Develop critical thinking skills related to uncertainty. SCO-P1: Demonstrate an understanding of the probability of an event. Students who have achieved this outcome should be able to: A. Calculate the probability of an event. B. Use tree diagrams to find sample spaces and compute probabilities. C. Use tables to find sample spaces and compute probabilities. SCO-P2: Interpret and assess the validity of odds and probability statements. Students who have achieved this outcome should be able to: A. Determine the probability of, or the odds for and against, an outcome in a situation. B. Express odds as a probability and vice-versa. C. Explain, using examples, the relationship between odds (part-part) and probability (part-whole). D. Solve a contextual problem that involves odds or probability. SCO-P3: Demonstrate an understanding of events that are independent and not independent. Students who have achieved this outcome should be able to: A. Determine whether two events are independent or dependent. B. Compute the probability for events that are independent. C. Explain what is meant by conditional probability. D. Use conditional probability to find the probability of two dependent events. SCO-P4: Demonstrate an understanding of events that are mutually exclusive and not mutually exclusive. Students who have achieved this outcome should be able to: A. Determine whether two events are mutually exclusive. B. Compute the probability for events that are mutually exclusive. C. Compute the probability for events that are not mutually exclusive. Math 521E Curriculum Outcomes Checklist Unit 4: Statistics Statistics (S) GCO: Develop statistical reasoning. SCO-S1: Demonstrate an understanding of data and statistics. Students who have achieved this outcome should be able to: A. Define data and statistics. B. Explain the difference between a population and a sample. C. Describe four basic methods of sampling. SCO-S2: Represent data visually in various ways. Students who have achieved this outcome should be able to: A. Construct a frequency distribution for a data set. B. Draw bar graphs and pie charts. C. Draw histograms and frequency polygons. D. Draw time series graphs. SCO-S3 – Demonstrate an understanding of central tendency by: Determining the measures of central tendency (mean, median, mode); Determining the most appropriate measures of central tendency to report findings. Students who have achieved this outcome should be able to: A. Determine mean, median, and mode for a given set of data, and explain why these values may be the same or different. B. Provide a context in which the mean, median, or mode is the most appropriate measure of central tendency to use when reporting findings. C. Solve a given problem involving the measures of central tendency. SCO-S4: Demonstrate an understanding of dispersion by: Determining the measures of dispersion (variation, standard deviation); Determining the most appropriate measures of dispersion to report findings. Students who have achieved this outcome should be able to: A. Determine variation and standard deviation for a given set of data, and explain why these values may be the same or different. B. Provide a context in which the range, variation or standard deviation is the most appropriate measure of variation to use when reporting findings. C. Solve a given problem involving quartiles or percentiles. D. Calculate the z-score of a data item in a sample or a population. SCO-S5: Demonstrate an understanding of correlation and regression. Students who have achieved this outcome should be able to: A. Construct scatter plots for two data sets. B. Calculate correlation coefficients. C. Determine if correlation coefficients are significant. D. Find a regression line for two data sets. E. Use regression lines to make predictions. SCO-S6: Demonstrate an understanding of the normal distribution. Students who have achieved this outcome should be able to: A. Demonstrate an understanding of continuous probability distributions. B. Explain, using examples, the properties of a normal curve, including the mean, median, mode, standard deviation, symmetry and area under the curve. C. Determine if a data set approximates a normal distribution, and explain the reasoning. D. Compare the properties of two or more normally distributed data sets. E. Explain, using examples that represent multiple perspectives, the application of standard deviation for making decisions in situations such as warranties, insurance or opinion polls. F. Solve a contextual problem that involves the interpretation of standard deviation. G. Determine, with or without technology, and explain the z-score for a given value in a normally distributed data set. H. Solve a contextual problem that involves normal distribution. I. Use the normal distribution to find percentages, probabilities and percentile ranks. Math 521E Curriculum Outcomes Checklist Unit 5: Financial Mathematics (FM) Financial Mathematics (FM) GCO: Develop number sense in financial applications. SCO-FM1: Demonstrate an understanding of income, including... Wages; Salary; Contracts; Commission; Piecework ...to calculate gross and net pay. Students who have achieved this outcome should be able to: A. Describe, using examples, various methods of earning income. B. Determine gross pay from given or calculated hours worked when given: The base hourly wage, with and without tips; The base hourly wage, plus overtime (time and a half, double time). C. Determine gross pay for earnings acquired by: Base wage, plus commission; Single commission rate. D. Complete an income tax form. E. Determine the Canadian Pension Plan (CPP), Employment Insurance (EI) and income tax deductions for a given gross pay. F. Determine the net pay when given deductions, e.g., health plans, uniforms, union dues, charitable donations, payroll tax. SCO-FM2: Solve problems that involve compound interest in financial decision making. Students who have achieved this outcome should be able to: A. Explain the advantages and disadvantages of compound interest and simple interest. B. Identify situations that involve compound interest. C. Compare, in a given situation, the total interest paid or earned for different compounding periods. D. Determine, given the principal, interest rate and number of compounding periods, the total interest of a loan. E. Determine, using technology, the total cost of a loan under a variety of conditions, e.g., different amortization periods, interest rates, compounding periods and terms. F. Compare and explain, using technology, different credit options that involve compound interest, including bank and store credit cards and special promotions. G. Calculate the effective annual rate of interest for a given situation. SCO-FM3: Analyse costs and benefits of renting, leasing and buying. Students who have achieved this outcome should be able to: A. Identify and describe examples of assets that appreciate or depreciate. B. Compare, using examples, renting, leasing and buying, and determine which would be the best choice for a specific set of circumstances. C. Calculate the mortgage payments for a given set of circumstances. SCO-FM4: Develop a budget for a given set of circumstances. Students who have achieved this outcome should be able to: A. Collect primary or secondary data (statistical or informational) related to the topic. B. Assess the accuracy, reliability and relevance of the primary and secondary data collected by: Identifying examples of bias and points of view; Identifying and describing the data collection methods; Determining if the data is relevant; Determining if the data is consistent with information obtained from other sources on the same topic. C. Interpret data, using statistical methods if applicable. D. Identify controversial issues, if any, and present multiple sides of the issues with supporting data. E. Organize and present the research project, with or without technology. Curriculum Guide Supplement This supplement to the Prince Edward Island MAT521E Mathematics Curriculum Guide is designed to parallel the primary resources, Geometry, Mathematics of Data Management, and MathPower 11. For each of the units, an approximate timeframe is suggested to aid teachers with planning. The timeframe is based on a total of 80 classes, each with an average length of 75 minutes: Chapter 01 – Tools of Geometry 02 – Reasoning and Proof 03 – Parallel and Perpendicular Lines 04 – Congruent Triangles 05 – Statistics of One Variable 06 – Statistics of Two Variables 07 – Introduction to Probability 08 – The Normal Distribution 09 – Personal Finance Suggested Time 11 Classes 12 Classes 5 Classes 12 Classes 11 Classes 6 Classes 8 Classes 7 Classes 8 Classes Each unit is divided into a number of sections. In this document, each section is supported by a one-page presentation, which includes the following information: The name and pages of the section in the text; The specific curriculum outcome(s) and achievement indicator(s) addressed in the section (see the first half of the curriculum guide for an explanation of symbols); The student expectations for the section, which are associated with the SCO(s); The new concepts introduced in the section; Other key ideas developed in the section; Suggested problems in Geometry, Mathematics of Data Management, or MathPower 11; Possible instructional and assessment strategies for the section.