Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Purpose • to define the required Advanced Stream Mathematics Student Learning Outcomes to be covered during the term for this grade • to recommend the pace at which the Student Learning Outcomes are to be covered. The term’s content is broken down into nine teaching weeks, allowing the coverage of topics within each week to be flexible. Assessment • Assessment details for Term 2 will be communicated separately. Teachers should incorporate the Standards for Mathematical Practice (SMPs) in their instruction when and where appropriate. The Standards for Mathematical Practice are 1. 2. 3. 4. 5. 6. 7. 8. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Why are the Standards for Mathematical Practice important? The Standards for Mathematical Practice set expectations for using mathematical language and representations to reason, solve problems, and model in preparation for careers and a wide range of college majors. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 1: Jan. 3 – 7, 2022 Integrated II Module 9 – Linear Equations, Inequalities, and Systems Lessons Student Learning Outcomes M9L4 – Solving Systems of Equations Graphically • Solve systems of linear equations by graphing. • Solve systems of equations by using the substitution method. Algebraically • Solve systems of equations by using the elimination method. • Solve systems of linear inequalities in two M9L6 – Solving Systems of Inequalities variables. M9L5 – Solving Systems of Equations Common Core State Standards A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A.REI.11 Explain why the π₯-coordinates of the points where the graphs of the equations π¦ = π(π₯) and π¦ = π(π₯) intersect are the solutions of the equation π(π₯) = π(π₯); ο¬nd the solutions approximately, e.g., using technology to graph the functions, make tables of values, or ο¬nd successive approximations. Include cases where π(π₯) and/or π(π₯) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 2: Jan. 10 – 14, 2022 Lessons Student Learning Outcomes M9L6 – Solving Systems of Inequalities M9L7 – Optimization with Linear Programming • Solve systems of linear inequalities in two variables. • Find maximum and minimum values of a functions over a region. • Solve real-world optimization problems by graphing systems of inequalities maximizing or minimizing constraints. Common Core State Standards A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 3: Jan. 17 – 21, 2022 Lessons Student Learning Outcomes M9L8 – Systems of Equations in Three Variables • Solve systems of linear equations in three variables. M9L9 – Solving Absolute Value Equations and Inequalities by Graphing • Solve absolute value equations. • Solve absolute value inequalities. Common Core State Standards A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 4: Jan. 24 – 28, 2022 Integrated II Module 13 – Trigonometric Equations and Identities Lessons Student Learning Outcomes M13L1 – Trigonometric Identities • Find trigonometric values by using trigonometric identities. • Simplify trigonometric expressions by using trigonometric identities. M13L2 – Verifying Trigonometric Identities • Verify trigonometric identities. M13L3 – Sum and Difference Identities • Find values of sine and cosine by using sum and difference identities. • Verify trigonometric identities by using sum and difference identities. Common Core State Standards F.TF.8 Prove the Pythagorean identity sin2 (π) + cos2 (π) = 1 and use it to ο¬nd sin(π), cos(π), or tan(π), given sin(π), cos(π), or tan(π), and the quadrant of the angle. F.TF.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 5: Jan. 31 – Feb. 4, 2022 Lessons Student Learning Outcomes M13L4 – Double-Angle and Half-Angle Identities M13L5 – Solving Trigonometric Equations Common Core State Standards • Find values of sine and cosine by using double-angle identities. • Find values of sine and cosine by using half-angle identities. F.TF.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. • Solve trigonometric equations. F.TF.8 Prove the Pythagorean identity sin2 (π) + cos2 (π) = 1 and use it to ο¬nd sin(π), cos(π), or tan(π), given sin(π), cos(π), or tan(π), and the quadrant of the angle. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 6: Feb. 7 – 11, 2022 Integrated III Module 1 – Quadratic Functions Lessons M1L1 – Graphing Quadratic Functions Student Learning Outcomes • Graph quadratic functions. • Find and interpret the average rate of change of quadratic functions given symbolically, in tables, and in graphs. M1L2 – Solving Quadratic Equations by • Solve quadratic equations by graphing. Graphing Common Core State Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a speciο¬ed interval. Estimate the rate of change from a graph. A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 7: Feb. 14 – 18, 2022 Lessons Student Learning Outcomes • M1L3 – Complex Numbers • • M1L4 – Solving Quadratic Equations by • Factoring Common Core State Standards N.CN.1 Know there is a complex number π such that π 2 = −1, and every complex number has the form π + ππ Perform operations with pure imaginary with π and π real. numbers. N.CN.2 Use the relation π 2 = −1 and the commutative, Perform operations with complex numbers. associative, and distributive properties to add, subtract, and multiply complex numbers. N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. N.CN.8 Extend polynomial identities to the complex numbers. For example, rewrite π₯ 2 + 4 as (π₯ + 2π)(π₯ − 2π). Solve quadratic equations by factoring. F.IF.8 Write a function defined by an expression in Solve quadratic equations by factoring different but equivalent forms to reveal and explain special products. different properties of the function. F.IF.8a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 8: Feb. 21 – 25, 2022 Lessons Student Learning Outcomes Common Core State Standards N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. F.IF.8a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. N.CN.8 Extend polynomial identities to the complex • Solve quadratic equations by using the numbers. For example, rewrite π₯ 2 + 4 as Quadratic Formula. (π₯ + 2π)(π₯ − 2π). • Determine the number and type of roots of A.SSE.1 Interpret expressions that represent a quantity a quadratic equation. in terms of its context. A.SSE.1b. Interpret complicated expressions by viewing one or more of their parts as a single entity. • Solve quadratic equations by using the Square Root Property. • Complete the square in quadratic M1L5 – Solving Quadratic Equations by expressions to solve quadratic equations. Completing the Square • Complete the square in a quadratic function to interpret key features of its graph. M1L6 – Using the Quadratic Formula and the Discriminant Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022 Week 9: Feb. 28 – March 4, 2022 Lessons M1L7 – Quadratic Inequalities Student Learning Outcomes Common Core State Standards A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, • Graph quadratic inequalities in two variables. and simple rational and exponential functions. • Solve quadratic inequalities in two variables A.CED.3 Represent constraints by equations or by graphing. inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Week 10: March 7 – 11, 2022 Week 11: March 14 – 18, 2022 Week 12: March 21 – 25, 2022 Term 2 Revision and End-of-Term Exam Exam date to be determined by the Assessment Directorate Grade 10 Advanced Stream Scheme of Work, Term 2, Academic Year 2021-2022
