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TEACHING PLAN 2B Stage 8 Learning Objectives Chapter 13 Trigonometric Ratios 1 • Understand the sine, cosine and tangent ratios for angles between 0 to 90 • Explore the properties and relations of trigonometric ratios • Explore the exact value of trigonometric ratios on special angles 30, 45 and 60 • Apply trigonometric ratios to find measures of 2-D figures Teaching Focus Let’s Review (p.246) Suggested No. of Periods • Students should be able to find: - the sine ratios in right-angled triangles. - the sine ratios using a calculator. - the angles from sine ratios using a calculator. - the lengths of sides in right-angled triangles. - the angles in right-angled triangles. Special Items 0.5 period • Worksheet 13.0 (Sets 1 & 2) • Test Bank 13.0 • E Textbook 2 periods • Additional Examples 13.1 – 13.6 • Worksheet 13.1 (Sets 1 & 2) • Workbook 13.1 • Ongoing Assessment Package: Quiz 13.1 • Test Bank 13.1 • E Textbook • PowerPoint Presentation • Inspiring Task 13.1 Exploring the Meaning of Sine Ratios (p.247) • e-Figure Gallery • Teachers can ask students to review the properties of similar triangles. • Teachers can ask students to review Pythagoras’ theorem. 13.1 Sine Ratio (pp.246 – 255) Consolidation & Assessment Additional Information Teaching Plan 2B Teaching Focus 13.2 Cosine Ratio (pp.256 – 263) Suggested No. of Periods 2 • Students should be able to find: - the tangent ratios in right-angled triangles. - the tangent ratios using a calculator. - the angles from tangent ratios using a calculator. - the lengths of sides in right-angled triangles. - the angles in right-angled triangles. Special Items 2 periods • Additional Examples • E Textbook 13.7 – 13.12 • PowerPoint • Worksheet 13.2 Presentation (Sets 1 & 2) • e-Figure Gallery • Workbook 13.2 • Ongoing Assessment Package: Quiz 13.2 • Test Bank 13.2 2 periods • Additional Examples • E Textbook 13.13 – 13.18 • PowerPoint • Worksheet 13.3 Presentation (Sets 1 & 2) • e-Figure Gallery • Workbook 13.3 • Ongoing Assessment Package: Quiz 13.3 • Test Bank 13.3 • Students should be able to find: - the cosine ratios in right-angled triangles. - the cosine ratios using a calculator. - the angles from cosine ratios using a calculator. - the lengths of sides in right-angled triangles. - the angles in right-angled triangles. 13.3 Tangent Ratio (pp.264 – 271) Consolidation & Assessment Additional Information New Progress in Junior Mathematics 2B Learning Objectives Learning Objectives Teaching Focus 13.4 Trigonometric Ratios of Some Special Angles (pp.272 – 276) Suggested No. of Periods 3 • Students should be able to find the sine, cosine or tangent ratio from a given sine, cosine or tangent ratio by constructing right-angled triangles. Special Items 1 period • Additional Examples • E Textbook 13.19 – 13.20 • PowerPoint • Worksheet 13.4 Presentation (Sets 1 & 2) • Inspiring Task 13.2 • Workbook 13.4 Exploring the • Ongoing Assessment Trigonometric Ratio Package: Quiz 13.4 30, 45 and 60 (p.272) • Test Bank 13.4 1 period • Additional Examples • E Textbook 13.21 – 13.23 • PowerPoint • Worksheet 13.5 Presentation (Sets 1 & 2) • Workbook 13.5 • Ongoing Assessment Package: Quiz 13.5 • Test Bank 13.5 • Inspiring task 13.2 helps students explore the exact values of the trigonometric ratios of 30, 45 and 60 by considering an isosceles right-angled triangle and an equilateral triangle. • Students should be able to make use of the exact values of the trigonometric ratios of 30, 45 and 60 to find the value of expressions and unknowns in geometric figures. 13.5 Finding Trigonometric Ratios by Using Right-Angled Triangles (pp.277 – 280) Consolidation & Assessment Additional Information Teaching Plan 2B Teaching Focus 13.6 Basic Trigonometric Identities (pp.280 – 286) Suggested No. of Periods 4 • Inspiring task 13.4 helps students explore the trigonometric identities of complementary angles by using the algebraic method. • Students should be able to use the trigonometric identities of complementary angles to simplify expressions and find values of them. Special Items 1 period • Additional Examples • E Textbook 13.24 – 13.28 • PowerPoint • Worksheet 13.6 Presentation (Sets 1 & 2) • Inspiring Task 13.3 • Workbook 13.6 A. Exploring the • Ongoing Assessment Ratio of sin to Package: Quiz 13.6 cos (p.280) • Test Bank 13.6 B. Exploring the Sum of sin2 and cos2 (p.281) 1 period • Additional Examples • E Textbook 13.29 – 13.31 • PowerPoint • Worksheet 13.7 Presentation (Sets 1 & 2) • Inspiring Task 13.4 • Workbook 13.7 Exploring the • Ongoing Assessment Trigonometric Package: Quiz 13.7 Identities of Complementary • Test Bank 13.7 Angles (p.286) • Inspiring task 13.3 helps students explore the basic trigonometric identities by using the algebraic method. • Students should be able to use the basic trigonometric identities to simplify expressions and find values of them. 13.7 Trigonometric Identities of Complementary Angles (pp.286 – 290) Consolidation & Assessment Additional Information New Progress in Junior Mathematics 2B Learning Objectives Learning Objectives Teaching Focus 13.8 Proving Simple Trigonometric Identities (pp.290 – 293) Suggested No. of Periods Consolidation & Assessment Special Items 2 periods • Additional Examples • E Textbook 13.32 – 13.33 • PowerPoint • Worksheet 13.8 Presentation (Sets 1 & 2) • Workbook 13.8 • Ongoing Assessment Package: Quiz 13.8 • Test Bank 13.8 2 periods • Additional Examples • E Textbook 13.34 – 13.36 • PowerPoint • Worksheet 13.9 Presentation (Sets 1 & 2) • Workbook 13.9 • Ongoing Assessment Package: Quiz 13.9 • Test Bank 13.9 • Students should be able to prove trigonometric identities. • Students should be able to determine whether equations involving trigonometric ratios are identities. Additional Information 5 13.9 Solving Trigonometric Equations (pp.293 – 295) • Students should be able to solve trigonometric equations. Teaching Plan 2B Teaching Focus Enrichment Mathematics – What Is Special about 0 and 90? (p.305) Suggested No. of Periods Consolidation & Assessment Special Items 0.5 period • This enrichment introduces the speciality of 0 and 90 in trigonometry. Total: 15 periods • TSA Supplementary Exercises 13 • Ongoing Assessment Package: Formative Assessment 13 • Open-ended Questions Additional Information New Progress in Junior Mathematics 2B Learning Objectives 6