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PANDA – Cycle 2 Basic Trigonometry Linda's Lesson Design Summary Lesson 1 TanA Three parts Note Resources Introducing trigonometry Suggested by the requirement from Pre-assessment with similar triangles the national curriculum and Edexcel Q1 from the Hermitage Academy Y10 Higher Homework Unit 12 Q2 exam broad (2015-2016 academic year). Q2 from Page 712, Section 1 Trigonometry in right-angled triangles, Chapter 38 Trigonometry, Mathematics GCSE for AQA (Student Book), Higher, Cambridge Find missing angles Use calculator to find angle, check Ex1 from http://www.resourceaholic.com/2014/10/trig.html the right mode (degree) Ex 2 from Three by one http://nrich.maths.org/1955 (recommended using calculator) PANDA – Cycle 2 Basic Trigonometry 8 methods at http://nrich.maths.org/1335 Find missing lengths There are three types, missing length Example 1 OCR Q20 (Foundation) at opposite, adjacent and mixed with Exercise 1: Edexcel Foundation Three-year scheme of work Term 5 Q3 angle or Pythagoras Exercise 2: Edexcel Foundation Three-year scheme of work Term 5 Q12 Exercise 3: AQA 90 problem-solving Right-Angled triangles Example 2: Edexcel Foundation Three-year scheme of work Term 5 Q11 Exercise 4: OCR Q11 (Higher) Lesson 2 𝒔𝒊𝒏𝜽 and 𝒄𝒐𝒔𝜽 Three parts Note Resources The trigonometry ratio: 1. The purpose of pre-assessment is to Pre-assessment: first 3 questions from the National project Mastery by St. Sine and Cosine consolidate basic skill to find the John's; the forth from OCR Higher check in 10.05 Q1 PANDA – Cycle 2 Basic Trigonometry missing length, when time or division Find sine ratio from http://www.resourceaholic.com/2014/10/trig.html 2. Similar method to find the sine and cosine ratio Find angles using two Tangent ratio has been mixed at Example 1: OCR foundation check in 10.05b &10.05C Q4 appropriate sides exercise Exercise 1: Find the missing angles from STEM Group activity shows the circle which Teaching mental Mathematics from level 5_ geometry card sort and use of unit circle will link with next lesson https://www.stem.org.uk/system/files/elibrary-resources/legacy_files_migrated/1 4066-Teaching%20mental%20maths%20from%20level%205%20-%20geometry.pdf Group activity: find the missing angles from the same document Find length using Sin or After group activity, 'Have a think' Example 1: OCR foundation check in 10.05b &10.05C Q2 Cos Suggested homework: links with next lesson. Group activity: Mixed sine and cosine ratio: OCR higher check in 10.05 Q7 PANDA – Cycle 2 Basic Trigonometry (1) computer game to find the missing lengths and angles https://www.mangahigh.com/en-gb/maths_games/shape/trigonometry/use_trigonometry_to_find_lengths https://www.mangahigh.com/en-gb/maths_games/shape/trigonometry/use_trigonometry_to_find_angles Or (2) Trigonometry puzzle from Activity 15.6 MEP Demonstration Project Y9B Unit 15 at Plymouth Univ https://www.stem.org.uk/elibrary/resource/25887 (see appendix A) Lesson 3 Exact value Three parts Notes Resources Trigonometry in unit circle Sine line, cosine line and tangent line From SMILE project The exact values of 𝑠𝑖𝑛𝜃 and 𝑐𝑜𝑠𝜃 for 𝜃 = 0°, 90°, 𝑡𝑎𝑛𝜃 for 𝜃 = 0° The exact values of 𝑠𝑖𝑛𝜃 , 𝑐𝑜𝑠𝜃 and Emphasis on reasoning rather than From OCR GCSE Mathematics recalling PANDA – Cycle 2 Basic Trigonometry 𝑡𝑎𝑛𝜃 for 𝜃 = 45° for 𝜃 = 30°, 60° memorising trigonometric ratios guide, recommended to print off and stick in student books. Practice Example 1 From AQA lesson plan, target grades B Example 2 From Shanghai textbook exercise Lesson 4 Problem-solving Three parts Notes Part 1 the history of There are three parts in NRICH trigonometry website introducing the history of Resources From Part 1 http://nrich.maths.org/6843 The deep understanding of trigonometry is that the three sets of ratio are equal rather than to emphasis on the symbol (sin, cos and tan). PANDA – Cycle 2 Basic Trigonometry trigonometry Part 2 With the base of Example 1 from MEP Teacher Support Unit 15 Trigonometry Extra isosceles triangle Exercises 15.3 Q4 Further question 1 from MEP Y9 Practice Book B 10.1 Q11 Further question 2 from MEP Teacher Support Unit 15 Trigonometry Extra Exercises 15.4 Q2 Part 3 The Ramp It is useful at real life, and also able to Question 1 from MEP Y9 Practice Book B 15.4 Q6 link with the concept of gradient of a Further Question from the same document Q11 straight line PANDA – Cycle 2 Basic Trigonometry Appendix A Suggested homework Show all the regions which display correct trigonometric ratios to find the hidden animal. From MEP at Plymouth Univ https://www.stem.org.uk/elibrary/resource/25887 The answer looks like a whale. PANDA – Cycle 2 Basic Trigonometry Photo taken from Durham Luminere 2015