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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