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Teacher(s) Ms Pushyami Chennupati Subject group and course Mathematics HL

Course part Trigonometry SL or HL/Year 1 or 2 Math AA HL Dates August – Sept 2022

and topic
Year 2

Unit description and texts DP assessment(s) for unit

(Trigonometry) Semester 3
 Pythagoras’ theorem and its converse

 Mid-point of a line segment and the distance between two points

in the Cartesian plane

 Geometric concepts: point, line, plane, angle

 Angle measurement in degrees, compass directions

 The triangle sum theorem

 Right-angle trigonometry, including simple applications for

solving triangles

 Three-figure bearings

INQUIRY: establishing purpose of the unit

Transfer goals
List here one to three big, overarching, long-term goals for this unit. Transfer goals are the major goals that ask students to “transfer”, or apply, their
knowledge, skills, and concepts at the end of the unit under new/different circumstances, and on their own without scaffolding from the teacher.

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  To introduce quantifying the real world
 to enhance spatial awareness in two and three dimensions
 Using Trigonometry for analysis, measurement and transformation of quantities, movements and relationships.

Essential understandings
List here the key content/skills/concepts that students will know/develop by the end of the unit.

Students will know the following content:

 Trigonometric ratios
 Inverse trigonometric ratios
 True bearings
Students will develop the following skills:
 Problem solving with trigonometry
 Solving right angled and non right angled trigonometry

Students will grasp the following concepts:

 The angle between a line and a plane
 Non right angled trigonometry

Missed concepts/misunderstandings
List here likely misunderstandings students may have during the unit with relation to skills, content and concepts.

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Content-based :
 bearings
Skills-based:
 difference between right angled and non right angled trigonometry

Concept-based:
 angle between line and plane

Inquiry questions
List here the understandings above written in question form, preferably as ones that inspire students to answer them. Feel free to create additional questions
that help inspire further inquiry in the unit but may not directly connect to an above essential understanding.
Content-based:

Q
skills-based:

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Concept-based:
Q.

ACTION: teaching and learning through inquiry

Essential understanding goals Assessment of essential understanding goals Learning process

Copy and paste the essential understanding goals from above Write a 1:1 matching assessment for all goals. Assessments Check the boxes for any
“Inquiry” section. should be labelled formative (F) or summative (S). pedagogical approaches used
during the unit. Aim for a
variety of approaches to help
facilitate learning.

Students will know the following content: Content-based: Lecture

 Trigonometric ratios Worksheets (F) would be given to the students Socratic seminar
 Inverse trigonometric ratios Small group/pair work
 True bearings
PowerPoint lecture/notes
Individual presentations
Students will develop the following skills:
Group presentations
 Problem solving with trigonometry Skills-based:
 Solving right angled and non right angled Student lecture/leading
Investigation Worksheet(F)
trigonometry

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 Peer teaching (F) Interdisciplinary learning
Details:
Other/s:
Peer teaching.
Students will grasp the following concepts: Concept-based:
 The angle between a line and a plane Worksheet (F)
 Non right angled trigonometry Sem 2 ( S)

Resources

HL Mathematics- Fabio critto

Haese & Harris Course Companion

HL Mathematics –Heinemann

GDC

Approaches to learning (ATL) Metacognition Differentiation:

Check the boxes for any explicit approaches to Check the boxes for any metacognitive approaches For more information on the IB’s approach to
learning connections made during the unit. For used that ask students to reflect on unit content, differentiation, please see the guide.
more information on ATL, please see the guide. their own skills, or unit concepts. For more
information on the IB’s approach to meta
cognition, please see the guide.

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 Thinking Reflection on content Affirm identity—build self-esteem
Social Reflection on skills Value prior knowledge
Communication Reflection on concepts Scaffold learning
Self-management Details: Extend learning
Research Reflection on Content Details:
Details: Concept map of the topics which discussed in the Value Prior Knowledge
class
Thinking: Students value the fundamental knowledge of
Reflection on Skills trigonometry . which will be applied in
Making them to create questions by giving them
different conditions Encouraging them to solve in multiple methods. making connections with next stage of the
same concepts
Communication: Reflection on Concept
Scaffold learning
Giving them opportunities to share their Making them to identify all the different methods
knowledge with the peers in every concept Students will be clear in concepts by making
mind map of the topic and they can work on
week areas by looking at the mind map.
Visual clarity helps them to get more clarity
on what needs to be more focused.
Extend learning
Student will get an opportunity to work
themselves to understand the few concepts
(sketching graphs of various functions) and
explain them to their peers
Students will be confident enough to take
challenges.

Language and learning TOK connections CAS connections

Check the boxes for any explicit language and Check the boxes for any explicit TOK connections Check the boxes for any explicit CAS connections.
learning connections made during the unit. For If you check any of the boxes, provide a brief note

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more information on the IB’s approach to made during the unit. in the “details” section explaining how students
language and learning, please see the guide. engaged in CAS for this unit.

Activating background knowledge Personal and shared knowledge Creativity

Scaffolding for new learning Ways of knowing Activity
Acquisition of new learning through practice Areas of knowledge Service
Demonstrating proficiency The knowledge framework Details: __
Details: Details:
Demonstrating proficiency Mathematics and knowledge claims.
Interpreting word problems and solve the  To what extent is mathematical
problems knowledge embedded in particular
traditions or bound to particular
Scaffolding for new learning cultures? How have key events in the
Practical applications for more interest in the history of mathematics shaped its
subject current form and methods?
Links to other subjects:
Diffraction patterns and circular motion (physics)

REFLECTION: Considering the planning, process and impact of the inquiry

What worked well What didn’t work well Notes/changes/suggestions:

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Transfer goals
List the transfer goals from the beginning of this unit planner.
 To introduce quantifying the real world
 to enhance spatial awareness in two and three dimensions
 Using Trigonometry for analysis, measurement and transformation of quantities, movements and relationships.

Transfer reflection
How successful were the students in achieving the transfer goals by the end of the unit?

Unit title: Geometry and Trigonometry Duration: 25 hours

Dates: August 1st to Sept 15th

Stage 1 - Desired results

Assessment Objectives (AO): Aims:

1. Knowledge and understanding 1. develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power
2. Problem solving 2. develop an understanding of the concepts, principles and nature of mathematics

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 3. Communication and interpretation 3. communicate mathematics clearly, concisely and confidently in a variety of contexts
4. Technology 4. develop logical and creative thinking, and patience and persistence in problem solving to
5. Reasoning instill confidence in using mathematics
6. Inquiry approaches 6. take action to apply and transfer skills to alternative situations, to other areas of knowledge
and to future developments in their local and global communities
9. appreciate the universality of mathematics and its multicultural, international and historical
perspectives
10. appreciate the contribution of mathematics to other disciplines, and as a particular “area of
Approaches to learning (ATL):
knowledge” in the TOK course
1. Thinking skills 11. develop the ability to reflect critically upon their own work and the work of others
2. Communication skills 12. independently and collaboratively extend their understanding of mathematics.
3. Social skills
4. Self-management skills
5. Research skills

Learner Profile Attributes:

Thinker, inquirer, communicator, open-minded,

knowledgeable, caring, reflective

Students will know….. Students will be able to…..

Distance between two points and midpoint Find distance between distance between two points and their midpoint.

Volume of 3D shapes Calculate volumes of sphere, hemisphere, pyramid and right cone.

Angle between lines and planes Find the angle between two lines and line and a plane.

Trigonometric ratios Use of sine, cosine and tangent ratios to find the
sides and angles of right-angled triangles.
Sine and cosine rules

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Ambiguous case Apply sine and cosine rule.

Area of triangles Identify and solve ambiguous case.

Angle of depression and elevation Solve problems involving angle of depression and elevation.

Arc and sector Calculate arc length and area of sector.

Radian Define sine and cosine using unit circle.

Unit circle State the exact values of trigonometric values of special angles.

Pythagorean identity State and use double angle identities.

Double angle identities Interpret graphs of trigonometric functions.

Amplitude and period Transform trigonometric functions.

Transformations of trigonometric graphs Solve trigonometric functions graphically and analytically.

Composite trigonometric functions

Trigonometric equations

Stage 2 - Assessment Evidence

Performance tasks Other evidence

Mindmap of the concepts learned per topic (AO 1) Topic test based on previous Math SL questions (AO 1, 2, 4)

Class activities as performance tasks: (AO 1-6) Previous IB Math questions (AO 1, 2, 4)

 problem solving (ATL 1) (Aim 2) Verbal assessment during review of previous lesson at the beginning of each class (ATL 2) (AO
 volume of the pyramid (ATL 5) (Aim 1)

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  calculating height (ATLs 1 and 2) (Aim 4) 1, 3)
 investigating simple harmonic motion (ATLs 1 and
5) (Aims 10 and 12) Daily homework from Oxford/Kognity textbook (ATL 4) (AO 1, 2)
 parallax method (ATL 2) (Aims 1 and 6)
 deriving sine and cosine rules (ATL 1)
 vector addition (ATL 1) (Aims 6 and 10)
 modelling yearly temperatures using database
(ATLs 1, 2, 3 and 5) (Aims 3, 6 and 11)

Stage 3 - Learning Plan

Learning Activities:

 What is the volume of the Great Pyramid of Giza? Students will calculate its volume and compare their values to the accepted value.
(Knowledgeable, reflective)
 Outdoor activity: How high is our school building? Students will work in pairs to determine the height of the school building using trigonometry.
(Knowledgeable, thinker)
 Numberphile Video: How many digits of π do you know? How many digits of π do you need?
 Class activities on deriving the sine rule and cosine rule. Students will work in pairs or groups to derive the rules on white boards. (Communicator)
 Connection to Physics: Adding vectors using components and using cosine rule. Students will add two force/velocity/momentum vectors using the
two methods. PHET link below will be used. (Knowledgeable)
 Activity on parallax method in Physics (Pendulum’s simple harmonic motion and Astrophysics – parsec): Discussion of small angle approximation.
Series expansion of sine function can be shown to explain the approximation. (Thinker, communicator)
 Kepler’s 2nd law and the speed of planets/satellites in relation to area of sectors and arc length. Why do planets slow down as they get far from the
Sun? (Thinker)
 Investigating sine rule – ambiguous case in pairs. Use Geogebra link below for demonstration. (Thinker)
 Investigating simple harmonic motion (SHM): What patterns can you identify in SHM? Students will observe/research simple harmonic motion and
model it using sine and cosine functions. They will reflect on their model and share their findings with the rest of the class. This can be extended to
oscillations with damping where the amplitude dies exponentially. Links to exponentials functions (Topic 2) and Calculus (Topic 5) should be made.
This activity can be done in pairs/groups. Possible tools that can be used include spring-mass system, camera, meterstick, MS Excel or Google
spreadsheet. (Inquirer, thinker)

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  Modelling average yearly temperature of a city over decades: Students will choose a city of their own interest and try to fit a trigonometric model
for its average monthly temperature throughout several years. They will interpret and share their results with the rest of the class using Google
spreadsheet. Can this be linked to global warming? Students will comment on their or their peers’ models. Can the students use their model to
make predictions? This is a database investigation. This activity can be done in pairs/groups. (Inquirer, caring, open-minded, reflective)
 Classwork in solving various Topic 3 problems using small white boards in groups, pairs or individually. (Knowledgeable, thinker, communicator)
 Class discussion on TOK and essential questions throughout the topic. (Thinker, communicator)

Stage 4 – Links

Interdisciplinary links: Trigonometric functions have so many applications in Physics, Chemistry and Earth Science. Periodic motion is represented by sine
or cosine functions: Simple harmonic motion, parallax method, 3-D molecular shapes etc. (Aim 10)

Essential Questions:

Are some units more fundamental than others (with reference to radian and degree)? Extension to SI units should be made. (ATL 1, 2) (Aim 3)

TOK: To what extend do human emotions interfere with the Scientific and Mathematical discoveries?

To what extent can Mathematics be arbitrary? (ATL 1, 2) (Aim 10)

International Mindedness: Discussion on the contributions of Egyptians, Greeks, Indians, Arabs and Persians to the development of trigonometry
throughout history. (ATL 3) (Aim 9)

Resources

Math SL by Oxford

Kognity textbook

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IB question bank

www.desmos.com

www.geogebra.com

The Great Pyramid of Giza: https://en.wikipedia.org/wiki/Great_Pyramid_of_Giza

Simple harmonic motion: http://www.animations.physics.unsw.edu.au/jw/SHM.htm

https://phet.colorado.edu/en/simulation/mass-spring-lab

PHET Pendulum lab: https://phet.colorado.edu/en/simulation/pendulum-lab

Vector addition: https://phet.colorado.edu/en/simulation/vector-addition

Numberphile on π: https://www.youtube.com/watch?v=FpyrF_Ci2TQ

Cosine rule: https://www.geogebra.org/m/CPeCKmBu

Sine rule ambiguous case: https://www.geogebra.org/m/w9BycHff

Parallax interactive: http://sci2.esa.int/interactive/media/flashes/2_1_1.htm

Kepler’s interactive:
https://highered.mheducation.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/KeplerThird_Nav.swf::Keplers%20Third
%20Law%20Interactive

Sample database for trigonometric modelling: https://www.weather.gov/media/okx/Climate/CentralPark/monthlyannualtemp.pdf

Stage 5 - Reflections

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