Mathematics: Applications and Interpretations II

5 Credits

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Grade 12: Unit One Trigonometry

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IB Learner ProfileIB Programs aim to develop internationally minded people who are striving to become:

Inquirers Their natural curiosity is nurtured. They acquire the skills necessary to conduct constructive inquiry and research, and become independent active learners. They actively enjoy learning and this love of learning will be sustained throughout their lives.

Knowledgeable They explore concepts, ideas and issues, which have global relevance and importance. In so doing, they acquire, and are able to make use of, a significant body of knowledge across a range of disciplines.

Critical thinkers They exercise initiative in applying thinking skills critically and creatively to approach complex problems and make reasoned decisions.

Communicators They understand and express ideas and information confidently and creatively in more than one language and in a variety of modes of communication.

Risk-takers They approach unfamiliar situations with confidence and forethought, and have the independence of spirit to explore new roles, ideas and strategies. They are courageous and articulate in defending those things in which they believe.

Principled They have a sound grasp of the principles of moral reasoning. They have integrity, honesty, a sense of fairness and justice and respect for the dignity of the individual.

Caring They show empathy, compassion and respect towards the needs and feelings of others. They have a personal commitment to action and service to make a positive difference to the environment and to the lives of others.

Open-minded Through an understanding and appreciation of their own culture, they are open to the perspectives, values and traditions of other individuals and cultures and are accustomed to seeking and considering a range of points of view.

Well-balanced They understand the importance of physical and mental balance and personal wellbeing for themselves and others. They demonstrate perseverance and self-discipline.

Reflective They give thoughtful consideration to their own learning and personal development. They are able to analyze their strengths and weaknesses in a constructive manner.

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Course DescriptionThis course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics.

The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures. Students should enjoy seeing mathematics used in real-world contexts and to solve real-world problems.

International Baccalaureate Organization. (2019). Mathematics: applications and interpretation guide (First assessment 2021) [Curriculum Guide]. Wales, United Kingdom: International Baccalaureate Organization (UK) Ltd.

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# Topic Suggested Timing

1 Introduction to Trigonometry 6 weeks

2 Probability 10 weeks

3 Statistics 10 weeks

4 Introduction to Calculus 10 weeks

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Educational TechnologyStandards

8.1.8.A.1, 8.1.8.B.1, 8.1.8.C.1, 8.1.8.D.1, 8.1.8.E.1, 8.1.8.F.1

Technology Operations and Concepts Create professional documents (e.g., newsletter, personalized learning plan, business letter or flyer) using advanced features of a

word processing program.

Creativity and Innovation Synthesize and publish information about a local or global issue or event on a collaborative, web-based service.

Communication and Collaboration Participate in an online learning community with learners from other countries to understand their perspectives on a global problem

or issue, and propose possible solutions.

Digital Citizenship Model appropriate online behaviors related to cyber safety, cyber bullying, cyber security, and cyber ethics.

Research and Information Literacy Gather and analyze findings using data collection technology to produce a possible solution for a content-related or real-world

problem.           

Critical Thinking, Problem Solving, Decision Making Use an electronic authoring tool in collaboration with learners from other countries to evaluate and summarize the perspectives of

other cultures about a current event or contemporary figure.   

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21st Century Life & Career SkillsStandards:

9.1.8.A.1, 9.1.8.A.2, 9.1.8.B.1, 9.1.8.C.1, 9.1.8.C.2, 9.1.8.C.3, 9.1.8.D.2, 9.1.8.D.3, 9.3.8.B.3

Learning and Innovation Skills: Creativity and Innovation

Use multiple points of view to create alternative solutions.

Critical Thinking and Problem Solving Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem-solving skills. Implement problem-solving strategies to solve a problem in school or the community.

Communication and Collaboration Skills Determine an individual’s responsibility for personal actions and contributions to group activities. Demonstrate the use of compromise, consensus, and community building strategies for carrying out different tasks, assignments,

and projects. Model leadership skills during classroom and extra-curricular activities.

Cross-Cultural Understanding and Interpersonal Communication Demonstrate the ability to understand inferences. Use effective communication skills in face-to-face and online interactions with peers and adults from home and from diverse

cultures.  

Career Exploration Evaluate personal abilities, interests, and motivations and discuss how they might influence job and career selection.       

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Career Ready PracticesCareer Ready Practices describe the career-ready skills that all educators in all content areas should seek to develop in their students. They are practices that have been linked to increase college, career, and life success. Career Ready Practices should be taught and reinforced in all career exploration and preparation programs with increasingly higher levels of complexity and expectation as a student advances through a program of study.

CRP1. Act as a responsible and contributing citizen and employee Career-ready individuals understand the obligations and responsibilities of being a member of a community, and they demonstrate this understanding every day through their interactions with others. They are conscientious of the impacts of their decisions on others and the environment around them. They think about the near-term and long-term consequences of their actions and seek to act in ways that contribute to the betterment of their teams, families, community and workplace. They are reliable and consistent in going beyond the minimum expectation and in participating in activities that serve the greater good.

CRP2. Apply appropriate academic and technical skills. Career-ready individuals readily access and use the knowledge and skills acquired through experience and education to be more productive. They make connections between abstract concepts with real-world applications, and they make correct insights about when it is appropriate to apply the use of an academic skill in a workplace situation.

CRP3. Attend to personal health and financial well-being. Career-ready individuals understand the relationship between personal health, workplace performance and personal well-being; they act on that understanding to regularly practice healthy diet, exercise and mental health activities. Career-ready individuals also take regular action to contribute to their personal financial well-being, understanding that personal financial security provides the peace of mind required to contribute more fully to their own career success.

CRP4. Communicate clearly and effectively and with reason. Career-ready individuals communicate thoughts, ideas, and action plans with clarity, whether using written, verbal, and/or visual methods. They communicate in the workplace with clarity and purpose to make maximum use of their own and others’ time. They are excellent writers; they master conventions, word choice, and organization, and use effective tone and presentation skills to articulate ideas. They are skilled at interacting with others; they are active listeners and speak clearly and with purpose. Career-ready individuals think about the audience for their

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Career Ready Practicescommunication and prepare accordingly to ensure the desired outcome. CRP5. Consider the environmental, social and economic impacts of decisions. Career-ready individuals understand the interrelated nature of their actions and regularly make decisions that positively impact and/or mitigate negative impact on other people, organization, and the environment. They are aware of and utilize new technologies, understandings, procedures, materials, and regulations affecting the nature of their work as it relates to the impact on the social condition, the environment and the profitability of the organization.

CRP6. Demonstrate creativity and innovation. Career-ready individuals regularly think of ideas that solve problems in new and different ways, and they contribute those ideas in a useful and productive manner to improve their organization. They can consider unconventional ideas and suggestions as solutions to issues, tasks or problems, and they discern which ideas and suggestions will add greatest value. They seek new methods, practices, and ideas from a variety of sources and seek to apply those ideas to their own workplace. They take action on their ideas and understand how to bring innovation to an organization.

CRP7. Employ valid and reliable research strategies. Career-ready individuals are discerning in accepting and using new information to make decisions, change practices or inform strategies. They use reliable research process to search for new information. They evaluate the validity of sources when considering the use and adoption of external information or practices in their workplace situation.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. Career-ready individuals readily recognize problems in the workplace, understand the nature of the problem, and devise effective plans to solve the problem. They are aware of problems when they occur and take action quickly to address the problem; they thoughtfully investigate the root cause of the problem prior to introducing solutions. They carefully consider the options to solve the problem. Once a solution is agreed upon, they follow through to ensure the problem is solved, whether through their own actions or the actions of others.

CRP9. Model integrity, ethical leadership and effective management. Career-ready individuals consistently act in ways that align personal and community-held ideals and principles while employing strategies to positively influence others in the workplace. They have a clear understanding of integrity and act on this understanding in every decision. They use a variety of means to positively impact the directions and actions of a team or organization, and they apply insights into human behavior to change

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Career Ready Practicesothers’ action, attitudes and/or beliefs. They recognize the near-term and long-term effects that management’s actions and attitudes can have on productivity, morals and organizational culture.

CRP10. Plan education and career paths aligned to personal goals. Career-ready individuals take personal ownership of their own education and career goals, and they regularly act on a plan to attain these goals. They understand their own career interests, preferences, goals, and requirements. They have perspective regarding the pathways available to them and the time, effort, experience and other requirements to pursue each, including a path of entrepreneurship. They recognize the value of each step in the education and experiential process, and they recognize that nearly all career paths require ongoing education and experience. They seek counselors, mentors, and other experts to assist in the planning and execution of career and personal goals.

CRP11. Use technology to enhance productivity. Career-ready individuals find and maximize the productive value of existing and new technology to accomplish workplace tasks and solve workplace problems. They are flexible and adaptive in acquiring new technology. They are proficient with ubiquitous technology applications. They understand the inherent risks-personal and organizational-of technology applications, and they take actions to prevent or mitigate these risks.

CRP12. Work productively in teams while using cultural global competence. Career-ready individuals positively contribute to every team, whether formal or informal. They apply an awareness of cultural difference to avoid barriers to productive and positive interaction. They find ways to increase the engagement and contribution of all team members. They plan and facilitate effective team meetings.

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Differentiated Instruction Accommodate Based on Students Individual Needs: Strategies

Time/General

Extra time for assigned tasks

Adjust length of assignment

Timeline with due dates for reports and projects

Communication system between home and school

Provide lecture notes/outline

Processing

Extra Response time

Have students verbalize steps

Repeat, clarify or reword directions

Mini-breaks between tasks

Provide a warning for transitions

Reading partners

Comprehension

Precise step-by-step directions

Short manageable tasks

Brief and concrete directions

Provide immediate feedback

Small group instruction

Emphasize multi-sensory learning

Recall

Teacher-made checklist

Use visual graphic organizers

Reference resources to promote independence

Visual and verbal reminders

Graphic organizers

Assistive Technology

Computer/whiteboard

Tape recorder

Spell-checker

Audio-taped books

Tests/Quizzes/Grading

Extended time

Study guides

Shortened tests

Read directions aloud

Behavior/Attention

Consistent daily structured routine

Simple and clear classroom rules

Frequent feedback

Organization

Individual daily planner

Display a written agenda

Note-taking assistance

Color code materials

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EnrichmentAccommodate Based on Students individual Needs: Strategies

Adaption of Material and Requirements

Evaluate Vocabulary

Elevated Text Complexity

Additional Projects

Independent Student Options

Projects completed individual or with Partners

Self Selection of Research

Tiered/Multilevel Activities

Learning Centers

Individual Response Board

Independent Book Studies

Open-ended activities

Community/Subject expert mentorships

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AssessmentsSuggested Formative/Summative Classroom Assessments

Timelines, Maps, Charts, Graphic Organizers

Teacher-created Unit Assessments, Chapter Assessments, Quizzes

DBQ, Essays, Short Answer

Accountable Talk, Debate, Oral Report, Role Playing, Think Pair, and Share

Projects, Portfolio, Presentations, Prezi, Gallery Walks

Homework

Concept Mapping

Primary and Secondary Source analysis

Photo, Video, Political Cartoon, Radio, Song Analysis

Create an Original Song, Film, or Poem

Glogster to make Electronic Posters

Internal and External IB Assessments

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Interdisciplinary Connections English Language Arts

Journal Writing Close reading of industry-related content Create a brochure for a specific industry Keep a running word wall of industry vocabulary

Social Studies Research the history of a given industry/profession Research prominent historical individuals in a given industry/profession Use historical references to solve problems

World Language Translate industry-content Create a translated index of industry vocabulary Generate a translated list of words and phrases related to workplace safety

Math Research industry salaries for a geographic area and juxtapose against local cost of living Go on a trigonometry scavenger hunt Track and analyze various data, such as industry’s impact on the GDP, career opportunities or among of individuals currently occupying careers

Fine & Performing Arts Create a poster recruiting young people to focus their studies on a specific career or industry Design a flag or logo to represent a given career field

Science Research the environmental impact of a given career or industry Research latest developments in industry technology Investigate applicable-careers in STEM fields

Course: Applications and Interpretations SL Topic: Trigonometry15 | P a g e

Unit 1: Trigonometry

Grade Level: 12

Description: Trigonometry allows us to quantify the physical world, enhancing our spatial awareness in two and three dimensions. This branch provides us with the tools for analysis, measurement and transformation of quantities, movements and relationships.

Suggested concepts embedded in this topic:Generalization, space, relationships, systems, representations

The aim of the trigonometry topic is to introduce students to appropriate skills and techniques for practical problem solving in two and three dimensions.

Throughout this topic students should be given the opportunity to use technology such as graphing packages, graphing calculators and dynamic geometry software to develop and apply their knowledge of geometry and trigonometry.

New Jersey Core Curriculum Content Standards (NJCCCS): HS.G.SRT: C6, C7, C8, D9, D10 and D11; MP 1-8.

IB MAI-SL Topics 3.2 and 3.3

NJDOE Student Learning Objective

Essential Questions Content Activities & Assessments

Resources

1. Recall, select and use their knowledge of trigonometric ratios, concepts and techniques in a variety of familiar and unfamiliar contexts. G-SRT.C6

What are the properties of side ratios in similar right-triangles?

How are the ratios between lengths of sides of right-angled triangles related to the angles of

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

In all areas of this topic, students should be encouraged to sketch well-

Activity: Grand Canyon Adventure; Triangular tangles

Create a flow chart to help choose the correct trigonometric ratios for any given problem.

Triangular tangles–SL applications Teacher Support Material (TSM)

Geometry and Trigonometry Math Studies Video Lessons

Geogebra Right Triangle Trigonometry Simulation

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NJDOE Student Learning Objective

Essential Questions Content Activities & Assessments

Resources

the triangle?

How can you sketch well-labeled diagrams to support your solution to a problem?

How are inverse functions relevant to finding angles of a triangle?

What is the relationship between the sine and cosine of complementary angles?

How can trigonometric ratios and the Pythagorean Theorem be used to solve right triangles in applied problems?

TOK: Is it ethical that Pythagoras gave his name to a theorem that may not have been his own creation? What criteria might we use to

labelled diagrams to support their solutions.

Application: finding the size of an angle between two intersecting lines or between a line and a plane.

Link to: inverse functions (SL2.2) when finding angles.

Other contexts: Triangulation, map-making.

Links to other subjects: Vectors (physics).

International-mindedness: Diagrams of Pythagoras’ theorem occur in early Chinese and Indian manuscripts. The earliest references to trigonometry are in Indian mathematics; the use of triangulation to find the curvature of the Earth in order to settle a dispute between England and France over Newton’s gravity.

Geogebra Conceptual Illustrations: Trigonometric Ratios within Right Triangles

Khan Academy: Trigonometry with Right Triangles

Texas Instruments TI84 Plus Graphing Display Calculator

IB Question bank

Desmos Online Graphing Calculator

www.geogebra.com

www.illustrativemathematics.org

www.illuminations..nctm.org

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NJDOE Student Learning Objective

Essential Questions Content Activities & Assessments

Resources

make such a judgment?2. Recall, select and use

their knowledge the Law of Sines in both abstract and real-world contexts to solve problems.G-SRT.D10, G-SRT.D11,SL Topic 3.2

How can you use right-triangle trigonometric ratios to prove the Laws of Sines and use it to solve problems?

How can you apply the Law of Sines to find unknown measurements in oblique triangles (e.g., surveying problems, resultant forces)?

How can you select the appropriate trigonometric rule to solve both abstract and real-world contexts involving triangles?

TOK: Is it ethical that Pythagoras gave his name to a theorem that may not have been his own creation? What criteria might we use to make such a judgment?

Use the sine rule to find side length or angle degree.

This section does not include the ambiguous case of the sine rule.

Other contexts: Triangulation, map-making.

Links to other subjects: Vectors (physics).

Activity: Create a flow chart to help choose the correct trigonometric law for any given problem.

Summative and Formative Assessments (Quizzes & Tests) for each topic.

Homework and Classwork assignments based on daily lessons.

International-mindedness: Diagrams of Pythagoras’ theorem occur in early Chinese and Indian manuscripts. The earliest references to trigonometry are in Indian mathematics; the use of triangulation to find the curvature of the Earth in order to settle a dispute between England and France over Newton’s gravity.

Texas Instruments TI84 Plus Graphing Display Calculator

IB Question bank

Geometer’s Sketchpad

Desmos Online Graphing Calculator

www.geogebra.com

www.Khanacademy.org www.illustrativemathematics.org

www.illuminations..nctm.org

www.youtube.com

http://ocw.mit.edu

www.NJCTL.org

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NJDOE Student Learning Objective

Essential Questions Content Activities & Assessments

Resources

3. Recall, select and use their knowledge the Law of Cosines in both abstract and real-world contexts to solve problems.G-SRT.D10, G-SRT.D11, MP1-8SL Topic 3.2

How can you use right-triangle trigonometric ratios to prove the Law of Cosines and use it to solve problems?

How can you apply the Law of Cosines to find unknown measurements in oblique triangles (e.g., surveying problems, resultant forces)?

How can you select the appropriate trigonometric rule to solve both abstract and real-world contexts involving triangles?

Use the cosine rule to find side length or angle degree.

Applications involving bearings.

Activity: Create a flow chart to help choose the correct trigonometric law for any given problem.

Summative and Formative Assessments (Quizzes & Tests) for each topic.

Homework and Classwork assignments based on daily lessons.

4. Recall, select and use their knowledge the area of an oblique triangle using

How can you derive the

formula A=12

ab sin Cfor

Find the area of oblique triangles while modeling and solving real life

Activity: Group work on past exam problems. Accountable talk, gallery

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NJDOE Student Learning Objective

Essential Questions Content Activities & Assessments

Resources

trigonometric ratios in both abstract and real-world contexts to solve problems.G-SRT.D9, SL Topic 3.2

the area of an oblique triangle?

What real-world problems can be solved using the trigonometric formula for the area of a triangle?

problems.

Derive the formulas A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite

side.

walk.

Summative and Formative Assessments (Quizzes & Tests) for each topic.

Homework and Classwork assignments based on daily lessons.

5. Transform common realistic contexts into angles of elevation and depression; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation; use appropriate notation and terminology. MP1-8

How can common realistic contexts be transformed into a diagram involving triangles?

How can the use of bearings be applied to problems involving angle of elevation and depression?

How are angles of elevation and depression related to the angles formed by a transversal with two parallel lines?

Other contexts: Triangulation, map-making, navigation and radio transmissions. Use of parallax for navigation.

Links to other subjects: Vectors, scalars, forces and dynamics (physics); field studies (sciences)

International-mindedness: The use of triangulation to find the curvature of the Earth in order to settle a dispute between England and France over Newton’s gravity.

Activity: Estimate the height of a tree or building by making real-world measurements.

Summative and Formative Assessments (Quizzes & Tests) for each topic. Homework and Classwork assignments based on daily lessons.

Aim 8: Who really invented Pythagoras’ theorem?

Aim 9: In how many ways can you prove Pythagoras’ theorem?

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NJDOE Student Learning Objective

Essential Questions Content Activities & Assessments

Resources

TOK: If the angles of a triangle can add up to less than 180°, 180° or more than 180°, what does this tell us about the nature of mathematical knowledge?

6. Students choose from a wide variety of activities to create an exploration paper on a topic of their choosing: for example, modelling, investigations and applications of mathematics. MP 1-8

What are the assessment criterion for the internal assessment?

What must be included in the draft and final product?

To what extent is collaboration and teamwork allowed?

What are the requirements for citation of outside sources of information?

The internally-assessed component in this course is a mathematical exploration. This is a short report written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area. The emphasis is on mathematical communication (including formulae, diagrams, graphs, tables and so on), with his or her own focus, with the teacher providing feedback via, for example, discussion and interview. This will allow the students to develop areas of interest to

The specific purposes of the exploration are to:

• develop students’ personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematics

• provide opportunities for students to complete a piece of mathematical work over an extended period of time

• enable students to experience the satisfaction of applying mathematical processes independently

• provide students with the opportunity to experience for themselves the beauty, power and usefulness of

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NJDOE Student Learning Objective

Essential Questions Content Activities & Assessments

Resources

How will time be allocated in and out of class?

What process will help ensure a well defined, concise topic, aim and rationale?

them without a time constraint as in an examination and allow all students to experience a feeling of success.

mathematics

• encourage students, where appropriate, to discover, use and appreciate the power of technology as a mathematical tool

• enable students to develop the qualities of patience and persistence, and to reflect on the significance of their work

• provide opportunities for students to show, with confidence, how they have developed mathematically.

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Unit 4 Vocabulary

Pythagorean triplesRight angled triangleHypotenuseTrigonometric ratioSineCosineTangentBearings

Pythagoras’ theoremAngle of elevationAngle of depressionSine ruleCosine ruleArea of an oblique triangleDistanceMidpoint

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TOK Connections

What is an axiomatic system? Are axioms self evident to everybody?

Is it ethical that Pythagoras gave his name to a theorem that may not have been his own creation? What criteria might we use to make such a judgment?

If the angles of a triangle can add up to less than 180°, 180° or more than 180°, what does this tell us about the nature of mathematical knowledge?

Does personal experience play a role in the formation of knowledge claims in mathematics? Does it play a different role in mathematics compared to other areas of knowledge?

Is the division of knowledge into disciplines or areas of knowledge artificial?

To what extent is mathematical knowledge embedded in particular traditions or bound to particular cultures? How have key events in the history of mathematics shaped its current form and methods?

What practical problems can or does mathematics try to solve? Why are problems such as the travelling salesman problem so enduring? What does it mean to say the travelling salesman problem is “NP hard”?

Contribution to the Development of Students’ Approaches to Learning Skills

Techniques to enhance the thinking skills of the students. Ask students to formulate a reasoned argument to support their opinion or conclusion. Give students time to think through their answers before asking them for a response. Set students a task which requires higher-order thinking skills such as analysis or evaluation. Build on specific prior tasks. Help students to make their thinking more visible, for example: use a strategy such as a thinking routine.

Problem solving is central to learning mathematics and involves the acquisition of mathematical skills and concepts in a wide range of situations, including non-routine, open-ended and real-world problems. Having followed a DP mathematics course, students will be expected to demonstrate

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the following:

Knowledge and understanding: Recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.

Problem solving: Recall, select and use their knowledge of mathematical skills, results and models in both abstract and real-world contexts to solve problems.

Communication and interpretation: Transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation; use appropriate notation and terminology.

Technology: Use technology accurately, appropriately and efficiently both to explore new ideas and to solve problems.

Reasoning: Construct mathematical arguments through use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions.

Inquiry approaches: Investigate unfamiliar situations, both abstract and from the real world, involving organizing and analyzing information, making conjectures, drawing conclusions, and testing their validity.

Contributions to the Development of the Attribute(s) of the Learner Profile

Students exercise initiative in applying thinking skills critically and creatively to recognize and approach complex problems and make reasoned ethical decisions. Inquiry approaches: investigate unfamiliar situations, both abstract and real-world, involving organizing and analyzing information or measurements, drawing conclusions, testing validity, and considering their scope and limitation. Reflective approaches: thoughtfully consider the world and our own ideas and experiences, extend what we learn in the classroom to life. The aims of all DP mathematics courses are to enable students to:1. develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power2. develop an understanding of the concepts, principles and nature of mathematics3. communicate mathematics clearly, concisely and confidently in a variety of contexts

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4. develop logical and creative thinking, and patience and persistence in problem solving to instil confidence in using mathematics5. employ and refine their powers of abstraction and generalization6. take action to apply and transfer skills to alternative situations, to other areas of knowledge and to future developments in their local and global communities7. appreciate how developments in technology and mathematics influence each other8. appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics9. appreciate the universality of mathematics and its multicultural, international and historical perspectives10. appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course11. develop the ability to reflect critically upon their own work and the work of others12. independently and collaboratively extend their understanding of mathematics.

Contributions to the Development of International Mindedness

Diagrams of Pythagoras’ theorem occur in early Chinese and Indian manuscripts. The earliest references to trigonometry are in Indian mathematics; the use of triangulation to find the curvature of the Earth in order to settle a dispute between England and France over Newton’s gravity.

Aim 8: Who really invented Pythagoras’ theorem?

The use of triangulation to find the curvature of the Earth in order to settle a dispute between England and France over Newton’s gravity.

Seki Takakazu calculating π to ten decimal places; Hipparchus, Menelaus and Ptolemy; why are there 360 degrees in a complete turn? Why do we use minutes and seconds for time?; Links to Babylonian mathematics.

The origin of the word “sine”; trigonometry was developed by successive civilizations and cultures; how is mathematical knowledge considered from a sociocultural perspective?

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