## Grade Twelve Mathematics

Students will develop an understanding of three general units: Trigonometry, Relations and Functions, and Permutations, Combinations, and Binomial Theorem. Math 30-1, 30-2, and 30-3 resources available.

Children’s early experiences shape what they imagine to be possible. Study after study has shown the value of exposing children with positive role models. Representation, including in the hours spent consuming media within the classroom, shape what they imagine to be possible for people who look like them, live where they live, or come from where they came from. Simply put, kids determine what they can be based on the examples around them. Therefore, we highly recommend you take 2-5 minutes everyday in your math class to introduce mathematicians of colour. We've made this easy for you by creating a presentation that you can use with a slide a day to showcase a new mathematician of diverse background. You could do this on a daily, weekly, bi-weekly or during a certain month. You could also make your own presentation and encourage this representation.

7-12 Mathematicians of Colour by Canadian Cultural Mosaic Foundation

__Mathematicians of colour to introduce to your class related to the Alberta curriculum__

**30-1: Permutations, Combinations and Binomial Theorem**

**A brief history of the numerical systems**

Alessandra King explains the origins of the numbers 1,2,3,4,5,6,7,8,9 and 0 along with the relevance of using decimals and a 60 base system.

**Curriculum connection:**

- 1. Apply the fundamental counting principle to solve problems**Suggested use:**

- View as a class to introducing rational and irrational numbers**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Mathematician and Astronomer: Brahmagupta**

Brahmagupta, an ancient Indian mathematician born in Northern India. The work of Brahmagupta found ways to determine both the cube and cube-roots of integers, as well as making rules to compute squares and square-roots.

**Curriculum connection:**

- 1. Apply the fundamental counting principle to solve problems**Suggested use:**

- View as a class to introduce perfect squares, lowest common multiple and greatest common factor**Accessibility:**

- Accessible for hard of hearing and nonverbal

- Additional accommodations needed for visually impaired students

**Science in the Golden Age - The Father of Algebra | Mathematician: Al-Khwarizmi**

From fast cars and aeroplanes to computer encryption – mathematics underpins so much of modern life. In this episode, Jim Al-Khalili uncovers how, between the 9th and 14th centuries, mathematicians from the Islamic world helped mathematicize science and lay the foundations of algebra.

**Curriculum connection:**

- 1. Apply the fundamental counting principle to solve problems**Suggested use:**

- Discussion/research on algebra history

- Hold a class discussion of the discovery of algebra in different communities**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

******History of Mathematics**

An animated video on the development of numbers throughout history.

**Curriculum connection:**

- 1. Apply the fundamental counting principle to solve problems**Suggested use:**

- Hold a class discussion after viewing the video on math across cultures and time; how do they differ? how are they the same?**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Ramanujan and the Number Pi | Mathematician: Ramanujan**

Short video biography of the mathematic contributions of the Indian mathematician Srinivasa Ramanujan. This video discusses more about where he originates from in India, giving a good overview of his contributions of number theory.

**Curriculum connection:**

- 1. Apply the fundamental counting principle to solve problems**Suggested use:**

- Discussion/research project about pioneering BIPOC in mathematics**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

- Manual transcription available

**30-1: Trigonometry********The Most Beautiful Equation in Math | Mathematician: Po-Shen Loh**

Professor of mathematical sciences Po-Shen Loh explains why Euler’s Equation is the most beautiful equation in math.

**Curriculum connection:**- 5. Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians**Suggested use:**- Explaining rational and irrational numbers

- Eulers' Identity

- Emphasizing and appreciating Math**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**The Founder of the Kerala School | Mathematician: Madhava**

Madhava, known as one of the greatest mathematician-astronomers of medieval India, was originally from Southern India. Madhava made great contributions to the development of various trigonometric functions like sine, cosine, tangent and arctangent functions. Additionally, Madhava was able to figure out the exact value of pi to thirteen decimal places, something that is commonly accredited to the mathematician Leibniz.

**Curriculum connection:**

- 4. Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems**Suggested use:**

- Introduction to trigonometry functions; assign basic worksheet where students can identify and complete introductory functions

- After viewing the resource have a class discussion about individuals in history stealing credit from others**Accessibility:**

- Accessible for hard of hearing and nonverbal

- Additional accommodations needed for visually impaired students

**Contribution in Mathematics | Mathematician: Nasir Al Din Al Tusi**

Short, biographical video about the creator of the trigonometric sine law, and a brief explanation of the formula itself.

**Curriculum connection:**

- 4. Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems**Suggested use:**

- Show video before starting trigonometry unit

- Use as introduction to sine law and its characteristics and use**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**The exceptional life of Benjamin Banneker | Mathematician: Benjamin Banneker**

A video about Banneker, a mostly self-educated man in mathematics and astrology, is best know for building America’s first clock—a wooden device that struck hourly. Using his rich understanding of trigonometry and astronomy, he accurately predicted a solar eclipse in 1789.

**Curriculum connection:**

- 2. Develop and apply the equation of the unit circle**Suggested use:**

- Introduction to using trigonometry**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**30-1: Relations and Functions********Meet the First Lady of Mathematics | Mathematician: Emmy Noether**

A video about Emmy Noether, who Einstein described as "the most important woman in mathematics." Her most important findings relate to the relationship between symmetries and conservation laws.

**Curriculum connection:**- 2. Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations**Suggested use:**- Introductory discussion on conservation laws and the relationships between them**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Math 30-2: Geometry****Mathematician: Maryam Mirzakhani**

The 2014 Fields medalist, Maryam Mirzakhani speaks about her contributions and interests in mathematics which include space and geometric structures. Can use with video resource and article.

**Curriculum connection:**

- 3. Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons**Suggested use:**

- Introduction to geometry

- Activity using geometric structures to solve equations**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Struggle to Success | Mathematician: Maryam Mirzakhani**

Biography of the Iranian mathematician Maryam Mirzakhani who contributed to the field of geometry. Mirzakhani was the first woman to ever win a Field Medal for mathematics in 2014. She grew up in Iran, and attended Harvard University in 2004.

**Curriculum connection:**

- 3. Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons**Suggested use:**

- Introduce a notable mathematician weekly

- Hook for math/art task using geometric shapes such as creating a unique print or pattern

- Discuss resilience and approaches to problem solving

- Hook for a written reflection on using problem solving techniques across the subjects**Accessibility:**

- Manual transcription available

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Miscellaneous - More mathematicians to introduce****Mathematician: Alberto Pedro Calderón**

Argentinian mathematician who developed theories leading to the advancement of differential calculus.

**Suggested use:**

- Read to understand the history of Mathematician Alberto Pedro Calderón, who is from Argentina, and how he led to developments in Mathematics

- Can use the following resources to have the students research different Mathematicians and their contributions to Mathematics**Accessibility:**

- Accessible for nonverbal and hard of hearing

- Additional accommodations required for visually impaired students

**One of the Greatest Mathematicians of the Islamic World | Mathematician: Jamshid Al-Kashi**

Video describing the like and mathematical contributions of Jamshid Al-Kashi. Al-Kashi was a Persian mathematician who contributed immensely to the fields of algebra, geometry and trigonometry.

**Suggested use:**

- Watch to develop an understanding of Persian influence on mathematics

- Students research different mathematicians and their contributions to mathematics**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**A Symbol of Human Triumph | Mathematician: John F. Nash Jr.**

Video about the brilliant John F. Nash, one of the most well-known people living with schizophrenia of his time, and his journey to winning a Nobel Prize in Economics.

**Suggested use:**

- Discuss the accessibility of math: How accessible is being a mathematician? How might we change our practices to make it more accessible for everyone?

- Students research different mathematicians and their contributions to mathematics**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**11 Famous African American Mathematicians You Should Know About**

A website containing 11 incredible African-American mathematicians and their stories.

**Mathematician: Gladys West**

Born and raised in Virginia, Gladys West leveraged her mathematical and programming expertise to invent an accurate model of the Earth which was used as the foundation for the creation of the Global Positioning System (GPS). She was the second black woman ever to be employed by the Naval Surface Warfare Center Dahlgren Division and was inducted into the United States Air Force Hall of Fame—one of the highest honours awarded by the Air Force.

**Mathematician: Charles Lewis Reason**

Website with a short biography of Charles Reason, the first African-American mathematics professor at a predominantly white college. Reason not only teach mathematics, but made significant contributions to the advancement of education for African-Americans. He was also part of one of the first movements to end racial segregation in the New York school district.

**Mathematician: Euphemia Lofton Haynes**

Website that gives a short biography of Euphemia Lofton Haynes who was the first African-American woman to gain a PhD in mathematics in 1943. She received this PhD from the Catholic University of America, and then went on to be a prominent mathematics educator, and later became a professor. She was very outspoken on segregation policies implemented in schools around Washington DC, and became known for her advocacy efforts in this area.

**Rare Video of Human Computer Shakuntala | Mathematician: Shakuntala Devi**

Video of the human computer Shakuntala Devi performing mathematical computing for a spot in the Guiness Book of World Records.

**Suggested use:**

- Hold class discussion on mathematical uses in real life

- Research careers in mathematics

- Discussion on significant individuals in mathematics, particularly women of colour**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Shanghai history | Mathematician: Xu Guangqi**

Xu Guangqi was a Chinese astronomer, mathematician, politician, and writer during the Ming dynasty. Some Chinese scholars credit Xu as having "started China's enlightenment" by translating part of Euclid's works.

**Suggested use:**

- Showcase the diversity that exists in the math world

- Introduce a notable mathematician weekly**Accessibility:**

- Captioned by creator

**Yaashwin Sarawanan is a Human Calculator!**

Yaashwin Sarawanan demonstrates his extraordinary mental math skills by competing in the Asia's Got Talent competition.

**Suggested use:**

- Use as a resource for problem solving, pull apart the steps to solve a problem connected to operations, have students share their preferred strategy**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Jake: Math prodigy proud of his autism**

Jake is a college sophomore and a math and science prodigy. Jake says his autism is key to his success.

**Suggested use:**

- Introduction to discussion about how stereotypes in the math world can impact students (willingness to take risks, try something that they are interested in, gender stereotypes)**Accessibility:**

- No captions; additional accommodations for hard of hearing students required

**The World's Best Mathematician | Mathematician: Terry Tao**

A video about Terry Tao and how he was so interested in math. Among current mathematicians, many people regard Professor Tao as the world's finest.

**Suggested use:**

- Showcase the diversity that exists in the math world

- Introduce a notable mathematician weekly**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**A Mathematician Who Dances to the Joys and Sorrows of Discovery | Mathematician: Federico Ardila**

Federico Ardila is a Colombian mathematician, teacher, and DJ. Article for further information on Ardila.

**Suggested use:**

- Use to highlight careers in math**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Mathematician: Bhaskaracharya**

A detailed video about the life and contributions to mathematics of Bhaskaracharya.

**Suggested use:**

- Showcase the diversity that exists in the math world

- Introduce a notable mathematician weekly**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**John Urschel: The NFL's Smartest Man**

A short, documentary-style video about John Urschel, a Canadian former NFL player who played for the Baltimore Ravens while pursuing his passion for mathematics by getting a PhD at MIT. He has published several papers and won multiple awards.

**Suggested use:**

- Introduction to discussion about how stereotypes in the math world can impact students (willingness to take risks, try something that they are interested in, gender stereotypes)**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Mathematics of the Americas: Activity Booklet**

PDF of various mathematics activities that incorporate lessons about mathematics developed in various South American civilizations (Aztec and Inca).

**Curriculum connection:**

- Covers various outcomes across all units**Suggested use:**

- The Mathematics of the Maya activities include: Place Value and Number Operations for Grades 9–12, where students calculate perimeter, area, surface area, and volume of the Mayan Pyramid and interpret linear, quadratic and cubic functions

- The Mathematics of the Inca activities include: Data Analysis, Numbers and Number Sense for Grades 9–12, where students create and explore the Inca “quipu,” knotted, color-coded cords, to represent collected data, and use a graphing calculator to represent the data as scatter plots and calculate linear regressions

- The Mathematics of the Aztec activities include: Geometry and Data Analysis for Grades 9–12, where students create and explore the Aztec calendar to compute areas of common geometric figures

- The Mathematics of the Navajo activities include: Geometry for Grades 9–12, where students learn the effect of transformations on figures in the coordinate plane and space**Accessibility:**

- Accessible for nonverbal and hard of hearing

**30-1: Algebra and Number********Vedic Mathematics**

PDF of traditional Hindu mathematics tricks that were outlined in the ancient Hindu vedas. Part of the PDF shows tricks for determining roots and powers.

**Curriculum connection:**- 1. Apply the fundamental counting principle to solve problems**Suggested use:**- After showing video have introduction discussion on determining roots and powers

- Great for discussion on similarities and differences in math in different cultures**Accessibility:**- Accessible for nonverbal and hard of hearing

**History of Algebra**

PDF document that describes the history of algebra and the instrumental contribution of Egyptian mathematicians to the development of algebraic principles. The document also details the contributions of South Asian and East Asian mathematicians. All of this is integrated in the general history of algebra including important European mathematicians.

- Curriculum
**connection**:

- 1. Apply the fundamental counting principle to solve problems **Suggested use:**- Cross-curricular with English and Social Studies

- Use as hook for each concept, provide the cultural connections to each mathematic concept**Accessibility:**- Accessible for nonverbal and hard of hearing

**30-2: Probability**

**First Nations Games of Chance**

List of traditional First Nations games of chance including instructions to these games.

**Curriculum connection:**- 1. Interpret and assess the validity of odds and probability statements.**Suggested use:**- Students can play these games to gain their understanding of probability**Accessibility:**- Accommodations required

**Miscellaneous****This is what India has Contributed to Mathematics**

Website with short descriptions of all of the ways that India has contributed to the development of mathematics throughout the years. Descriptions also focus on how the narrative around the development of mathematics was generally Eurocentric and has since been appropriated by Western culture.

**Suggested use:**

- Read through to see the various ways that South Asians have contributed to the development of mathematics**Accessibility:**

- Accessible for nonverbal and hard of hearing

**Mayan Mathematics**

Short history of Mayan mathematics systems that were responsible for the development of the first Mayan calendar. In order to create this calendar, the Mayan's had to develop a number system with the base number of 20. This calendar has informed the common calendar used around the world today.

**Suggested use:**

- Read through to have a comprehensive understanding of how mathematics have been developed by the Mayans as well as various groups throughout history**Accessibility:**

- Accessible for nonverbal and hard of hearing

**TNJ 25 Influential Black Women in Business - Janeen T Uzzell**

Janeen Uzzell is a Global Technology Executive and Chief Operating Officer of the Wikimedia Foundation. She previously served as Director of Healthcare Programs in Africa and Head of Women in Technology for General Electric.

**Suggested use:**

- Highlights the importance of careers in STEM**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Teaching Mathematics for Social Justice: Conversations with Educators**

Book that discusses the challenges and strengths of incorporating anti-racism and social justice into mathematics education. The book describes ways to do this and the nuances and sensitivities needs to do this properly in a classroom setting. Note: This book is $36.95.

**Suggested use:**

- Use to inform your teaching practice to relate math and social justice issues

**Mathematics is the sense you never knew you had**

In this TED Talk, Eddie Woo believes that mathematics can be embraced and even enjoyed by absolutely everybody. He was named Australia's Local Hero and was a Top 10 Finalist in the Global Teacher Prize for his love of teaching mathematics.

**Suggested use:**

- Use to hook students on the importance and beauty of math