## Grade Eight Mathematics

Students will develop an understanding of four general units: Numbers, Patterns and Relations, Shape and Space; Measurement, and 3-D/2-D objects, Statistics and Probability.

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__

__NUMBERS__

**An Indian Mathematician and Astronomer | Mathematician: Bhaskaracharya**

Shorter video about the findings of Bhaskaracharya, which includes the discovery that any number divided by zero is equal to infinity.

**Curriculum connection:**

- 1a. Demonstrate an understanding of perfect squares and square roots concretely and pictorially along with symbolically (limited to whole numbers)**Suggested use:**

- Discussion on the division of zero and the idea of infinity**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Terence Tao on Prime Numbers | Mathematician: Terence Tao**

Mathematician Terence Tao explains the Euclid's theorem for prime numbers. Article available for more information on Euclid's theorem.

**Curriculum connection:**- 2a. Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers)**Suggested use:**- Discussion on the infinity of prime numbers**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**The Murder of Ancient Alexandria's Greatest Scholar | Mathematician: Hypatia**

Biography of the Egyptian mathematician and philosopher Hypatia. Hypatia contributed significantly to the development of long division.

**Curriculum connection:**- 7a. Demonstrate an understanding of multiplication and division of integers, concretely, pictorially and symbolically**Suggested use:**- Hook for math task involving division

- Use video to begin discussion about the historical and culturally diverse contributions made to development of math**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Black Mathematicians**

Rap video celebrating African-American pioneers in Mathematics. Mathematicians mentioned include:

Benjamin Banneker, Mary Jackson, Katherine Johnson, Elbert Cox, Martha Haynes, Dudley Woodard, David Blackwell, Annie Easley, Evelyn Granville, Emery Brown, Marjorie Brown, William Claytor, Charles Reason.

**Curriculum connection:**- 7a. Demonstrate an understanding of multiplication and division of integers, concretely, pictorially and symbolically**Suggested use:**- Introduce and discuss notable mathematicians of color

- Students choose a mathematician from the video to research about

- Word problems with references to mathematicians from the video**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**PATTERNS AND RELATIONS: VARIABLES AND EQUATIONS**

**Why Algorithms are called Algorithms | Mathematician: Muhammad al-Khwarizmi**

Extension of the biography of Al-Khwarizmi who helped to develop algebra and the idea of an algorithm.

**Curriculum connection:**

- 2c. Model and solve problems concretely, pictorially and symbolically, using linear equations of the form: ax = b; x/a = b, a ≠ 0; ax + b = c; x/a + b = c, a ≠ 0; a(x + b) = c; where a, b and c are integers**Suggested use:**

- Representation of BIPOC in math

- Discussion/research on algebra history**Accessibility:**

- Manual transcription available

**Mathematician: Abu Jaf'ar Muhammad ibn Musa Al-Khwarizmi**

Biography of a Persian mathematician that is known as one of the "fathers of algebra". The biography details his contributions to algebra and the general details of his life.

**Curriculum connection:**

- 2c. Model and solve problems concretely, pictorially and symbolically, using linear equations of the form: ax = b; x/a = b, a ≠ 0; ax + b = c; x/a + b = c, a ≠ 0; a(x + b) = c; where a, b and c are integers**Suggested use:**

- Discussion/research on algebra history**Accessibility:**

- Accessible for nonverbal, hard of hearing, and visually impaired; additional accommodations may be required

**Mathematican: Seki Takakazu**

Seki Takakazu was a Japanese mathematician, whose most important research was about algebra. He lived during the same era as Newton, but the two could not exchange information, and therefore developed and studied their ideas seperately.

**Curriculum connection:**- 2c. Model and solve problems concretely, pictorially and symbolically, using linear equations of the form: ax = b; x/a = b, a ≠ 0; ax + b = c; x/a + b = c, a ≠ 0; a(x + b) = c; where a, b and c are integers**Suggested use:**- Introduction to algebra

- Discussion of similarities in math across cultures**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

__SHAPE AND SPACE: MEASUREMENT__**What do you know about the Muslim scientist Abu Kamil “The Reckoner”? | Mathematician: Abu Kamil**

A short video about Abu Kamil, an Egyptian Mathematician during the Islamic Golden Age. He is known to be the first to solve complex algebraic equations, and geometric equations.

**Curriculum connection:**

- 1d. Develop and apply the Pythagorean theorem to solve problems**Suggested use:**

- Introduction to algebra/geometry, assign and discuss a variety of equations**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**SHAPE AND SPACE: 2-D SHAPES AND 3-D OBJECTS****Mathematician: William Claytor**

Biography of mathematician William Claytor. Claytor was the third African-American man to earn a PhD in mathematics in the US. Claytor contributed greatly to the field of mathematical topology, a branch of geometry.

**Curriculum connection:**

- 1e. Draw and interpret top and front and side views of 3-D objects composed of right rectangular prisms**Suggested use:**

- Representation of BIPOC in math

- Introduction into geometry

- Have students complete topology worksheets**Accessibility:**

- Accessible for nonverbal, hard of hearing, and visually impaired; additional accommodations may be required

**Mathematician: Maryam Mirzakhani**

The 2014 Fields medalist, Maryam Mirzakhani speaks about her contributions and interests in mathematics which include: space and geometric structures.

**Curriculum connection:**

- 1e. Draw and interpret top and front and side views of 3-D objects composed of right rectangular prisms**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:**

- 1e. Draw and interpret top and front and side views of 3-D objects composed of right rectangular prisms**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**Accessibility:**

- Manual transcription available

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Mathematician: Brahmagupta**

Brahmagupta, the greatest of ancient Indian mathematicians, first showed how to use zero as a number and made many other important discoveries in algebra, geometry, and trigonometry

**Curriculum connection:**- 1e. Draw and interpret top and front and side views of 3-D objects composed of right rectangular prisms**Suggested use:**- Representation of BIPOC in math

- Introductory discussion on algebra/geometry and trigonometry

- Research project of BIPOC in geometry and their contributions**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**STATISTICS AND PROBABILITY****Remembering David Blackwell | Mathematician: David Blackwell**

Brief biography of the mathematical contributions of African American statistician David Blackwell. Blackwell made significant contributions to the field of probability.

**Curriculum connection:**

- 2h. Solve problems involving the probability of independent events**Suggested use:**

- Introduction to probability unit have students complete an introductory worksheet on probability

- Class discussion on real life situations involving probability**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**MISCELLANEOUS: MORE MATHEMATICANS TO INTRODUCE****India's Human Computer | Mathematician: Shakuntala Devi**

An interview with the impressive Shakuntala Devi, known for her fast calculations, earning her a place in the Guinness World Record Book.

**Suggested use:**- Hold class discussion on mathematical uses in real life

- Research careers in mathematics

- Discussion on significant individuals in mathematics**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**

Born in 1731 to formerly enslaved parents on a farm in Baltimore, Benjamin Banneker was obsessed with math and science. And his appetite for knowledge only grew as he taught himself astronomy, mathematics, engineering, and the study of the natural world. Rose-Margaret Ekeng-Itua details the numerous accomplishments of Benjamin Banneker.

**Suggested use:**- Use an example of resilience in the math world, noting how he overcame many barriers (including racism) to pursue his passions**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**The 11-Year-Old Math Marvel**

A video about the young girl, Aarushi. At 8, she ranked second among her peers in Singapore at the Singapore and Asian Schools Math Olympiad. At 11, she's solving puzzles taught at university, and playing chess blindfolded. But Aarushi is finding out that with such gifts comes the pressure of expectations.

**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

- Highlight that everyone (no gender) can excel at math

- 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

**Mathematician: Shen Kuo**

A video about Shen Kuo, an acclaimed mathematician that is said to have been years ahead of European mathematicians and scientists of his time. He was the first to discover that a compass does not point exactly North, but to the magnetic north pole.

**Suggested use:**- 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

**Great Muslim Minds | Mathematician: Omar Khayyam**

A short video detailing the life of Omar Khayyam, a Persian mathematician, astronomer, and poet. He calculated an extremely accurate year length in the form of the Jalali calendar. This format is still used today as the official calendar in Iran and Afghanistan.

**Suggested use:**- Discussion/research on calendars from other cultures**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Mathematician: Dudley Weldon Woodard**

Website with a short biography on the life of Dudley Weldon Woodard, the second African-American man to earn a PhD in the US. Woodard was a professor of mathematics at various universities including Columbia University, Howard University and the University of Chicago. He received his PhD from the University of Pennsylvania in 1928, and made significant contributions to the advancement of mathematics education.

**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.

**Suggested use:**- Research project on the first Black men of mathematics and the different contributions they provided**Accessibility:**- Accessible for nonverbal, hard of hearing, and visually impaired; additional accommodations may be required

**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.

**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:**

- Accessible for nonverbal, hard of hearing, and visually impaired; additional accommodations may be required

**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

**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

**The Blind Mathematician | Mathematician: Abraham Nemeth**

An inspirational video about the life of Abraham Nemeth, who created a braille-like system to solve complex mathematical equations, which is still used today.

**Suggested use:**

- Hold a class discussion about math and accessibility

- Introduction to symbols and other signs in math**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**Hidden Figuras: Mary Golda Ross**

A video about the life of Mary Golda Ross, the first Indigenous engineer in the United States.

**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

**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

**Mathematician: Annie Easley**

Short video about the career of Annie Easley, one of NASA's first computer scientists, then referred to as simply "computers." Her contributions had a lasting impact, even after she retired from NASA, helping to launch the Cassini Probe, the first spacecraft to orbit Saturn.

**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

**Indigenous Math Games**

Rules and instructions of various First Nations math games. These games pan across various different units, allowing teachers to pick and choose which games fit in their classrooms. Each games also contains a list of math links to each game, making it easier for teachers to link the games to the curriculum.

**Curriculum connection:**

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

- Games can be used to teach and strengthen different concepts in math

- Once students know these games, they can be used when students are completed math work or in small math groups**Accessibility:**

- Additional accommodations required for all nonverbal, hard of hearing, and 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 4–8, where students explore different Mayan calendars and focus on the least common multiple of two numbers

- The Mathematics of the Inca activities include: Data Analysis, Numbers and Number Sense for Grades 4–8, where students create the Inca “quipu,” knotted, color-coded cords, to explore the concept of ratio

- The Mathematics of the Aztec activities include: Algebra for Grades 4–8, where students explore Aztec pyramids and the ratio of the height to the setback of the wall

- The Mathematics of the Navajo activities include: Geometry and Measurement for Grades 4–8, where students create a Navajo rug investigating transformations, symmetry, and area of different geometric designs**Accessibility:**

- Accessible for nonverbal and hard of hearing

__NUMBERS__

**History of Mathematics**

An animated video on the development of numbers throughout history.

**Curriculum connection:**- 1a. Demonstrate an understanding of perfect squares and square roots concretely and pictorially along with symbolically (limited to whole numbers)**Suggested use:**- Introduce the history of number and make connections to all contributions

- Discussion on how math and numbers have changed across cultures through history**Accessibility:**- Manual transcription available

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**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:**- 1a. Demonstrate an understanding of perfect squares and square roots concretely and pictorially along with symbolically (limited to whole numbers)**Suggested use:**- Introduction of sexagesimal/ base unit systems**Accessibility:**- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

**PATTERNS AND RELATIONS: VARIABLES AND EQUATIONS**

**The Most Beautiful Equation in Math Professor: Po-Shen Loh**

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

**Curriculum connection:**

- 2c. Model and solve problems concretely, pictorially and symbolically, using linear equations of the form: ax = b; x/a = b, a ≠ 0; ax + b = c; x/a + b = c, a ≠ 0; a(x + b) = c; where a, b and c are integers**Suggested use:**

- Introduction to Euler's number/equation and conservation dynamics**Accessibility:**

- Closed captioning available on video

- Accessible for hard of hearing and nonverbal

- No descriptive captioning available for visually impaired students

__SHAPE AND SPACE: MEASUREMENT__

**Dajae Williams Formula Songs**

Dajae Williams is a NASA engineer and educator. She created songs on the quadratic formula, unit conversions and order of operations.

**Curriculum connection:**- 1d. Develop and apply the Pythagorean theorem to solve problems**Suggested use:**- After listening to the song hold a class discussion on the quadratic formula**Accessibility:**- No captions; additional accommodations required for hard of hearing students

__SHAPE AND SPACE: 2-D SHAPES AND 3-D OBJECTS__

**Birch Bark Biting**

Website with lesson plans to teach student about the art of Birch Bark Biting in Aboriginal culture. These projects make a cross-curricular connection to art, allowing teachers to integrate math with art projects. The main math link in these projects relates to geometry of the birch biting design.

**Curriculum connection:**- 1e. Draw and interpret top and front and side views of 3-D objects composed of right rectangular prisms**Suggested use:**- Cross curricular connections (between Social, Science and Math)

- Inquiry based project to explore geometry and angles**Accessibility:**- Accessible for nonverbal, hard of hearing

- Additional accommodations required for visually impaired students

**STATISTICS AND PROBABILITY: CHANCE AND UNCERTAINTY**

**First Nations Games of Chance**

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

**Curriculum connection:**- 2h. Solve problems involving the probability of independent events**Suggested use:**- Students can play these games to gain their understanding of probability**Accessibility:**- Accessible for nonverbal, hard of hearing, and visually impaired; additional accommodations may be required

**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

__PATTERNS AND RELATIONS: VARIABLES AND EQUATIONS__**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:**

- 2c. Model and solve problems concretely, pictorially and symbolically, using linear equations of the form: ax = b; x/a = b, a ≠ 0; ax + b = c; x/a + b = c, a ≠ 0; a(x + b) = c; where a, b and c are integers**Suggested use:**

- Use as an introduction or extension assignment