Content/Topic: Secondary Math: Algebra II

Author:Theressa Smith

Content/Topic: Secondary Math: Algebra II

Title (as it appears on first slide): Sophie Germain

Intended audience: 10th & 11th grade students

Subject area: Algebra II

Grade level: 10 & 11

NETS-T standards being met by the teacher:

1. Facilitate and inspire student learning and creativity Teachers use their knowledge of subject matter, teaching and learning, and technology to facilitate experiences that advance student learning, creativity, and innovation in both face-to-face and virtual environments.

a. Promote, support, and model creative and innovative thinking and inventiveness

c. Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative processes

2. Design and develop digital age learning experiences and assessments Teachers design, develop, and evaluate authentic learning experiences and assessments incorporating contemporary tools and resources to maximize content learning in context and to develop the knowledge, skills, and attitudes identified in the Standards•S.

a. Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity

Wyoming Common Core standards being met by the student:

Each student will research a different function so each sub-standard will be completed by individual groups as a review activity.

Analyze functions using different representations

7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

1. Graph linear and quadratic functions and show intercepts, maxima, and minima.
2. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
3. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
4. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
5. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Answer the following questions (Goals/Objectives):

Sophie Germain explores the life and accomplishments of Sophie Germain. This is intended to be used as an example for students. Students will break up into groups of 3-4 and create their own video based on a famous mathematician (Pythagoras, Euclid, Euler, Fibonacci, Lagrange, Pascal, Newton, Archimedes, Gauss, Einstein, Fermat, or Boule). Their presentation will also feature the equations these mathematicians created that were studied in class. This lesson is designed to help students review the major math equations they have learned.

I chose Sophie Germain because her story is one of perseverance. Often at the end of the year students can become disheartened so I wanted to share this story to encourage them.

Rationale for Audience Appropriateness: My story is appropriate for high school algebra students because it will be a review activity for students. I have designed this project to be a fun new look at the history of mathematics so that the lesson is review but students will use their research skills and creativity to create their stories. This project will entail students creating a video telling the history behind the mathematicians who created the formulas and equations we studied in class this year. Each group will pick a mathematician and will create a video about their story. These stories will feature the math equation their mathematician created.

Slide # 1

Narration: / Media:
Hi, my name is Sophie Germain. I am a young middle class French girl growing up in during the French Revolution. /
Transitions / Estimated Timing: 10 seconds

Media Selection Rationale: This introduces Sophie Germain.

Slide # 2

Narration: / Media:
One day I was reading in my father’s study when I came across the legend of Archimedes. /
Transitions / Estimated Timing: 6 seconds

Media Selection Rationale: This leads into the story of Archimedes.

Slide # 3

Narration: / Media:
According to the legend, Archimedes was working on a geometry problem when his town was invaded by Roman soldiers. The soldiers ordered Archimedes to move but he wouldn’t since he wasn’t finished with his problem. /
Transitions / Estimated Timing: 12 seconds

Media Selection Rationale: This is the legend of Archimedes’ death (part I).

Slide # 4

Narration: / Media:
So the soldiers speared him. /
Transitions / Estimated Timing: 3

Media Selection Rationale: This is the legend of Archimedes’ death (part II). This would inspire Sophie.

Slide # 5

Narration: / Media:
I was so inspired! If Archimedes was so engrossed in math that he was willing to die, then math must be fascinating. /
Transitions / Estimated Timing: 7

Media Selection Rationale: This explains why Sophie was so moved by Archimedes’ death.

Slide # 6

Narration: / Media:
This made me want to learn everything I could about math. /
Transitions / Estimated Timing: 2

Media Selection Rationale: Sophie decided she wanted to dedicate her life to the study of mathematics.

Slide # 7

Narration: / Media:
So I started to teach myself calculus. /
Transitions / Estimated Timing: 3

Media Selection Rationale: Sophie began to study Calculus.

Slide # 8

Narration: / Media:
My parents did not approve. It was not proper for girls of my status to study mathematics. /
Transitions / Estimated Timing: 6

Media Selection Rationale: Her parents became worried (which was normal during this time) about Sophie because her studies were improper for a middle class woman.

Slide # 9

Narration: / Media:
So to stop me from studying, my parents disposed of my books and candles. /
Transitions / Estimated Timing: 4

Media Selection Rationale: Her parents threw away her books, hid her candles, and turned off the heat.

Slide # 10

Narration: / Media:
But I wasn’t going to let that stop me from studying math, it was my passion! /
Transitions / Estimated Timing: 4

Media Selection Rationale: But Sophie would not be deterred.

Slide # 11

Narration: / Media:
My parents saw this and began turning off the heat at night so that I would be too cold to study. My ink would freeze because it was so cold! I often hid candles and quilts so that I could use them to keep warm while I studied. /
Transitions / Estimated Timing: 13

Media Selection Rationale: She found ways to continue her studies, even without heat!

Slide # 12

Narration: / Media:
Eventually my persistence paid off. My parents gave in and allowed me to study. /
Transitions / Estimated Timing: 6

Media Selection Rationale: Eventually her parents gave in.

Slide # 13

Narration: / Media:
It was my dream to attend school, but girls were not allowed unless they were very wealthy. /
Transitions / Estimated Timing: 5

Media Selection Rationale: Sophie wanted to attend school but most* girls were not allowed.

*Only wealthy women were permitted to attend college.

Slide # 14

Narration: / Media:
I was only a middle class woman so following my dream called for drastic measures. I decided to impersonate the student M. Le Blanc since he had dropped out from the university and went home. /
Transitions / Estimated Timing: 12

Media Selection Rationale: Sophie decides to impersonate the student M. Le Blanc so that she could “attend” school.

Slide # 15

Narration: / Media:
I could not attend class but my friends would give me their lecture notes so I could keep up with the lessons. /
Transitions / Estimated Timing: 6

Media Selection Rationale: Her friends gave her their lecture notes since she could not go to school without being caught.

Slide # 16

Narration: / Media:
Eventually my teacher, Lagrange, found out my secret. He was surprised that I was a woman but was delighted with my work. He was so impressed that he offered to become my mentor. /
Transitions / Estimated Timing: 11

Media Selection Rationale: Lagrange found out she was a girl but was impressed with her work so he offered to become her mentor. This would open many doors for Sophie.

Slide # 17

Narration: / Media:
My new mentor introduced me to one of the greatest mathematicians of my time, Gauss. We started a correspondence and became close friends. We often discussed number theory and later Fermont’s last theory. /
Transitions / Estimated Timing: 14

Media Selection Rationale: Sophie’s correspondence with Gauss would lead to some of her greatest works.

Slide # 18

Narration: / Media:
In 1810 a new mathematics competition was announced. I was intrigued and decided to enter a paper. I was the only person to submit a paper. /
Transitions / Estimated Timing: 10

Media Selection Rationale: This competition would be a turning point in her career.

Slide # 19

Narration: / Media:
My paper was rejected. The contest was extended so I decided to submit a revised paper after Lagrange corrected my errors. /
Transitions / Estimated Timing: 8

Media Selection Rationale: Her first paper was rejected even though it was the only one submitted.

Slide # 20

Narration: / Media:
This time I got an honorable mention for my efforts. Still no one won the contest so it was extended once more. Once again I submitted my paper, hoping for the best. /
Transitions / Estimated Timing: 11

Media Selection Rationale: Her second paper only received an honorable mention, even with the corrections Lagrange made.

Slide # 21

Narration: / Media:
This time I won! /
Transitions: Chimes / Estimated Timing: 4

Media Selection Rationale: Her third paper won. Finally.

Slide # 22

Narration: / Media:
I was rewarded for my efforts with an achievement medal. /
Transitions / Estimated Timing: 3

Media Selection Rationale: She was awarded an achievement medal.

Slide # 23

Narration: / Media:
I also received a letter from the Institute de France. I was the first woman that was not a wife of a mathematician to be invited. /
Transitions / Estimated Timing: 8

Media Selection Rationale: She received a letter from the Institute de France, which was an honor.

Slide # 24

Narration: / Media:
After so many years of working in mathematics I decided to take a break and pursue physics. /
Transitions / Estimated Timing: 7

Media Selection Rationale: Sophie then took a break from mathematics to focus on physics.

Slide # 25

Narration: / Media:
My old friend Gauss often advocated my work and nominated me to receive an honorary degree in mathematics for my contributions. /
Transitions / Estimated Timing: 9

Media Selection Rationale: Gauss would later advocate for her to receive an honorary degree for her efforts and contributions.

Slide # 26

Narration: / Media:
Unfortunately I died of breast cancer before I could receive my degree. /
Transitions / Estimated Timing: 4

Media Selection Rationale: But Sophie died before she could receive her degree.

Slide # 27

Narration: / Media:
Transitions / Estimated Timing: 16

Media Selection Rationale: This is a slide that depicts Sophie’s legacy.

Slide # 28

Narration: / Media:
Transitions / Estimated Timing: 3

Media Selection Rationale: The end.

Slide # 29

Narration: / Media:
Credits:
Original cartoons created by Theressa Smith using Toondoo.com
Information about Sophie Germain was gathered from the following articles:
Sophie Germain by Amanda Swift

Sophie Germain French Mathematician by June Barrow-Green

Marie-Sophie Germain by J J O'Connor and E F Robertson

Math's Hidden Woman by Simon Singh

Transitions / Estimated Timing: 10