**DRAFT:**This module has unpublished changes.

**DRAFT:**This module has unpublished changes.

After persecution for his homosexuality, Alan Turing is now considered the father of computer science. He is celebrated by the math and computer science communities for his contributions and his open sexuality. How can we get beyond people’s differences and appreciate each person for who they are and what they do? Can you think of any examples of underappreciated or targeted groups or individuals in our society?

**Rationale:**

Matrices are an important part of any Algebra II curriculum. Matrices expose students to a new way of organizing and manipulating data in interesting ways and have many practical applications. Working with matrices requires familiarity with inverse matrices, matrix multiplication, and finding determinants. My lesson incorporates all these concepts by connecting them with coding and decoding secret messages (in this case, facts about the LGBT community).

Cryptanalysis is essential to our current society (especially with the emergence of the internet) as well as in history. Alan Turing was a cryptanalyst during World War Two and was central to cracking the German Enigmas. Turing was persecuted for his homosexuality despite his important contributions to the allied efforts in the war. Although we will not be using the early computer science methods that Turing used, much of the same logic he used can be applied to deciphering matrix encoded messages.

Day One

1. Discuss Alan Turing’s contributions to deciphering German Engimas in WWII.

2. Discuss how we are going to encode and decode messages using matrices.

3. Introduce matrix notation and operations.

4. Have students to play with multiplying, inverting, and finding determinants of given matrices on their own. Allow students to work with each other if they want. Be sure to walk around to room to make sure students are staying on task.

5. Discuss which matrices were invertible and which weren’t. What needs to be true for a matrix to invert? Why is it useful to find the determinant?

Day Two:

1. Show and discuss how matrices can be used to decode messages. Demonstrate how to decode a message using a matrix dimension rules. What are the limitations of matrix ciphers?

2. Have students in groups decode messages (facts about the LGBT community) Give the students the coded messages, and the key matrices but do not tell them which matrix will decode which message. The students will need to work together and use the process of elimination to decode the LGBT facts.

3. Have students write all the decoded LGBT facts on a display to show their work.

4. Discuss how we would code a secret message. Have students brainstorm which matrix operation to use to code.

5. For homework have students code an idea that they have learned from the LBGT awareness week.

**DRAFT:**This module has unpublished changes.

**DRAFT:**This module has unpublished changes.

Day Three:

1. Quick quiz to assess how well students understand matrix operations and cryptography.

2. Have students exchange their coded messages that they made for homework.

3. Bring class together for group discussion on Alan Turing’s contributions and persecution. Are there any groups in today’s society that are underappreciated or unfairly targeted?

4. Bring in surprise panel of gay math major friends from BU. Have the panel share their experiences of being gay and being a mathematician with the class. Allow plenty of time for questions.

**DRAFT:**This module has unpublished changes.

**DRAFT:**This module has unpublished changes.

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