**Title:** Vigenere Cipher: Student Reproducible

**Description:**
This reproducible worksheet, from an Illuminations lesson, poses several questions to students about the Vigenere cipher, which is a more complex form of the Caesar cipher.
**Standard(s): **

[MA2015] AL2 (9-12) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [S-CP9]

**Subject:**Mathematics

**Title:**Vigenere Cipher: Student Reproducible

**Description:**This reproducible worksheet, from an Illuminations lesson, poses several questions to students about the Vigenere cipher, which is a more complex form of the Caesar cipher.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Code Crackers

**Description:**
In this unit of two lessons, from Illuminations, students learn about two simple coding methods, the Caesar cipher and the Vigenere cipher. Students then use matrices and their inverses to create more sophisticated codes.
**Standard(s): **

[MA2015] AM1 (9-12) 6: (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network, including linear programming. [N-VM6] (Alabama)

**Subject:**Mathematics

**Title:**Code Crackers

**Description:**In this unit of two lessons, from Illuminations, students learn about two simple coding methods, the Caesar cipher and the Vigenere cipher. Students then use matrices and their inverses to create more sophisticated codes.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Combinations

**Description:**
This unit of two lessons, from Illuminations, focuses on combinations, a subject related to the probability-and-statistics strand of mathematics. Students are encouraged to discover all the combinations for a given situation using problem-solving skills (including elimination and collection of organized data) and drawing conclusions. The use of higher-level thinking skills (synthesis, analysis, and evaluations) is the overall goal.
**Standard(s): **

[MA2015] DM1 (9-12) 12: Use combinatorial reasoning and counting techniques to solve application-based problems. (Alabama)

**Subject:**Mathematics

**Title:**Combinations

**Description:**This unit of two lessons, from Illuminations, focuses on combinations, a subject related to the probability-and-statistics strand of mathematics. Students are encouraged to discover all the combinations for a given situation using problem-solving skills (including elimination and collection of organized data) and drawing conclusions. The use of higher-level thinking skills (synthesis, analysis, and evaluations) is the overall goal.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Birthday Paradox

**Description:**
This Illuminations lesson demonstrates the birthday paradox, using it as a springboard into a unit on probability. Students use the TI-83 graphing calculator to run a Monte Carlo simulation with the birthday paradox and engage in a graphical analysis of the birthday-problem function.
**Standard(s): **

[MA2015] PRE (9-12) 51: (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. [S-MD2]

**Subject:**Mathematics

**Title:**Birthday Paradox

**Description:**This Illuminations lesson demonstrates the birthday paradox, using it as a springboard into a unit on probability. Students use the TI-83 graphing calculator to run a Monte Carlo simulation with the birthday paradox and engage in a graphical analysis of the birthday-problem function.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8,9,10,11,12

**Title:** Stick or Switch?

**Description:**
This lesson, from Illuminations, presents a version of a classic game-show scenario. You pick one of three doors in hopes of winning the prize. The host opens one of the two remaining doors, which reveals no prize, and then asks if you wish to stick or switch. Which choice gives you the best chance to win? Students explore different approaches to this problem including guesses, experiments, computer simulations, and theoretical models.
**Standard(s): **

[MA2015] PRE (9-12) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [S-MD1]

**Subject:**Mathematics

**Title:**Stick or Switch?

**Description:**This lesson, from Illuminations, presents a version of a classic game-show scenario. You pick one of three doors in hopes of winning the prize. The host opens one of the two remaining doors, which reveals no prize, and then asks if you wish to stick or switch. Which choice gives you the best chance to win? Students explore different approaches to this problem including guesses, experiments, computer simulations, and theoretical models.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8,9,10,11,12

**Title:** Sticks and Stones Demo

**Description:**
This student interactive, from an Illuminations lesson, allows students to generate random throws for the game '' Sticks and Stones.'' In the game, three sticks are tossed and a player moves his or her marker according to how the sticks land.
**Standard(s): **

[MA2015] PRE (9-12) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [S-MD1]

**Subject:**Mathematics

**Title:**Sticks and Stones Demo

**Description:**This student interactive, from an Illuminations lesson, allows students to generate random throws for the game '' Sticks and Stones.'' In the game, three sticks are tossed and a player moves his or her marker according to how the sticks land.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Sticks and Stones

**Description:**
In this Illuminations lesson, students play Sticks and Stones, a game based on the Apache game Throw Sticks, which was played at multi-nation celebrations. Students collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game.
**Standard(s): **

[MA2015] PRE (9-12) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [S-MD1]

**Subject:**Mathematics

**Title:**Sticks and Stones

**Description:**In this Illuminations lesson, students play Sticks and Stones, a game based on the Apache game Throw Sticks, which was played at multi-nation celebrations. Students collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8

**Title:** Road Trip!

**Description:**
In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others.
**Standard(s): **

[MA2015] ALT (9-12) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]

**Subject:**Mathematics

**Title:**Road Trip!

**Description:**In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Vigenere Cipher

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students learn about the polyalphabetic Vigenere cipher. They encode and decode text using inverse operations.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**Vigenere Cipher

**Description:**In this lesson, one of a multi-part unit from Illuminations, students learn about the polyalphabetic Vigenere cipher. They encode and decode text using inverse operations.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Vigenere Grid

**Description:**
This reproducible transparency, from an Illuminations lesson, depicts a Vigenere Grid, which is used for encoding a message using a polyalphabetic cipher.
**Standard(s): **

[MA2015] AL1 (9-12) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2]

**Subject:**Mathematics

**Title:**Vigenere Grid

**Description:**This reproducible transparency, from an Illuminations lesson, depicts a Vigenere Grid, which is used for encoding a message using a polyalphabetic cipher.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12