**Title:** Dice Roll Project

**Description:**
This project is a fun way for students to observe the integration of a probability lesson with spreadsheet software. Students will record 36 rolls of a pair of dice. After they record their data, students will manually calculate the mean, median, mode and range. Students will then observe how quickly a computer can do those same calculations and many more things with that same data. Students will also compare experimental outcomes to the theoretical outcome.
**Standard(s): **

**Subject:**Mathematics (7 - 12), or Technology Education (9 - 12)

**Title:**Dice Roll Project

**Description:**This project is a fun way for students to observe the integration of a probability lesson with spreadsheet software. Students will record 36 rolls of a pair of dice. After they record their data, students will manually calculate the mean, median, mode and range. Students will then observe how quickly a computer can do those same calculations and many more things with that same data. Students will also compare experimental outcomes to the theoretical outcome.

**Title:** Check That Digit

**Description:**
In this Illuminations lesson, students are introduced to a common and practical use of modular arithmetic. First the barcode system is examined, specifically UPC and ISBN bar coding. Then, students discover the applications of modular arithmetic as applied to credit card numbers. There are also links to an online activity sheet and other related resources.
**Standard(s): **

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

**Subject:**Mathematics

**Title:**Check That Digit

**Description:**In this Illuminations lesson, students are introduced to a common and practical use of modular arithmetic. First the barcode system is examined, specifically UPC and ISBN bar coding. Then, students discover the applications of modular arithmetic as applied to credit card numbers. There are also links to an online activity sheet and other related resources.

**Thinkfinity Partner:**Illuminations

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

**Title:** Check That Digit Activity Sheet

**Description:**
This reproducible worksheet, from an Illuminations lesson, guides students as they learn how modular arithmetic is applied to UPC and ISBN bar coding.
**Standard(s): **

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

**Subject:**Mathematics

**Title:**Check That Digit Activity Sheet

**Description:**This reproducible worksheet, from an Illuminations lesson, guides students as they learn how modular arithmetic is applied to UPC and ISBN bar coding.

**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:** Tower of Hanoi

**Description:**
This student interactive, from Illuminations, presents a tower of from three to 20 disks, initially stacked in increasing size on one of three pegs. The goal is to move all the discs from the left peg to the right one using the smallest number of moves possible.
**Standard(s): **

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

**Subject:**Mathematics

**Title:**Tower of Hanoi

**Description:**This student interactive, from Illuminations, presents a tower of from three to 20 disks, initially stacked in increasing size on one of three pegs. The goal is to move all the discs from the left peg to the right one using the smallest number of moves possible.

**Thinkfinity Partner:**Illuminations

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