**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:** Explorations with Chance

**Description:**
In this lesson, from Illuminations, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities for the learning phases of predicting results, playing the games, and calculating probability ratios.
**Standard(s): **

[MA2015] ALT (9-12) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6]

**Subject:**Mathematics

**Title:**Explorations with Chance

**Description:**In this lesson, from Illuminations, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities for the learning phases of predicting results, playing the games, and calculating probability ratios.

**Thinkfinity Partner:**Illuminations

**Grade Span:**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:** Fire

**Description:**
In this student interactive, from Illuminations, students can see the results of a fire if a forest is densely planted in a rectangular grid. Students are able to choose a starting place for the fire and enter the probability that a given tree will burn.
**Standard(s): **

**Subject:**Mathematics

**Title:**Fire

**Description:**In this student interactive, from Illuminations, students can see the results of a fire if a forest is densely planted in a rectangular grid. Students are able to choose a starting place for the fire and enter the probability that a given tree will burn.

**Thinkfinity Partner:**Illuminations

**Grade Span:**3,4,5,6,7,8,9,10,11,12