**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:** Northwestern Crows

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops by viewing a video clip; then, they plan a classroom experiment to model the dropping of whelks in order to collect and analyze data.
**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,Science

**Title:**Northwestern Crows

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate the relationship between the height of the drop and the number of drops by viewing a video clip; then, they plan a classroom experiment to model the dropping of whelks in order to collect and analyze data.

**Thinkfinity Partner:**Illuminations

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

**Title:** Conduct an Experiment

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate whether the crows minimize their work by dropping whelks as they do. The amount of work depends upon the height of the drop and the number of times the crow has to fly to this height. To answer the question, students explore the relationship between the height of the drop and the number of drops needed.
**Standard(s): **

[MA2015] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama)

**Subject:**Mathematics,Science

**Title:**Conduct an Experiment

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use rational functions to investigate the feeding behavior of Northwestern Crows. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. Students investigate whether the crows minimize their work by dropping whelks as they do. The amount of work depends upon the height of the drop and the number of times the crow has to fly to this height. To answer the question, students explore the relationship between the height of the drop and the number of drops needed.

**Thinkfinity Partner:**Illuminations

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