**Title:** I'm Going to Design a "'STUD'y Muffin"

**Description:**
This lesson is an introduction to help students see how people think and react to certain things. This lesson highlights the differences between observational study, experiment, and survey, including biased and unbiased statements.
This is a College- and Career-Ready Standards showcase lesson plan.
**Standard(s): **

[MA2015] PRE (9-12) 48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

**Subject:**Literacy Standards (6-12) (11 - 12), or Mathematics (9 - 12)

**Title:**I'm Going to Design a "'STUD'y Muffin"

**Description:**This lesson is an introduction to help students see how people think and react to certain things. This lesson highlights the differences between observational study, experiment, and survey, including biased and unbiased statements. This is a College- and Career-Ready Standards showcase lesson plan.

**Title:** Graphical Analysis

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. Students examine a graph of the data then use an interactive graphing tool to investigate three different situations.
**Standard(s): **

[MA2015] PRE (9-12) 48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

**Subject:**Mathematics,Science

**Title:**Graphical Analysis

**Description:**In this lesson, one of a multi-part unit from Illuminations, students use iteration, recursion, and algebra to model and analyze a changing fish population. Students examine a graph of the data then use an interactive graphing tool to investigate three different situations.

**Thinkfinity Partner:**Illuminations

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

**Title:** Make a Conjecture

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
**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:**Health,Mathematics

**Title:**Make a Conjecture

**Description:**In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.

**Thinkfinity Partner:**Illuminations

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

**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:** 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:** Sports Rankings

**Description:**
In this Science Update, from Science NetLinks, you'll hear how mathematicians at the Rochester Institute of Technology are suggesting changes to the ranking systems in sports. Project leader Darren Narayan says the goal is to factor in head-to-head competition. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources.
**Standard(s): **

[MA2015] PRE (9-12) 49: Evaluate reports based on data. [S-IC6]

**Subject:**Mathematics, Physical Education

**Title:**Sports Rankings

**Description:**In this Science Update, from Science NetLinks, you'll hear how mathematicians at the Rochester Institute of Technology are suggesting changes to the ranking systems in sports. Project leader Darren Narayan says the goal is to factor in head-to-head competition. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources.

**Thinkfinity Partner:**Science NetLinks

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

**Title:** Whelk-Come to Mathematics

**Description:**
In this four-lesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. 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.
**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:**Whelk-Come to Mathematics

**Description:**In this four-lesson unit, from Illuminations, students make a conjecture, conduct an experiment, analyze data and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. 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.

**Thinkfinity Partner:**Illuminations

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

**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

**Title:** Shrinking Candles, Running Water, Folding Boxes

**Description:**
This lesson, from Illuminations, allows students to look for functions within a given set of data. After analyzing the data, the students should be able to determine the type of function that represents the data.
**Standard(s): **

[MA2015] PRE (9-12) 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)

**Subject:**Mathematics

**Title:**Shrinking Candles, Running Water, Folding Boxes

**Description:**This lesson, from Illuminations, allows students to look for functions within a given set of data. After analyzing the data, the students should be able to determine the type of function that represents the data.

**Thinkfinity Partner:**Illuminations

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

**Title:** The Effects of Outliers

**Description:**
This lesson, one of a multi-part unit from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computer-based interactive tool. Using the Regression Line Applet, students investigate the effect of outliers on a regression line and easily see their significance.
**Standard(s): **

[MA2015] PRE (9-12) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1]

**Subject:**Mathematics

**Title:**The Effects of Outliers

**Description:**This lesson, one of a multi-part unit from Illuminations, provides students with the opportunity to investigate the relationship between a set of data points and a curve used to fit the data points, using a computer-based interactive tool. Using the Regression Line Applet, students investigate the effect of outliers on a regression line and easily see their significance.

**Thinkfinity Partner:**Illuminations

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

**Title:** Sports Rankings

**Description:**
In this Science Update, from Science NetLinks, you'll hear how mathematicians at the Rochester Institute of Technology are suggesting changes to the ranking systems in sports. Project leader Darren Narayan says the goal is to factor in head-to-head competition. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources.
**Standard(s): **

[MA2015] PRE (9-12) 49: Evaluate reports based on data. [S-IC6]

**Subject:**Mathematics, Physical Education

**Title:**Sports Rankings

**Description:**In this Science Update, from Science NetLinks, you'll hear how mathematicians at the Rochester Institute of Technology are suggesting changes to the ranking systems in sports. Project leader Darren Narayan says the goal is to factor in head-to-head competition. Science Updates are audio interviews with scientists and are accompanied by a set of questions as well as links to related Science NetLinks lessons and other related resources.

**Thinkfinity Partner:**Science NetLinks

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

**Title:** Adjustable Spinner

**Description:**
This student interactive, from Illuminations, allows students to create their own spinners and examine the outcomes given a specified number of spins. Students learn that experimental probabilities differ according to the characteristics of the model.
**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:**Adjustable Spinner

**Description:**This student interactive, from Illuminations, allows students to create their own spinners and examine the outcomes given a specified number of spins. Students learn that experimental probabilities differ according to the characteristics of the model.

**Thinkfinity Partner:**Illuminations

**Grade Span:**K,PreK,1,2,3,4,5,6,7,8,9,10,11,12