**Title:** Predict the Future?

**Description:**
Students will use data collected and a "best-fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.
**Standard(s): **

[MA2015] PRE (9-12) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (*Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.*)* [F-IF4] (Alabama)

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

**Title:**Predict the Future?

**Description:**Students will use data collected and a "best-fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.

**Title:** Investigating Parabolas in Standard Form

**Description:**
Students explore the coefficients of a quadratic function using a graphing calculator. This is an inquiry lesson to be used as an introduction to translations and dilations of functions.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
**Standard(s): **

[MA2015] ALT (9-12) 34: Identify the effect on the graph of replacing *f*(*x*) by *f*(*x*) + *k*, *k* *f*(*x*), *f*(*kx*), and *f*(*x* + *k*) for specific values of *k* (both positive and negative); find the value of *k* given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[F-BF3]

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

**Title:**Investigating Parabolas in Standard Form

**Description:**Students explore the coefficients of a quadratic function using a graphing calculator. This is an inquiry lesson to be used as an introduction to translations and dilations of functions.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

**Title:** Exponential Growth and Decay

**Description:**
This lesson on exponential growth and decay involves a variety of teaching resources. There are a variety of websites used to teach and reinforce how to identify exponential growth or decay and how to solve problems relating to growth and decay. There is a lab provided that will help model these concepts being taught and computer based practice on these concepts. Videos are provided that give a picture image of how exponential growth and decay works. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
**Standard(s): **

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

**Subject:**Mathematics (9 - 12)

**Title:**Exponential Growth and Decay

**Description:**This lesson on exponential growth and decay involves a variety of teaching resources. There are a variety of websites used to teach and reinforce how to identify exponential growth or decay and how to solve problems relating to growth and decay. There is a lab provided that will help model these concepts being taught and computer based practice on these concepts. Videos are provided that give a picture image of how exponential growth and decay works. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

**Title:** You Mean ANYTHING To The Zero Power Is One?

**Description:**
This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization.
**Standard(s): **

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

**Title:**You Mean ANYTHING To The Zero Power Is One?

**Description:**This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization.

**Title:** Exact Ratio

**Description:**
This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.
**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:**Exact Ratio

**Description:**This reproducible activity sheet, from an Illuminations lesson, features a series of questions pertaining to exact ratios and geometric sequences. In the lesson, students measure lengths on stringed musical instruments and discuss how the placement of frets on a fretted instrument is determined by a geometric sequence.

**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:** Graph Chart

**Description:**
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Graph Chart

**Description:**This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.

**Thinkfinity Partner:**Illuminations

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

**Title:** Graphing What

**Description:**
This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Graphing What

**Description:**This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.

**Thinkfinity Partner:**Illuminations

**Grade Span:**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:** Do You Hear What I Hear?

**Description:**
In this lesson, from Illuminations, students explore the dynamics of a sound wave. Students use an interactive Java applet to view the effects of changing the initial string displacement and the initial tension.
**Standard(s): **

[MA2015] PRE (9-12) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama)

**Subject:**Mathematics,Science

**Title:**Do You Hear What I Hear?

**Description:**In this lesson, from Illuminations, students explore the dynamics of a sound wave. Students use an interactive Java applet to view the effects of changing the initial string displacement and the initial tension.

**Thinkfinity Partner:**Illuminations

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

**Title:** Automobile Mileage: Comparing and Contrasting

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students compare and contrast their findings from previous lessons of the unit. This lesson allows students the time they need to think about and discuss what they have done in the previous lessons. This lesson provides the teacher with another opportunity to listen to student discourse and assess student understanding.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Automobile Mileage: Comparing and Contrasting

**Description:**In this lesson, one of a multi-part unit from Illuminations, students compare and contrast their findings from previous lessons of the unit. This lesson allows students the time they need to think about and discuss what they have done in the previous lessons. This lesson provides the teacher with another opportunity to listen to student discourse and assess student understanding.

**Thinkfinity Partner:**Illuminations

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

**Title:** Bathtub Water Levels

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students examine real-life data that illustrates a negative slope. Students interpret the meaning of the negative slope and y-intercept of the graph of the real-life data. By examining the graphical representation of the data, students relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the least squares regression line. This lesson incorporates an interactive regression line applet.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Bathtub Water Levels

**Description:**In this lesson, one of a multi-part unit from Illuminations, students examine real-life data that illustrates a negative slope. Students interpret the meaning of the negative slope and y-intercept of the graph of the real-life data. By examining the graphical representation of the data, students relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the least squares regression line. This lesson incorporates an interactive regression line applet.

**Thinkfinity Partner:**Illuminations

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

**Title:** Exploring Linear Data

**Description:**
In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Exploring Linear Data

**Description:**In this lesson, from Illuminations, students model linear data in a variety of settings. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.

**Thinkfinity Partner:**Illuminations

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

**Title:** Gallery Walk

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students view the work of other students in the class and explain their own work. Students move from graph to graph during this time and, without any talking, view the work of their classmates. While on their Gallery Walk, the students think about the data their classmates plotted and whether or not the information accompanying each graph seems appropriate. Each pair of students then stands next to their own work and explains one of the graphs.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Gallery Walk

**Description:**In this lesson, one of a multi-part unit from Illuminations, students view the work of other students in the class and explain their own work. Students move from graph to graph during this time and, without any talking, view the work of their classmates. While on their Gallery Walk, the students think about the data their classmates plotted and whether or not the information accompanying each graph seems appropriate. Each pair of students then stands next to their own work and explains one of the graphs.

**Thinkfinity Partner:**Illuminations

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

**Title:** Least Squares Regression

**Description:**
In this nine-lesson unit, from Illuminations, students interpret the slope and y-intercept of least squares regression lines in the context of real-life data. Students use an interactive applet to plot the data and calculate the correlation coefficient and equation of the least squares regression line. These lessons develop skills in connecting, communicating, reasoning, and problem solving as well as representing fundamental ideas about data.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Least Squares Regression

**Description:**In this nine-lesson unit, from Illuminations, students interpret the slope and y-intercept of least squares regression lines in the context of real-life data. Students use an interactive applet to plot the data and calculate the correlation coefficient and equation of the least squares regression line. These lessons develop skills in connecting, communicating, reasoning, and problem solving as well as representing fundamental ideas about 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:** Traveling Distances

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students interpret the meaning of the slope and y-intercept of a graph of real-life data. By examining the graphical representation of the data, students relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the resulting least squares regression line. This lesson incorporates an interactive regression line applet.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Traveling Distances

**Description:**In this lesson, one of a multi-part unit from Illuminations, students interpret the meaning of the slope and y-intercept of a graph of real-life data. By examining the graphical representation of the data, students relate the slope and y-intercept of the least squares regression line to the real-life data. They also interpret the correlation coefficient of the resulting least squares regression line. This lesson incorporates an interactive regression line applet.

**Thinkfinity Partner:**Illuminations

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

**Title:** Graphing Periodic Functions

**Digital Tool:**
Height of Waist - Graphing Stories in 15 seconds **Web Address URL:**
http://graphingstories.com/Axh **Standard(s): **

[MA2015] PRE (9-12) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (*Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.*)* [F-IF4] (Alabama)**Digital Tool Description:** Graphing Stories is a website that provides short videos of real world activities that can be translated to graphs. The Height of Waist video models a person in a swing. The graph should be a periodic function.

**Title:**Graphing Periodic Functions

**Digital Tool:**Height of Waist - Graphing Stories in 15 seconds

**Digital Tool Description:**Graphing Stories is a website that provides short videos of real world activities that can be translated to graphs. The Height of Waist video models a person in a swing. The graph should be a periodic function.

**Title:** Isosceles Triangle Investigation

**Description:**
This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Isosceles Triangle Investigation

**Description:**This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base.

**Thinkfinity Partner:**Illuminations

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

**Title:** Tube Viewer Simulation

**Description:**
This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change.
**Standard(s): **

[MA2015] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

**Subject:**Mathematics

**Title:**Tube Viewer Simulation

**Description:**This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change.

**Thinkfinity Partner:**Illuminations

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