**Title:** Determining Percent of Seed Germination-Enhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom

**Description:**
In this project, students will conduct an experiment to determine the percentage of seed that will germinate in a given time frame. Students will produce charts and graphs to represent the results algebraically. Mathematics and career/technical students can participate in this lab experiment together, or the activity can be conducted separately in either classroom. The mathematics teacher will want to adapt the student handouts to provide additional emphasis on mathematics and to remove emphasis on the career/technical.
This integrated lesson is the result of collaboration between Chip Blanton, an agriculture teacher, and Greg Pendergrass, a math teacher (Fort Payne HS). For information about using the eight step model for developing integrated projects developed by the Southern Regional Education Board, contact Leslie Carson at leslie.carson@sreb.org. For information about the project implementation, contact Chip Blanton (cblanton@ftpayk12.org) or Greg Pendergrass (gpendergrass@ftpayk12.org).
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Agriculture, Food, and Natural Resources (9 - 12), or Mathematics (9 - 12)

**Title:**Determining Percent of Seed Germination-Enhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom

**Description:**In this project, students will conduct an experiment to determine the percentage of seed that will germinate in a given time frame. Students will produce charts and graphs to represent the results algebraically. Mathematics and career/technical students can participate in this lab experiment together, or the activity can be conducted separately in either classroom. The mathematics teacher will want to adapt the student handouts to provide additional emphasis on mathematics and to remove emphasis on the career/technical. This integrated lesson is the result of collaboration between Chip Blanton, an agriculture teacher, and Greg Pendergrass, a math teacher (Fort Payne HS). For information about using the eight step model for developing integrated projects developed by the Southern Regional Education Board, contact Leslie Carson at leslie.carson@sreb.org. For information about the project implementation, contact Chip Blanton (cblanton@ftpayk12.org) or Greg Pendergrass (gpendergrass@ftpayk12.org).

**Title:** Math is Functional

**Description:**
This lesson is a technology-based activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and y-intercept will help students conceptualize material normally presented in Algebra I textbooks.
**Standard(s): **

[MA2015] AL1 (9-12) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]

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

**Title:**Math is Functional

**Description:**This lesson is a technology-based activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and y-intercept will help students conceptualize material normally presented in Algebra I textbooks.

**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:** Swimming Pool Math

**Description:**
Students will use a swimming pool example to practice finding perimeter and area of different rectangles.
**Standard(s): **

[MA2015] (8) 24: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems. [8-G9]

**Subject:**Mathematics (6 - 12)

**Title:**Swimming Pool Math

**Description:**Students will use a swimming pool example to practice finding perimeter and area of different rectangles.

**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:**
Using this reproducible chart, from an Illuminations lesson, students record the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. This resource can also be used as an overhead transparency so students can share their results with their classmates.
**Standard(s): **

[MA2015] AL1 (9-12) 28: 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.** [F-IF4]

**Subject:**Mathematics

**Title:**Graph Chart

**Description:**Using this reproducible chart, from an Illuminations lesson, students record the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. This resource can also be used as an overhead transparency so students can share their results with their classmates.

**Thinkfinity Partner:**Illuminations

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

**Title:** Automobile Mileage: Years Since 1990 vs. Mileage

**Description:**
This lesson, one of a multi-part unit from Illuminations, is another representation of the automobile mileage data used in previous lessons of this unit. This lesson provides another opportunity for students to analyze how changing the independent variable in a set of data can result in a different least squares regression line. Students can then use the new equation to make some of the same predictions they made in Lessons Five and Six. This lesson incorporates an interactive regression line applet.
**Standard(s): **

[MA2015] AL1 (9-12) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2]

**Subject:**Mathematics

**Title:**Automobile Mileage: Years Since 1990 vs. Mileage

**Description:**This lesson, one of a multi-part unit from Illuminations, is another representation of the automobile mileage data used in previous lessons of this unit. This lesson provides another opportunity for students to analyze how changing the independent variable in a set of data can result in a different least squares regression line. Students can then use the new equation to make some of the same predictions they made in Lessons Five and Six. This lesson incorporates an interactive regression line applet.

**Thinkfinity Partner:**Illuminations

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

**Title:** Counting Embedded Figures

**Description:**
In this Illuminations lesson, students look for patterns in an embedded-square problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills.
**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:**Counting Embedded Figures

**Description:**In this Illuminations lesson, students look for patterns in an embedded-square problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**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:** Think of a Graph

**Description:**
This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis.
**Standard(s): **

[MA2015] ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)

**Subject:**Mathematics

**Title:**Think of a Graph

**Description:**This reproducible transparency, from an Illuminations lesson, asks students to sketch a graph in which the side length of a square is graphed on the horizontal axis and the perimeter of the square is graphed on the vertical axis.

**Thinkfinity Partner:**Illuminations

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

**Title:** Inclined Plane

**Description:**
In this multiple-day activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved.
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Mathematics,Science

**Title:**Inclined Plane

**Description:**In this multiple-day activity, from Illuminations, students time balls rolling down inclines of varying lengths and heights. They then try to make inferences about the relationships among the variables involved.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Finding Our Top Speed

**Description:**
This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected.
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Mathematics,Science

**Title:**Finding Our Top Speed

**Description:**This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Apple Pie Recording Chart

**Description:**
This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects.
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Mathematics

**Title:**Apple Pie Recording Chart

**Description:**This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects.

**Thinkfinity Partner:**Illuminations

**Grade Span:**6,7,8

**Title:** Automobile Mileage: Age vs. Mileage

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret the meaning of the slope and y-intercept of the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and y-intercept of the line and put those meanings in the context of the real-life application. This lesson incorporates an interactive regression line applet.
**Standard(s): **

**Subject:**Mathematics

**Title:**Automobile Mileage: Age vs. Mileage

**Description:**In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret the meaning of the slope and y-intercept of the least squares regression line. By examining the graphical representation of the data, students analyze the meaning of the slope and y-intercept of the line and put those meanings in the context of the real-life application. This lesson incorporates an interactive regression line applet.

**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:** Investigating Pick's Theorem

**Description:**
In this unit of three lessons, from Illuminations, students rediscover Pick's Theorem, which they were likely introduced to in middle school, and use algebra to determine the coefficients of the equation. They explore the concept of change as a mechanism for finding the coefficients of Pick's Theorem.
**Standard(s): **

[MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]

**Subject:**Mathematics

**Title:**Investigating Pick's Theorem

**Description:**In this unit of three lessons, from Illuminations, students rediscover Pick's Theorem, which they were likely introduced to in middle school, and use algebra to determine the coefficients of the equation. They explore the concept of change as a mechanism for finding the coefficients of Pick's Theorem.

**Thinkfinity Partner:**Illuminations

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

**Title:** Escape from the Tomb Activity

**Description:**
This reproducible activity sheet, from an Illuminations lesson, includes instructions and questions for a mathematical adventure game. In the game, students are given a problem in which two bowls are suspended from the ceiling by springs, and one bowl is lower than the other. Students must work out how many items should be placed in each bowl so that the heights of the bowls are the same.
**Standard(s): **

[MA2015] AL2 (9-12) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]

**Subject:**Mathematics

**Title:**Escape from the Tomb Activity

**Description:**This reproducible activity sheet, from an Illuminations lesson, includes instructions and questions for a mathematical adventure game. In the game, students are given a problem in which two bowls are suspended from the ceiling by springs, and one bowl is lower than the other. Students must work out how many items should be placed in each bowl so that the heights of the bowls are the same.

**Thinkfinity Partner:**Illuminations

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

**Title:** Flowing Through Mathematics

**Description:**
This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.
**Standard(s): **

[MA2015] ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama)

**Subject:**Mathematics

**Title:**Flowing Through Mathematics

**Description:**This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.

**Thinkfinity Partner:**Illuminations

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