**Title:** The Need for Speed

**Description:**
After viewing an introductory illustrated podcast on speed, distance, time, and velocity, students explore distance-time graphs using interactive websites. Working in cooperative learning groups, students will investigate the motion of toy pull-back racers and collect data to analyze the speed of the cars between various positions marked on the race track. Students will use the data to create graphs, analyze data and present findings to the class.
**Standard(s): **

[TC2] (6-8) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information.

**Subject:**Mathematics (8), or Credit Recovery Science (8), or Science (8), or Technology Education (6 - 8)

**Title:**The Need for Speed

**Description:**After viewing an introductory illustrated podcast on speed, distance, time, and velocity, students explore distance-time graphs using interactive websites. Working in cooperative learning groups, students will investigate the motion of toy pull-back racers and collect data to analyze the speed of the cars between various positions marked on the race track. Students will use the data to create graphs, analyze data and present findings to the class.

**Title:** Midpoint of a Line Segment.

**Description:**
Investigate finding the midpoint of a line segment and derive the formula for the midpoint of two points on a coordinate plane.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics (8)

**Title:**Midpoint of a Line Segment.

**Description:**Investigate finding the midpoint of a line segment and derive the formula for the midpoint of two points on a coordinate plane. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Heads Up!

**Description:**
The lesson is a hands-on project. Students will work in pairs to gather various measurements, organizing the data into a provided chart. The measurements will be used to review, reinforce, and introduce skills such as measures of central tendency, coordinate graphing, and various ways of representing data (i.e., stem-and-leaf plots, box-and-whisker plots, frequency tables, etc.).
**Standard(s): **

[MA2015] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8-F5]

**Subject:**Mathematics (7 - 8)

**Title:**Heads Up!

**Description:**The lesson is a hands-on project. Students will work in pairs to gather various measurements, organizing the data into a provided chart. The measurements will be used to review, reinforce, and introduce skills such as measures of central tendency, coordinate graphing, and various ways of representing data (i.e., stem-and-leaf plots, box-and-whisker plots, frequency tables, etc.).

**Title:** What is the slope of the stairs in front of the school?

**Description:**
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
**Standard(s): **

[MA2015] GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]

**Subject:**Mathematics (8 - 12)

**Title:**What is the slope of the stairs in front of the school?

**Description:**The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.

**Title:** Finding the Slope of a Line

**Description:**
This lesson will use a slide presentation to facilitate teaching students how to find the slope of a line when given the graph of the line or two points. Students will interact with the presentation in two ways: first, by taking notes and practicing examples, and second, by linking to a slope activity on the Internet. This lesson may be done in one ninety-minute block or broken up over two fifty-minute periods. This lesson would be incorporated in a unit on graphing linear equations.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics (8 - 12)

**Title:**Finding the Slope of a Line

**Description:**This lesson will use a slide presentation to facilitate teaching students how to find the slope of a line when given the graph of the line or two points. Students will interact with the presentation in two ways: first, by taking notes and practicing examples, and second, by linking to a slope activity on the Internet. This lesson may be done in one ninety-minute block or broken up over two fifty-minute periods. This lesson would be incorporated in a unit on graphing linear equations.

**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:** Travel in the Solar System: Lesson 1

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students consider the amount of time that space travelers must spend on their journey. Students improve their concept of time and distance.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics,Science

**Title:**Travel in the Solar System: Lesson 1

**Description:**In this lesson, one of a multi-part unit from Illuminations, students consider the amount of time that space travelers must spend on their journey. Students improve their concept of time and distance.

**Thinkfinity Partner:**Illuminations

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

**Title:** Travel in the Solar System: Lesson 2

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics,Science

**Title:**Travel in the Solar System: Lesson 2

**Description:**In this lesson, one of a multi-part unit from Illuminations, students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey.

**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:** Printing Books

**Description:**
In this lesson, from Illuminations, students explore the relationships among lines, slopes, and y-intercepts using the real-world situation of the printing of their textbook. They use data presented in tables, graphs, and equation form for problem-solving.
**Standard(s): **

[MA2015] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3]

**Subject:**Mathematics

**Title:**Printing Books

**Description:**In this lesson, from Illuminations, students explore the relationships among lines, slopes, and y-intercepts using the real-world situation of the printing of their textbook. They use data presented in tables, graphs, and equation form for problem-solving.

**Thinkfinity Partner:**Illuminations

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

**Title:** Taking Its Toll

**Description:**
In this Illuminations lesson, students compare the price of a toll to the distance traveled. Students investigate data numerically and graphically to determine the per-mile charge, and they predict the cost if a new tollbooth were added along the route.
**Standard(s): **

[MA2015] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3]

**Subject:**Mathematics

**Title:**Taking Its Toll

**Description:**In this Illuminations lesson, students compare the price of a toll to the distance traveled. Students investigate data numerically and graphically to determine the per-mile charge, and they predict the cost if a new tollbooth were added along the route.

**Thinkfinity Partner:**Illuminations

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

**Title:** Bagel Algebra

**Description:**
In this Illuminations lesson, a real life example--taken from a bagel shop--is used to get students to think about solving a problem symbolically. Students must decipher a series of equations and interpret results to understand the point that the bagel shop s owner is trying to make about the price of his bagels compared to that of his competitor.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics

**Title:**Bagel Algebra

**Description:**In this Illuminations lesson, a real life example--taken from a bagel shop--is used to get students to think about solving a problem symbolically. Students must decipher a series of equations and interpret results to understand the point that the bagel shop s owner is trying to make about the price of his bagels compared to that of his competitor.

**Thinkfinity Partner:**Illuminations

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

**Title:** Bagel Comparison

**Description:**
This reproducible transparency, from an Illuminations lesson, presents information from a sign displayed by a real bagel retailer, comparing the price of their bagels to that of their competitor.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics

**Title:**Bagel Comparison

**Description:**This reproducible transparency, from an Illuminations lesson, presents information from a sign displayed by a real bagel retailer, comparing the price of their bagels to that of their competitor.

**Thinkfinity Partner:**Illuminations

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

**Title:** Movement with Functions

**Description:**
In this unit of 3 lessons from Illuminations, students use movement to reinforce the concepts of linear functions and systems of equations. Multiple representations are used throughout, along with tools such as motion detectors and remote-controlled cars. Students explore how position, speed, and varying motion are reflected in graphs, tables, and algebraic equations.
**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:**Movement with Functions

**Description:**In this unit of 3 lessons from Illuminations, students use movement to reinforce the concepts of linear functions and systems of equations. Multiple representations are used throughout, along with tools such as motion detectors and remote-controlled cars. Students explore how position, speed, and varying motion are reflected in graphs, tables, and algebraic equations.

**Thinkfinity Partner:**Illuminations

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

**Title:** Rise-Run Triangles

**Description:**
This lesson offers students a method for finding the slope of a line from its graph. The skills from this lesson can be applied as a tool to real-world examples of rate of change and slope.
**Standard(s): **

[MA2015] (8) 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation *y* = *mx* for a line through the origin and the equation *y* = *mx* + *b* for a line intercepting the vertical axis at b. [8-EE6]

**Subject:**Mathematics

**Title:**Rise-Run Triangles

**Description:**This lesson offers students a method for finding the slope of a line from its graph. The skills from this lesson can be applied as a tool to real-world examples of rate of change and slope.

**Thinkfinity Partner:**Illuminations

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

**Title:** How Did I Move?

**Description:**
In this Illuminations lesson, students are provided with a method for understanding that for y = mx + b, m is a rate of change and b is the value when x = 0. This kinesthetic activity allows students to form a physical interpretation of slope and y-intercept by running across a football field. Students will be able to verbalize the meaning of the equation to reinforce understanding and discover that slope (or rate of movement) is the same for all sets of points given a set of data with a linear relationship.
**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:**How Did I Move?

**Description:**In this Illuminations lesson, students are provided with a method for understanding that for y = mx + b, m is a rate of change and b is the value when x = 0. This kinesthetic activity allows students to form a physical interpretation of slope and y-intercept by running across a football field. Students will be able to verbalize the meaning of the equation to reinforce understanding and discover that slope (or rate of movement) is the same for all sets of points given a set of data with a linear relationship.

**Thinkfinity Partner:**Illuminations

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

**Title:** How Steep Can You Be?

**Description:**
In this lesson, one of a multi-part unit from Illuminations, students consider the construction of a tool that will measure percent slope. They then use ideas about percent slope to determine recommended defensible space distances near a home, in relation to protecting the home from wildfires.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics

**Title:**How Steep Can You Be?

**Description:**In this lesson, one of a multi-part unit from Illuminations, students consider the construction of a tool that will measure percent slope. They then use ideas about percent slope to determine recommended defensible space distances near a home, in relation to protecting the home from wildfires.

**Thinkfinity Partner:**Illuminations

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

**Title:** The Next Billion

**Description:**
In this lesson, from Illuminations, students predict when the world's population will reach 7 billion. To do so, they use an on-line counter that simulates the changing world population. They time the counter to find how long it takes for the population to increase by 50 or 100 people. They use that measurement to predict how long it would take for the population to increase by 1 billion. Students discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth.
**Standard(s): **

[MA2015] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]

**Subject:**Mathematics

**Title:**The Next Billion

**Description:**In this lesson, from Illuminations, students predict when the world's population will reach 7 billion. To do so, they use an on-line counter that simulates the changing world population. They time the counter to find how long it takes for the population to increase by 50 or 100 people. They use that measurement to predict how long it would take for the population to increase by 1 billion. Students discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth.

**Thinkfinity Partner:**Illuminations

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

**Title:** On Fire

**Description:**
This unit of five lessons, from Illuminations, introduces the components of a fire-safe and fire-wise environment. Students create a fire-wise location through calculations and measurement of percent slope, defensible space distance and various vegetation separation distances. The unit plan culminates with students designing a fire-wise property and testing their fire-wise IQ.
**Standard(s): **

[MA2015] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3]

**Subject:**Mathematics

**Title:**On Fire

**Description:**This unit of five lessons, from Illuminations, introduces the components of a fire-safe and fire-wise environment. Students create a fire-wise location through calculations and measurement of percent slope, defensible space distance and various vegetation separation distances. The unit plan culminates with students designing a fire-wise property and testing their fire-wise IQ.

**Thinkfinity Partner:**Illuminations

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

**Title:** Bean Counting

**Description:**
By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The number-sense of recognizing equivalent fractions is useful when students study slope and proportions.
**Standard(s): **

[MA2015] ALC (9-12) 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama)

**Subject:**Mathematics

**Title:**Bean Counting

**Description:**By using sampling from a large collection of beans, students get a sense of equivalent fractions, which leads to a better understanding of proportions. Equivalent fractions are used to develop an understanding of proportions. The number-sense of recognizing equivalent fractions is useful when students study slope and proportions.

**Thinkfinity Partner:**Illuminations

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