Title  Description  Thumbnail Image 

Linear Function Models 
In this module students learn the properties of linear functions. They look at data sets, graphs of coordinates, and algebraic representations of functions. Then students go on a field trip to the US Mint to see how money is printed. From this they develop linear function models for calculating the number of bills printed, along with their dollar value. Students begin by analyzing linear function data by identifying the common difference. The goal is to see the relationship among the common difference and the slope of the linear function. Students use the Desmos graphing calculator to explore graphs of data and equations. Both types of linear functions are explored:
Students then watch a video about the US mint and how currency is created. Students use the information in the video to develop two linear function models: one for calculating the number of bills produced for every sheet of printed bills, plus another for calculating the dollar value of the printed bills. Note: Be sure students are familiar with the concept of slope and the basic definition of a function.


Linear Functions: Distance vs. Time 
In this module students apply their knowledge of linear functions to the context of distance vs. time graphs. They look at data sets, graphs of coordinates, and algebraic representations of distance vs. time functions. Then students go on a field trip to a Nascar race to see how timing at the pit stop has an impact on distance vs. time data. Students begin by analyzing linear function data by identifying the common difference. The goal is to see the relationship among the common difference and the slope of the linear function. Students use the Desmos graphing calculator to explore graphs of data and equations. Both types of linear functions are explored:
The goal here is to connect the slope of the distance vs. time graph to the speed of the car. Students then explore the graphs of cars with different speeds and initial distances. Students then watch a video about Nascar pit crews and learn about the rapidresponse pit crews who change the tires on the race cars and how the timing of this affects the distance vs. time graph of the cars. Students use the information in the video to analyze linear function models for different pit crew times. Note: Be sure students are familiar with the concept of slope and the basic definition of a linear function. Throughout the lesson various assessment items are included, which are then scored. A teacher's guide includes a detailed description of all components of this lesson. This lesson addresses the Grade 8 Common Core Standards but it can also be used in grades 9 and 10 for review purposes. This lesson can be assigned to individual students or teams of students. The lesson can be completed in about 20 to 25 minutes. 

Slope and Grade 
In this lesson students learn how to use the slope formula to calculate steepness. In particular, students learn how to calculate steepness in the context of cycling. Cyclists use a measure called grade to calculate the steepness of a hill or mountain. Students apply their knowledge of slope to the concept of grade. 

Applications of Linear Functions: Hooke's Law 
In this module, students explore a physicsbased application of linear functions: Hooke's Law. By exploring the properties of springs, a simple linear model is developed. Students then explore applications of Hooke's Law, from weight scales to bungee cords. Students investigate the properties of springs and identify two variables: the displacement of the spring (extension or compression) and the amount of force involved. From this students identify the independent variable and dependent variable. A graphing calculator activity (using the Desmos graphing tool) allows students to explore the value of k in the function F = kx. 

Applications of Linear Functions: Speed and Acceleration 
When a rocket is launched into space, it starts from rest and within minutes reaches speeds of tens of thousands kilometers per hour. In other words, the rocket accelerates. In this module, students apply their knowledge of linear functions to explore the speed vs. time function. In the process they learn about acceleration, as well as the properties of this linear function. Students first explore the equation for calculating acceleration. Then they use that to develop the speed vs. time linear function. This module can be completed in about 20 minutes. Make sure that students understand the basics of linear functions in slopeintercept form. 

Applications of Linear Functions: Temperature Conversion 
Temperature is one of the most important measurements that we deal with on a daily basis. Weather, climate, food preparation, health, and other phenomena involve some type of temperature measure. The two most common units of temperature measure are Fahrenheit and Celsius. There is a linear function that allows you to convert from one unit to another. In this module, you'll learn about this linear function. In fact, students will learn about this function and its inverse. The module starts with an analysis of CelsiustoFahrenheit data. They look at the functional relationship between the variables and develop a linear model using the Desmos graphing calculator. They analyze the properties of this linear function and look at its graph. Next, students analyze FahrenheittoCelsius data. They also develop a linear function model using the Desmos graphing calculator. Finally, they compare the graphs of the first function and its inverse to identify properties of functions and their inverses. 

What Is Function Notation? 
Cheetahs can accelerate up to 75 mph and can easily outpace a gazelle. But gazelles have adapted to keep cheetahs at bay long enough to tire them out. We can analyze this phenomenon mathematically through the use of some basic concepts involving functions. In this highly engaging module students learn about functions, domain, range, and mathematical modeling. They will look at the following types of functions:
These three functions are analyzed using function notation, and the domains and ranges are clearly defined. Students explore a mathematical model that shows whether a cheetah will catch the gazelle or if the gazelle escapes. This module also uses the Desmos graphing calculator extensively. 

Why Are Castles So Tall? 
In this module students explore indirect measurement by seeing how simple angle measure, height measurements, and tangent ratios can be used to calculate distances. The context of castles provides a historically relevant military purpose for the tallness of castles. This module explores Himeji Castle in Japan, as well as other castles. Some of the concepts explored in this module include:
This module provides a nice blend of algebra and geometry topics and can be used in an algebra unit on linear functions, a geometry unit on tangent ratios, or even a precalculus lesson on tangent ratios and functions. 

Algebra Applications Teacher's Guide: Linear Functions 
This is the Teacher's Guide that accompanies Algebra Applications: Linear Functions. To view the full video: https://www.media4math.com/library/videoalgebraapplicationslinearfunctions This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebraapplicationslinearfunctions 

Algebra Nspirations Teacher's Guide: Linear Functions 
This is the Teacher's Guide that accompanies Algebra Nspirations: Linear Functions. This video, Algebra Nspirations: Linear Functions, includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebranspirationslinearfunctions This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebranspirationslinearfunctions This video includes a Promethean Flipchart: https://www.media4math.com/library/prometheanflipchartalgebranspirationslinearfunctions 

VIDEO: Algebra Nspirations: Linear Functions 
In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide realworld examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TINspire. Algebra teachers looking to integrate handheld technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slopeintercept form, pointslope form, solving linear equations. This video includes a Teacher's Guide: https://www.media4math.com/library/algebranspirationsteachersguidelinearfunctions This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebranspirationslinearfunctions This video includes a Promethean Flipchart: https://www.media4math.com/library/prometheanflipchartalgebranspirationslinearfunctions 

VIDEO: Algebra Nspirations: Linear Functions, Segment 1 
In this Investigation we look at linear models for objects moving at a constant speed. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 1 and 2 are grouped together. To access Algebra Nspirations: Linear Functions, Segment 2, click the following link: • https://www.media4math.com/library/algebranspirationslinearfunctionssegment2 A Video Transcript for Algebra Nspirations: Linear Functions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/videotranscriptalgebranspirationslinearfunctionspart1 

VIDEO: Algebra Nspirations: Linear Functions, Segment 2 
In this Math Lab we explore slope in the context of the steepness of staircases. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 1 and 2 are grouped together. To access Algebra Nspirations: Linear Functions, Segment 2, click the following link: • https://www.media4math.com/library/algebranspirationslinearfunctionssegment1 A Video Transcript for Algebra Nspirations: Linear Functions, Segments 1 and 2 is available via the following link: • https://www.media4math.com/library/videotranscriptalgebranspirationsinequalitiespart1 

VIDEO: Algebra Nspirations: Linear Functions, Segment 3 
In this Investigation we look at a linear regression for carbon dioxide emission data. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 3 and 4 are grouped together. To access Algebra Nspirations: Linear Functions, Segment 4, click the following link: • https://www.media4math.com/library/algebranspirationslinearfunctionssegment4 A Video Transcript for Algebra Nspirations: Linear Functions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/videotranscriptalgebranspirationslinearfunctionspart2 

VIDEO: Algebra Nspirations: Linear Functions, Segment 4 
In this Math Lab we explore a linear model through a datagathering activity. This video is Segment 4 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 3 and 4 are grouped together. To access Algebra Nspirations: Linear Functions, Segment 3, click the following link: • https://www.media4math.com/library/algebranspirationslinearfunctionssegment3 A Video Transcript for Algebra Nspirations: Linear Functions, Segments 3 and 4 is available via the following link: • https://www.media4math.com/library/videotranscriptalgebranspirationslinearfunctionspart2 

Brief Review: Linear Equations in Standard Form 
In this presentation we show how to convert a linear equation in Standard Form to a linear function in Slope Intercept Form. We go over the reason for such a conversion and applications that give rise to these equations. Note: The download is a PPT. 

Closed Captioned Video: Algebra Applications: Linear Functions, Segment 2: Cycling 
The relationship between slope and grade in cycling is explored. Go on a tour of Italy through the mountains of Tuscany and apply students' understanding of slope. A Video Transcript is available for this tutorial at this Link Note: The download is Media4Math's guide to closed captioned videos. Other Closed Captioned VideosTo see the complete collection of Closed Captioned Videos, click on this Link 

Closed Captioned Video: Algebra Applications: Linear Functions 
In this episode of Algebra Applications, three realworld explorations of linear functions are developed: Sports. The relationship between slope and grade in cycling is explored. Oil Exploration. A linear regression of oil consumption data over the past 25 years reveals an interesting pattern. Health. The maximum heart rate from aerobic exercise is a linear function dependent on age. Students are asked to develop a data table based on the function. A Video Transcript is available for this tutorial at this Link Note: The download is Media4Math's guide to closed captioned videos. Other Closed Captioned VideosTo see the complete collection of Closed Captioned Videos, click on this Link 

Closed Captioned Video: Algebra Applications: Linear Functions, Segment 1: Introduction 

Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration 
The potential for oil exploration in the controversial Alaska National Wildlife Refuge (ANWR) sets the scene for this problem. A linear regression of oil consumption data over the past 25 years reveals an interesting pattern. How could new oil fields like ANWR help in breaking our dependence on foreign oil? A Video Transcript is available for this tutorial at this Link Note: The download is Media4Math's guide to closed captioned videos. Other Closed Captioned VideosTo see the complete collection of Closed Captioned Videos, click on this Link 

Closed Captioned Video: Algebra Applications: Linear Functions, Segment 4: Exercise 
Exercise needs to become a consistent part of everyone's lifestyle. In particular, aerobic exercises, which vigorously exerts the heart, is an important form of exercise. The maximum heart rate from aerobic exercise is a linear function dependent on age. Students are asked to develop a data table based on the function. A Video Transcript is available for this tutorial at this Link Note: The download is Media4Math's guide to closed captioned videos. Other Closed Captioned VideosTo see the complete collection of Closed Captioned Videos, click on this Link 

Closed Captioned Video: Algebra Nspirations: Linear Functions 
In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide realworld examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TINspire. Algebra teachers looking to integrate handheld technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slopeintercept form, pointslope form, solving linear equations. A Video Transcript is available for this tutorial at this Link Note: The download is Media4Math's guide to closed captioned videos. Other Closed Captioned VideosTo see the complete collection of Closed Captioned Videos, click on this Link 

Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 1 
In this Investigation we look at linear models for objects moving at a constant speed. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 1 and 2 are grouped together. To access Algebra Nspirations: Linear Functions, Segment 2, click the following link: • https://www.media4math.com/library/algebranspirationslinearfunctionssegment2 A Video Transcript is available for this tutorial at this Link Note: The download is Media4Math's guide to closed captioned videos. Other Closed Captioned VideosTo see the complete collection of Closed Captioned Videos, click on this Link 

Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 3 
In this Investigation we look at a linear regression for carbon dioxide emission data. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 3 and 4 are grouped together. To access Algebra Nspirations: Linear Functions, Segment 4, click the following link: • https://www.media4math.com/library/algebranspirationslinearfunctionssegment4 A Video Transcript is available for this tutorial at this Link Note: The download is Media4Math's guide to closed captioned videos. Other Closed Captioned VideosTo see the complete collection of Closed Captioned Videos, click on this Link 

Instructional Resource: Applications of Linear Functions: Circumference vs. Diameter 
In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter. Note: The download is a PPT file. Related ResourcesTo see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN 