Title  Description  Thumbnail Image  Curriculum Topics 

Accident Investigation 
When a driver slams the brakes on a car, skid marks are created on the road. Accident investigators can measure the length of the skid marks to estimate the speed of the car. This involves using a quadratic function. In this module, students use a quadratic model to predict the length of skid marks for various car speeds. The derivation of the quadratic model is shown algebraically and graphically. Students then use the model to solve a quadratic equation, given the total stopping distance. This module assumes that students are familiar with quadratic functions. Students will get a real understanding for how quadratic functions are used in the real world. 

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: Cricket Chirps 
Crickets are known for their chirping sounds. But did you know that the number of times a cricket chirps per minute is an indicator of the outside temperature? In fact, the relationship between cricket chirps and the outside temperature can be modeled by a linear function. In this module, students will explore the function that can be used to determine the outside temperature based on the number of times a cricket chirps per minute. First, students watch a video that describes the chirptemperature phenomenon. Students are then walked through the process of developing the linear model. They look at inputs and outputs, determine the dependent and independent variables, and explore the linear function with a graphing calculator activity. 

Applications of Linear Functions: Circumference vs. Diameter 
As the size of a circle changes, so does the size of the diameter and that of the circumference. In fact, there is a linear relationship between these two measures. This relationship can be modeled with a linear function. In this module students will study this linear function and examine its properties, including the fact that the slope of this function is π itself. This is a handson module in which students will measure the diameters and circumferences of a number of different containers. This data gathering will lead to graphing the data. From that students develop a linear model using the Desmos graphing tool. Students will see that the relationship between circumference and diameter has to do with π. In fact, the slope of the linear function is π itself. For the handson part of the lesson, make sure you have all the materials: Different size cylindrical containers (bottles, cups, etc.), string, marker, and a ruler (preferably a caliper). Collect all the student data and use the embedded Desmos graphing tool to graph the data and explore the linear function. The module concludes with an overview video about the number π. 

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.


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. 

What Is a Function? 
In algebra, the topic of functions is extremely important. But what is a function? In this module students will learn what a function is and how to represent it. They'll explore data tables, graphs, and equations. Plus, they'll see the connection from one to the other. Students will learn about function machines, and we draw an analogy to actual machines. A short video shows how a flat disk of aluminum (the input) is turned into a soda can (the output) by a series of machines that stretch and shape the disk into the can. Want to learn more about our Subscription packages? Click here to learn more.


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. 

What Is a Function? 
In algebra, the topic of functions is extremely important. But what is a function? In this module students will learn what a function is and how to represent it. They'll explore data tables, graphs, and equations. Plus, they'll see the connection from one to the other. Students will learn about function machines, and we draw an analogy to actual machines. A short video shows how a flat disk of aluminum (the input) is turned into a soda can (the output) by a series of machines that stretch and shape the disk into the can. Want to learn more about our Subscription packages? Click here to learn more.


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. 

What Are Domain and Range? 
What do drones have to do with domain and range? In this module, students learn about an emerging hightech delivery system and use that as a vehicle for learning about a function's domain and range. Students will graph data from a table and explore domain and range, and then they graph a continuous function. This highly engaging module will give students a solid understanding of algebraic functions, specifically domain and range. In this module students will learn the following concepts:


Algebra Applications Teacher's Guide: Functions and Relations 
This is the Teacher's Guide that accompanies Algebra Applications: Functions and Relations. To view the full video: https://www.media4math.com/library/algebraapplicationsfunctionsandrelations This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebraapplicationsfunctionsandrelations 
Applications of Functions and Relations  
Algebra Applications Teacher's Guide: Functions and Relations 
This is the Teacher's Guide that accompanies Algebra Applications: Functions and Relations. To view the full video: https://www.media4math.com/library/algebraapplicationsfunctionsandrelations This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebraapplicationsfunctionsandrelations 
Applications of Functions and Relations  
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 
Applications of Linear 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 
Applications of Linear Functions  
Algebra Applications Teacher's Guide: Quadratic Functions 
This is the Teacher's Guide that accompanies Algebra Applications: Quadratic Functions. To view the full video: https://www.media4math.com/library/algebraapplicationsquadraticfunctions This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebraapplicationsquadraticfunctions 
Applications of Quadratic Functions  
Algebra Applications Teacher's Guide: Quadratic Functions 
This is the Teacher's Guide that accompanies Algebra Applications: Quadratic Functions. To view the full video: https://www.media4math.com/library/algebraapplicationsquadraticfunctions This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebraapplicationsquadraticfunctions 
Applications of Quadratic Functions  
Algebra Nspirations Teacher's Guide: Functions and Relations 
This is the Teacher's Guide that accompanies Algebra Nspirations: Functions and Relations. To view the full video: https://www.media4math.com/library/algebranspirationsfunctionsandrelations This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebranspirationsfunctionsandrelations This video includes a Promethean Flipchart: https://www.media4math.com/library/prometheanflipchartalgebranspirationsfunctionsandrelations 
Applications of Functions and Relations  
Algebra Nspirations Teacher's Guide: Functions and Relations 
This is the Teacher's Guide that accompanies Algebra Nspirations: Functions and Relations. To view the full video: https://www.media4math.com/library/algebranspirationsfunctionsandrelations This video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebranspirationsfunctionsandrelations This video includes a Promethean Flipchart: https://www.media4math.com/library/prometheanflipchartalgebranspirationsfunctionsandrelations 
Applications of Functions and Relations  
Algebra Nspirations Teacher's Guide: Quadratic Functions 
This is the Teacher's Guide that accompanies Algebra Nspirations: Quadratic Functions. The Algebra Nspirations: Quadratic Functions video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebranspirationsquadraticfunctions Video: Algebra Nspirations: Quadratic Functions: https://www.media4math.com/library/algebranspirationsquadraticfunctions This video includes a Promethean Flipchart: https://www.media4math.com/library/prometheanflipchartalgebranspirationsquadraticfunctions 
Applications of Quadratic Functions  
Algebra Nspirations Teacher's Guide: Quadratic Functions 
This is the Teacher's Guide that accompanies Algebra Nspirations: Quadratic Functions. The Algebra Nspirations: Quadratic Functions video includes a Video Transcript: https://www.media4math.com/library/videotranscriptalgebranspirationsquadraticfunctions Video: Algebra Nspirations: Quadratic Functions: https://www.media4math.com/library/algebranspirationsquadraticfunctions This video includes a Promethean Flipchart: https://www.media4math.com/library/prometheanflipchartalgebranspirationsquadraticfunctions 
Applications of Quadratic Functions  
VIDEO: Algebra Nspirations: Functions and Relations, Segment 3 
In this Investigation we look at functions. This video is Segment 3 of a 4 segment series related to Functions and Relations. Segments 3 and 4 are grouped together. To access Functions and Relations, Segment 4, click the following link: • https://www.media4math.com/library/algebranspirationsfunctionsandrelationssegment4 A Video Transcript for Functions and Relations, Segments 3 and 4 is available via the following link: 
Applications of Functions and Relations, Conic Sections, Relations and Functions, Geometric Constructions with Circles  
VIDEO: Algebra Nspirations: Functions and Relations, Segment 3 
In this Investigation we look at functions. This video is Segment 3 of a 4 segment series related to Functions and Relations. Segments 3 and 4 are grouped together. To access Functions and Relations, Segment 4, click the following link: • https://www.media4math.com/library/algebranspirationsfunctionsandrelationssegment4 A Video Transcript for Functions and Relations, Segments 3 and 4 is available via the following link: 
Applications of Functions and Relations, Conic Sections, Relations and Functions, Geometric Constructions with Circles  
VIDEO: Algebra Nspirations: Functions and Relations, Segment 3 
In this Investigation we look at functions. This video is Segment 3 of a 4 segment series related to Functions and Relations. Segments 3 and 4 are grouped together. To access Functions and Relations, Segment 4, click the following link: • https://www.media4math.com/library/algebranspirationsfunctionsandrelationssegment4 A Video Transcript for Functions and Relations, Segments 3 and 4 is available via the following link: 
Applications of Functions and Relations, Conic Sections, Relations and Functions, Geometric Constructions with Circles  
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 
Special Functions, Applications of Linear Functions 