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:

• y = ax
• y = mx + b

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.

 

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:

• y = ax
• y = mx + b

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 rapid-response 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. 

This is the Teacher's Guide that accompanies Algebra Applications: Functions and Relations.

To view the full video: https://www.media4math.com/library/algebra-applications-functions-and-relations

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-functions-and-relations

This is the Teacher's Guide that accompanies Algebra Applications: Linear Functions.

To view the full video: https://www.media4math.com/library/video-algebra-applications-linear-functions

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-linear-functions

This is the Teacher's Guide that accompanies Algebra Applications: Quadratic Functions.

To view the full video: https://www.media4math.com/library/algebra-applications-quadratic-functions

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-applications-quadratic-functions

This is the Teacher's Guide that accompanies Algebra Nspirations: Functions and Relations.

To view the full video: https://www.media4math.com/library/algebra-nspirations-functions-and-relations

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-nspirations-functions-and-relations

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-algebra-nspirations-functions-and-relations

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/video-transcript-algebra-nspirations-quadratic-functions

Video: Algebra Nspirations: Quadratic Functions: https://www.media4math.com/library/algebra-nspirations-quadratic-functions

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-algebra-nspirations-quadratic-functions

An overview of the key topics to be covered in the video.

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 Videos

To see the complete collection of Closed Captioned Videos, click on this Link

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 Videos

To see the complete collection of Closed Captioned Videos, click on this Link

The definition of the term "Function Table."

Note: The download is a JPG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Explore Fahrenheit-vs-Celsius graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx + b.

Explore Cost-vs-Time graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx.

Explore Cost-vs-Time graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx + b.

Explore Cricket Chirps-vs-Temperature graphs using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx + b.

Explore Distance-vs-Time graphs using this Desmos graphing calculator activity. This activity explores linear functions of the form y = mx.

Explore Distance-vs-Time graphs using this Desmos graphing calculator activity. This activity explores linear functions of the form y = mx + b.

Explore Hooke's Law using this Desmos graphing calculator activity. In this activity explore linear functions of the form y = mx.

This slide show provides 8 examples of quadratic functions in factored form and analyzes their graphs. Note: The download is a PPT file.

This slide show provides 18 examples of quadratic functions in standard form and analyzes their graphs. Note: The download is a PPT file.

This slide show provides 8 examples of quadratic functions in vertex form and analyzes their graphs. Note: The download is a PPT file.

In this drag-and-drop game, match f(x) with f(a) for a given value of a. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. Note: The download is the Teacher's Guide.

In this drag-and-drop game, match the linear function in standard form with its slope-intercept counterpart. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. Note: The download is the Teacher's Guide.

This is part of a collection of math clip art images that shows how to use linear and quadratic functions to model speed and acceleration equations.

Note: The download is a PNG file.

Related Resources

To see the complete collection of Math Clip Art, click on this link: https://www.media4math.com/Math-Clip-Art

This is part of a collection of math clip art images that shows how to use linear and quadratic functions to model speed and acceleration equations.

Note: The download is a PNG file.

Related Resources

To see the complete collection of Math Clip Art, click on this link: https://www.media4math.com/Math-Clip-Art

This is part of a collection of math clip art images that shows how to use linear and quadratic functions to model speed and acceleration equations.

Note: The download is a PNG file.

Related Resources

To see the complete collection of Math Clip Art, click on this link: https://www.media4math.com/Math-Clip-Art