NYS

These are the resources that support this NYS Standard.

NY-8.F.5

There are 116 resources.
Title Description Thumbnail Image Curriculum Topics

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 slope-intercept form.

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 hands-on 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 hands-on 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. 

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.

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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.

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:

  • Speed vs. distance
  • Distance vs. time
  • Displacement vs. time

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.

Algebra Application: Accident Investigation

In this Algebra Application, students develop a quadratic mathematical model for calculating the speed of a car based on the length of its skid marks. Using this model, students investigate the corresponding parabola. The math topics covered include:

  • Mathematical modeling
  • Quadratic functions in standard form
  • Square root formula
  • Data analysis

The culminating activity is for students to write a program, using either a spreadsheet or a computer language like Python, that can calculate the speed of a car, given the skid mark length and coefficient of friction as the two inputs.

Note: The download is a PDF file that includes the link to the GoogleDoc version.

Applications of Quadratic Functions, Quadratic Equations and Functions

Algebra Application: Fireworks Displays

In this Algebra Application, students develop a quadratic mathematical model based for the path of fireworks. Using this model, students investigate the properties of parabolas, including orientation, y-intercept, and vertex. The math topics covered include:

  • Mathematical modeling
  • Quadratic functions in standard, vertex, and factored form
  • Curve fitting
  • Solving equations

The culminating activity is for students to plan a fireworks displays that mathematically uses the properties of quadratics restricted to the first quadrant. Given the coordinates of the vertices, what are the equations of parabolas that fit the given parameters.

Note: The download is a PDF file that includes the link to the GoogleDoc version.

Applications of Quadratic Functions, Quadratic Equations and 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/algebra-nspirations-functions-and-relations-segment-4

A Video Transcript for Functions and Relations, Segments 3 and 4 is available via the following link:

https://www.media4math.com/library/video-transcript-algebra-nspirations-functions-and-relations-part-2

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 Videos

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

AlgApps--LinearFunctions02.jpg Special Functions, Applications of Linear Functions

Closed Captioned Video: Algebra Applications: Linear Functions

In this episode of Algebra Applications, three real-world 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 Videos

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

AlgApps--LinearFunctions00.jpg Special Functions, Applications of Linear Functions

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 Videos

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

AlgApps--LinearFunctions03.jpg Special Functions, Applications of Linear Functions

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 Videos

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

AlgApps--LinearFunctions04.jpg Special Functions, Applications of Linear Functions

Closed Captioned Video: Linear Functions: Negative Slope, Negative y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a negative y-intercept. 

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

VideoTutorial--LinearFunctions5.jpg Graphs of Linear Functions

Closed Captioned Video: Linear Functions: Negative Slope, Positive y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a positive y-intercept. 

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

VideoTutorial--LinearFunctions4.jpg Graphs of Linear Functions

Closed Captioned Video: Linear Functions: Negative Slope, Zero y-Intercept

Video Tutorial: Linear Functions: Negative Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a negative slope and a zero y-intercept. 

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

VideoTutorial--LinearFunctions6.jpg Graphs of Linear Functions

Closed Captioned Video: Linear Functions: Positive Slope, Negative y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Negative y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a negative y-intercept. 

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

VideoTutorial--LinearFunctions2.jpg Graphs of Linear Functions

Closed Captioned Video: Linear Functions: Positive Slope, Positive y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Positive y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a positive y-intercept. 

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

VideoTutorial--LinearFunctions1.jpg Graphs of Linear Functions

Closed Captioned Video: Linear Functions: Positive Slope, Zero y-Intercept

Video Tutorial: Linear Functions: Positive Slope, Zero y-Intercept. In this video tutorial, students learn the basics of linear functions in slope-intercept form. In particular, look at the case of a linear function with a positive slope and a zero y-intercept. 

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

VideoTutorial--LinearFunctions3.jpg Graphs of Linear Functions

Definition--Functions and Relations Concepts--Absolute Value Function

This is a collection of definitions related to the topic of functions and relatinos. This includes general definitions for functions and relations, as well as terms related to types of functions, visualization models, other related terms.

Note: The download is a PNG file.

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Defintion--FunctionsAndRelations--AbsoluteValueFunction.png Relations and Functions

Definition--Functions and Relations Concepts--Composite Function

This is a collection of definitions related to the topic of functions and relatinos. This includes general definitions for functions and relations, as well as terms related to types of functions, visualization models, other related terms.

Note: The download is a PNG file.

Related Resources

To see the complete collection of Math Definitions on this topic, click on this Link.

Defintion--FunctionsAndRelations--CompositeFunction.png Relations and Functions

Definition--Functions and Relations Concepts--Conic Sections

This is a collection of definitions related to the topic of functions and relatinos. This includes general definitions for functions and relations, as well as terms related to types of functions, visualization models, other related terms.

Note: The download is a PNG file.

Related Resources

To see the complete collection of Math Definitions on this topic, click on this Link.

Defintion--FunctionsAndRelations--ConicSections.png Relations and Functions

Definition--Functions and Relations Concepts--Constant Function

This is a collection of definitions related to the topic of functions and relatinos. This includes general definitions for functions and relations, as well as terms related to types of functions, visualization models, other related terms.

Note: The download is a PNG file.

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To see the complete collection of Math Definitions on this topic, click on this Link.

Defintion--FunctionsAndRelations--ConstantFunction.png Relations and Functions

Definition--Functions and Relations Concepts--Continuous Function

This is a collection of definitions related to the topic of functions and relatinos. This includes general definitions for functions and relations, as well as terms related to types of functions, visualization models, other related terms.

Note: The download is a PNG file.

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Defintion--FunctionsAndRelations--ContinuousFunction.png Relations and Functions

Definition--Functions and Relations Concepts--Decreasing Function

This is a collection of definitions related to the topic of functions and relatinos. This includes general definitions for functions and relations, as well as terms related to types of functions, visualization models, other related terms.

Note: The download is a PNG file.

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Defintion--FunctionsAndRelations--DecreasingFunction.png Relations and Functions

Definition--Functions and Relations Concepts--Dependent Variable

This is a collection of definitions related to the topic of functions and relatinos. This includes general definitions for functions and relations, as well as terms related to types of functions, visualization models, other related terms.

Note: The download is a PNG file.

Related Resources

To see the complete collection of Math Definitions on this topic, click on this Link.

Defintion--FunctionsAndRelations--DependentVariable.png Relations and Functions