Classroom Resources

This self-checking online assessment has 10 questions that will help students practice solving functions to determine if the relationship between the variables shows concavity or inflection. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

This self-checking online assessment has 10 questions that will help students practice solving problems to identify and describe the relationship between variables as extrema. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

Given a set of information on the key properties of a function, you can sketch the graph. Before we proceed, make an attempt to summarize what you think are key properties. Often, the key properties of a function are not all presented to you directly but must be determined from the information at hand.

This informational material will explain how to analyze graphs of functions and identify the graph's key features. The article includes many examples of graphs and functions related to this concept. Practice questions with a PDF answer key are provided.

This interactive will help students practice analyzing graphs of rational functions to identify key features. 

Analyzing functions helps one to derive key information that can be used to determine the equation of certain functions. In the interactive, students are given a rational function r(x) = 1 / x-h + k, where h and k are real numbers.

In this interactive, students will:

• • move the red point to translate the function.
  • observe how the key properties of the function change when you move the function.  

In this video lesson, students will learn to provide a satisfying conclusion to their story by ending with the character’s feelings and their responses to what happened in the story.

Remember how to compute the volume of a cylinder or prism using the cross-sectional area and length (height) of the object? If the cross-sectional area is known and constant along the height, the volume calculation is easy. But, what if the cross-sectional area changes in a known manner along the line that is the height, like it does for a cone or pyramid? How could a single method in calculus be used to determine the volume of either of these types of solids?

This informational material will explain how to calculate the volume of special solid figures, like cones, by using cross-sections from the solid figure. The three-dimensional case of Cavalieri's Principle is introduced. There are corresponding videos available. Practice questions with a PDF answer key are provided.

Students will test their knowledge of calculating the volume of cones using cross-sections on a graph in this interactive.

How do you find the volume of a cone given its cross-section? Consider half the cross-section of the cone where the region is formed by the lines y = 0, x = 45 and the changing standard equation.  

In this interactive, students will:

• • move the red point in order to change the standard equation of a line and the cross-section associated with it.
  • move the blue point in order to traverse through the cross-section.
  • see how the radius of the circle changes when you are traversing through the solid.

This informational material will explain how to solve problems using trigonometric identities by using trigonometric substitution. There are corresponding videos available. Practice questions with a PDF answer key are provided.  

This Khan Academy video on the CK-12 website will demonstrate how to solve problems using trigonometric identities with substitution.

Is it possible to make a bad picture into a good picture with photo editing? When scientists enhance pictures from telescopes, are they really doing science, or are they just indulging their imaginations? Just how far can you zoom in to get information? When you're manipulating images, you have to be able to separate usable information from background noise.

This article will explain how photo editing software uses trigonometric identities and substitution to adjust the value of pixels in an image. There is a corresponding video and links to additional information.

This informational material will explain how to evaluate integrals with infinite limits to find the value of a variable. It gives examples of integrals with limits of infinity or negative infinity that converge or diverge. There are corresponding videos available. Practice questions with a PDF answer key are provided.  

This self-checking online assessment has 10 questions that will help students practice solving functions with infinite limits that converge or diverge. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

When the rate of change of the amount of a substance, or a population, is proportional to the amount present at any time, we say that this substance or population is going through either a decay or a growth, depending on the sign of the constant of proportionality. Do you know how to write a differential equation that expresses this condition? This kind of growth or decay, common in nature and in the business world, is called exponential growth or exponential decay and is characterized by rapid change.

This informational material will explain how to find solutions to differential equations that represent rapid change. It will explain real-life applications of these equations, such as radioactive decay and compound interest. There are corresponding videos available. Practice questions with a PDF answer key are provided.   

This interactive will model exponential growth using the following scenario:

An ancient legend tells of a wise man who advises a king during a time of famine. As a reward for his help, the man asks the miserly king for grains of rice every day.  He asks the king to put a single grain on the first square of a chessboard on the first day, two grains on the second square on the second day, double that amount on the third square on the third day, and so on. The amount of rice grows exponentially.

In this interactive, students will:

• move the grains of rice to the squares on the chessboard to show how quickly a single grain of rice can become many grains.

After engaging with this interactive, students should be able to explain the key features of exponential functions. 

This video from MIT Open CourseWare on the CK-12 website will explore the meaning of exponential growth or decay by solving a differential equation that models such growth or decay.

This self-checking online assessment has 10 questions that will help students practice solving differential equations that represent exponential change. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

This informational material will explain how to identify the zeroes and intercepts of polynomial functions using graphs and equations. There are corresponding videos available. Practice questions with a PDF answer key are provided.  

This interactive will help students practice identifying zeroes and intercepts of polynomial functions using graphical representations. 

In this interactive, students will:

• • move the red line to see the intersections between the blue function and the red line.
    (The blue points are the places where the red line intersects the blue function.)
  • hover over the blue intercepts to see their coordinate values.

This self-checking online assessment has 10 questions that will help students practice finding the zeroes and intercepts of polynomial functions. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

Travis found the following equation in his math book

d=rt−16t2

It is an equation to calculate velocity. In fact, it is a function. Being an avid sports player, Travis was very interested in figuring out how to use the equation, but he isn’t even sure what kind of a function it is. Can you identify this function? In this concept, you will learn to recognize a quadratic function as an equation in two variables with a specific form.

This informational material will help students identify key features of and solutions for quadratic functions.  Practice questions with a PDF answer key are provided.  

This video will explain how to identify components of quadratic functions and solve the function for each variable. 

In this lesson, students will choreograph a sequence of ballet movements to tell a story.  

Throughout this lesson, students will: 

• • Define ballet vocabulary and movement.
  • Apply the basic concept of rhythm to classical music.
  • Compare the relationship between classical ballet and classical music.
  • Research and gather information about the history of classical ballet.
  • Describe the physical fitness benefits, entertainment, and career options for classical ballet dancers and musicians.
  • Create a storyline for a ballet.
  • Choreograph an original story.
  • Discuss the production with the audience both pre-performance and post-performance. 

In this lesson, students will choreograph simple dances in small groups and perform them for the class. Students will learn elements of dance and vocabulary by demonstrating various movements. Students will create a K-W-L chart about dance.  They will share in pairs and report findings to the class.  They will work in pairs to choreograph a 64 beat dance.  

In this lesson, students will discover how hula dance tells a story through rhythmic patterns and gestures. Students will gather information about the history of hula. Students will observe hula movements and identify the meanings of gestures.  They will work in groups to choreograph an original hula dance that tells a story. They will perform their dance for the class.    

In this lesson, students will pantomime a variety of scenarios.  They will analyze The Nutcracker and identify how the characters tell a story through dance.  They will re-enact a scene from The Nutcracker. Students will emotionally and physically tell a story through dance and pantomime.

In this lesson, students will identify how animals and elements of nature are represented by dancers. They will read poetry by Indigenous and Native Peoples of North America.  Using basic locomotor movement, students will choreograph and perform a dance from a poem.    

In this lesson, students will research and gather information about human body systems and functions. The students will explore creative movement. The students will examine the relationship between creative movement and the human body. The students will choreograph a series of dance phrases representing the human body systems and functions and then erform a choreographed dance for an audience.

In this video, experience a sample of the Dancing Wheels Company & School's training methods in physically integrated dance, a method that allows those with and without disabilities to learn and perform a dance together.  The video included movements are brush, turn, and jump. These ideas can be used in choreography for students with different abilities.  

Students will watch Erika Malone demonstrate how to choreograph a dance based on their emotions.  They will perform the dance with Erika while watching a video.  After watching the video, the students can choreograph their own dance based on their emotions. 

Students will research Ireland and Irish culture, including traditional dance and music. They will work in groups to choreograph a Céilís to traditional Irish music. 

In this lesson, students will learn the Russian folk danceTroika. They will research and gather information on Russian culture and history. Students will create their own rendition of a Russian folk dance using the same organizational pattern and music.

Students will read about choreographers and what they do.  The famous choreographers mentioned are Bob Fosse, George Balanchine, Alvin Ailey, and Martha Graham.  Students will research dances by choreographers and choreograph their own routines.  

This informational material allows the class to read about flamenco dancing and identify the three parts of modern flamenco dancing: guitar, song, and dance. Students can dance along with a video of flamenco dancing and make their own castanets. 

Students will read about the history of line dancing. They will watch some instructional videos and choreograph their own line dance. 

In this lesson, students observe symmetry, geometric shapes, and angles in two Early American dances, and then choreograph their own dance with symmetrical figures. Three options are provided in this lesson depending on the time in class.  In all three options, students will observe symmetry in dance.