Your river sportsmen will explore an example of paddling upstream as they build functions modeling speed and time in terms of the speed of the current. They then use their algebraic models to interpret features of the function related to...

Explore scientific notation in this mathematics lesson. Young mathematicians explore multiple representations of large number in scientific notation through the use of models, visual representation and expanded form. The lesson provided...

Your algebra learners explore the values of two types of functions in order to compare growth rates in this short cooperative task. Two types of solutions are given, using a table of values and an abstract argument.

Investigate how public key cryptography works. Scholars continue their study of one-way functions and asymmetric keys and apply this information to public key cryptography. They use an app to explore public key cryptography and its...

Students investigate topology. In this Applied Science activity students explore higher, more abstract mathematics using tangles. Students make topologically related shapes.

What determines whether a function has an inverse? Learners investigate that criteria when they examine values in a partially completed input-output table for two different functions. The task is to complete the table so that one of the...

Knowing the addition formulas allows for the calculations of double and half formulas. The fourth installment of 16 has the class use the addition formula to develop the double angle trigonometric formulas. Using the double formula,...

Ideal for use as an introduction to the idea of inverse functions, this activity investigates rainfall as a function of time. Learners use the data displayed in a table of values to analyze the function and its inverse, including why the...

Learners investigate the relationship between the Fahrenheit and Celsius temperature scales. Given two data points, they construct a linear function to describe the relationship, find the inverse of the function, and make observations...

Explore the relationship between the population of foxes and rabbits in a national park using trigonometric models. Plot data and find the appropriate trigonometric functions. Two questions require interpretation and explanation of...

This activity presents a real-world problem about an epidemic of influenza spreading through a city. Learners refer to a graph that shows the number of individuals infected in relation to the number of weeks that have elapsed since...

In this college level mathematics worksheet, students solve rational equations and identify the extraneous solutions.  The two page worksheet contains fifty-eight problems.  Answers are included. 

Sixth graders interpret linear and nonlinear graphs. They create graphs based on a problem set. Next, they represent quantitive relationships on a graph and write a story related to graphing.

Here is an activity that presents a real-world problem about the relationship between crude oil production and the gas mileage of modern automobiles. After learners write functions to describe the relationships, they are asked to...

This is not your typical Ferris wheel problem. In this exercise, your class will combine their knowledge of sinusoidal functions as well as linear motion to come up with parametric equations that model the position of a point on the edge...

This is a wonderful exercise for learners to apply their critical thinking skills along with their knowledge of quadratic functions and parabolas. Young mathematicians investigate a real-world scenario about the height a baseball reaches...

Many problems in life have more than one possible solution, and the same is true for advanced mathematics. Scholars solve seven problems that all have at least two solutions. Then three higher-level thinking questions challenge them to...

This activity presents a problem about a computer game which uses functions to simulate the path of an arrow fired by an archer. Learners use the given function to determine where the archer must stand in order to fire an arrow that will...

The behavior of a rational function near a vertical asymptote is the focus around this trip up a river. Specifically, numerical and graphical understanding is studied. The canoe context pushes the variables as numbers, rather than as...

Your learners will write quadratic functions whose graphs include specific points and explore how these graphs are related to each other.

Your learners analyze the familiar model of a cold beverage warming when it is taken out of the refrigerator. The general form of the equation and its graph are presented. Learners learn about the specific pieces of the function by...

Here is an activity that presents a good example of a function modeling a relationship between two quantities. John is making DVDs of his friend's favorite shows and needs to know how much to charge his friend to cover the cost of making...

Everything you wanted to know about calculus—and more! The resource is a complete Calculus textbook with explanations, examples, and practice problems. 

Tell the story of the math. Given a graph of a linear system, learners write a story that models the graph before crafting the corresponding functions. Graphs intersect at an estimated point, allowing for different variations in the...