An Algebra II lesson draws the connection between the exponential function and its inverse. By graphing an exponential function and using tables and a calculator, students graph the logarithmic function. The plan comes with a...

The structure of an expression is a descriptive feature. Learners build a solid understanding of quadratic functions using an analysis of expressions in different forms. The seventh module in a series of nine includes 12 lessons...

Which function models the data best? Pupils work through several activities to model data with a variety of functions. Individuals begin by reviewing the shapes of the functions and finding functions that will fit plotted data points. By...

Not all continuous functions are differentiable. Pupils find three types of functions that are defined everywhere but not differentiable for all values of x. Along with providing examples of each type of function, students...

The midline of the mathematical model of the number of hours of sunlight is not 12 hours. Pupils use the modeling cycle to determine a function that will model the number of hours of sunlight at a location of their choosing. Using...

Continue the study of transformations with an examination of horizontal stretches, shrinks, and reflections. Individuals use the same process used in parts one and two of this series to examine horizontal changes. The resource also...

The coordinate plane links key geometry and algebra concepts in this approachable but rigorous unit. The class starts by developing the distance formula from the Pythagorean Theorem, then moves to applications of slope. Activities...

How old is the plant? Here is a task that presents the exponential decay function for carbon 14 in a plant. Pupils use the function to estimate the amount of carbon 14 in the plant when it died and analyze the function to find what...

Create polynomials with specific values. The task consists of writing three polynomial functions that evaluate to specific values for any given number. Scholars first find a polynomial that evaluates to one for a given value, then a...

Represent the ups and downs of a bank account. The two-part task points out that some types of graphs may better show discrete functions than others. Pupils analyze a graph on how well it represents the situation. They develop their own...

Discover an inverse variation pattern. A simple lesson plan design allows learners to explore a nonlinear pattern. Scholars analyze a distance, speed, and time relationship through tables and graphs. Eventually, they write an equation to...

Don't let a little challenge get between your pupils and their learning! Scholars compare two absolute value functions to recognize patterns and use them to build their own functions with outputs that are between the given. They then...

Two for one—create an invertible and non-invertible function from the same data. The task presents a function table with missing outputs for the class to use to create two functions. One of the functions should have an inverse while the...

Challenge your classes to think between the curves. Given two function formed by the combination of two exponential functions, individuals must write three functions in which all values would lie between the given. The question is...

Leaners investigate families of linear functions through dance. They choreograph dance moves to model nine unique linear functions of their choosing. Using their dance moves, teams create a video presentation complete with music and...

Take a unique approach to study the graphing of trigonometric functions. Young scholars consider two sine functions and write three functions that will lie between the two given. They use a graphing utility to assist in their explorations.

Weight is a function of the distance from sea level. Learners explore the many implications of this fact in an inquiry-based task. Given the function, pupils answer questions before manipulating the function to rewrite the distance...

That's the ticket! Pupils write and investigate two linear functions representing the cost of printing tickets. Individuals then determine which of two printing companies would be a better buy.

Examine and compare a linear and step function. The task provides two scenarios, one modeled by a linear function and the other a step function. Pupils create a graph for each and explain how each compares to the other.

Get moving to a better understanding of graphs of derivatives. Using motion sensors, scholars vary their velocities to create graphs of the first derivative of a function. The activity challenges groups to first create a script of the...

How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...

How many intersections can two absolute value functions have? Young scholars consider the question and then develop a set of rules that describe the number of solutions a given system will have. Using the parent function and the standard...

The plot thickens to get a functional understanding. After a short review of plotting points on the coordinate plane, class members learn the difference between functions and relations in the second lesson in a series of nine. They...

Model the difference between the graphs of discrete and continuous functions. Scholars examine two scenarios and construct graphs to model the situation. They then compare their graphs that illustrate the subtle difference between these...