Notation in mathematics can be intimidating. Use this lesson to expose pupils to the various ways of representing a function and the accompanying notation. The material also addresses the importance of including a domain if necessary....

What do you get when you cross piecewise functions with transformations?  An engaging lesson plan! The conclusion of a four-part series on the transformations of functions asks class members to apply transformations to piecewise...

Discrete or not discrete? Individuals learn about the difference between discrete and non-discrete functions in the fourth installment of a 12-part module. They classify some examples of functions as being either discrete or non-discrete.

You can learn to graph as well as a calculator using calculus. The lesson introduces using derivatives to find critical points needed to graph polynomials. Pupils learn to find local maximums and minimums and intervals of increase...

Time to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.

Show your class members that if they can graph a linear function, they can graph an absolute value function. Groups create an absolute value graph using a table, then entertain the idea of an absolute value function defined as two...

If you know one, you know them all! Parent functions all handle translations the same. This instructional activity examines the quadratic, absolute value, and square root functions. Pupils discover the similarities in the behavior of the...

Help learners discover the unique characteristics of the tangent function. Working in teams, pupils create tables of values for different intervals of the tangent function. Through teamwork, they discover the periodicity, frequency, and...

Why is that graph wider? Pupils learn about stretching and shrinking graphs of square root, absolute value, cubic, and quadratic functions. They study both vertical and horizontal stretches and shrinks in addition to reflections. 

Formalize the notion of a function. Scholars continue their exploration of functions in the second instructional activity of the module. They consider functions as input-output machines and develop function rules for selected functions.

Connect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...

Build a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function. 

Looking for an application for step functions? This activity uses real data to examine piecewise step functions. Groups create a list of data from varying scenarios and create a model to use to make recommendations to increase...

Explore the graphs of functions and equations with a resource that teaches scholars how to graph functions as a set of input-output points. They learn how the graph of a function is the graph of its associated equation.

Don't allow those polynomial functions to misbehave! Understand the end behavior of a polynomial function based on the degree and leading coefficient. Learners examine the patterns of even and odd degree polynomials and apply them to...

Math is all about finding solutions and connections you didn't expect! Young mathematicians often first discover nonlinear patterns when graphing quadratic functions. The lesson begins with the vocabulary of a quadratic graph and uses...

Connect functions to geometry. In the ninth installment of a 12-part module, young mathematicians create functions by investigating situations in geometry. They look at both area and volume of figures to complete a well-rounded lesson plan.

Explore linear and nonlinear models to help your class build their function skills. In a continuation of the previous lesson, learners continue to analyze and sketch functions that model real-world situations. They progress from linear...

Turn your class upside down as they explore the reciprocal functions. Scholars use the unit circle to develop the definition of the secant and cosecant functions. They analyze the domain, range, and end behavior of each function.

Model situations with graphs. In the fourth installment of a 16-part module, scholars learn to qualitatively analyze graphs of piecewise linear functions in context. They learn to sketch graphs for different situations.

Have class members going in circles as they model the path of a Ferris Wheel using trigonometric functions. Building on the previous lesson in this series on transformations, learners use trigonometric functions to model wheels of...

Begin the discussion of domain and range using something familiar. Before introducing numbers, the lesson uses words to explore the idea of input and outputs and addresses the concept of a function along with domain and range. 

Discover an important property of linear functions. Learners use the slope formula to calculate the rates of change of linear functions. They find that linear functions have constant rates of change and use this property to determine if...

Doing is more effective than watching. Learners use spaghetti to discover the relationship between the unit circle and the graph of the sine and cosine functions. As they measure lengths on the unit circle and transfer them to a...