Teach collaboration and communication skills in addition to graphing logarithmic functions. Scholars in different groups graph different logarithmic functions by hand using provided coordinate points. These graphs provide the basis for...

What do you get when you cross piecewise functions with transformations?  An engaging lesson! 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.

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.

Graphing by hand does have its advantages. The 19th installment of a 35-part module prompts pupils to use skills from previous lessons to graph exponential and logarithmic functions. They reflect each function type over a diagonal line...

Introducing inverse functions! The 20th installment of a 35-part lesson encourages scholars to learn the definition of inverse functions and how to find them. The lesson considers all types of functions, not just exponential and...

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

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...

The Function That Shall Not Be Named? The eighth installment of a 35-part module uses a WhatPower function to introduce scholars to the concept of a logarithmic function without actually naming the function. Once pupils are...

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 lesson 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...

Everybody loves video day! Grab your class's attention with this well-designed and engaging resource about graphing. The video introduces a scenario that will be graphed with a piecewise function, then makes a connection to domain...

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...

Exploring families of functions allows young scholars compare and contrast properties of functions.  Students discuss properties that include symmetry, max and min points, asymptotes, derivatives, etc.

What does dropping a ball look like as a graph? An engaging activity asks learners to record a video of dropping a ball and uploading the video to software for analysis. They compare the position of the ball to time and calculate the...

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.

If two is company and three's a crowd, then what's e? Scholars observe how changes in the base affect the graph of a logarithmic function. They then graph the natural logarithm function and learn that all logarithmic functions can be...

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

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.