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...

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.

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.

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 if a coordinate plane becomes a slope-intercept plane? What does the graph of a linear function look like? Learners explore these questions by graphing the y-intercept of a linear equation as a function of its slope. The result is a...

Piece by piece ... dismantling a function can highlight interesting patterns. The task asks learners to slice functions in sections with the same vertical change. They then recreate the graph with these slices positioned horizontally....

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...

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...

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...

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...

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.

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.

Playing with matches (unlit, of course) becomes an engaging learning experience in this fun instructional unit. Teach pupils how to apply properties of exponential functions to solve problems. They differentiate between quadratic 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. 

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...

Solve a real-life problem using function-building skills. Presented with an open-ended question, scholars complete a checklist to create and justify a solution in an interesting algebra project. The checklist asks for justifications of...

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...

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...

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...

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...

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.

Middle schoolers describe plotting functions on the Cartesian coordinate plane. They solve functions on paper and using an online tool to plot points on a Cartesian coordinate plane creating lines and parabolas.