Not all linear functions are linear transformations, only those that go through the origin. The third lesson in the 32-part unit proves that linear transformations are of the form f(x) = ax. The lesson plan takes another look at examples...

Examine trends in student-to-teacher ratios over time. Building from the first task in the two-part series, classes now explore the pattern of student-to-teacher ratios using a non-linear function. After trying to connect the pattern to...

Find the how long it has been raining based upon the amount of rainfall. Scholars analyze a table of the amount of rainfall as a function of time. Pupils first determine whether the function is invertible, then they find and interpret...

This activity begins with a review of linear functions and segues nicely over its fifteen examples and problems into a deep study of exponential functions. Linear and exponential growth are compared in an investment task. Data tables are...

Don't forget the tables! The previous lessons in this five-part series examined the linear equation and graph relationship. The current lesson adds tables to the mix. At completion, individuals should be able to create a table of values,...

In the activity on this webpage, learners use interactive graphing technology to investigate transformations of graphs. In the first part of the task, they look at the graph of a quadratic function with coordinates of a few points...

Use an activity to illustrate the different forms of a quadratic function. Here, the task asks learners to use composition of given functions to build an explicit function. The process emphasizes the impact of the order of...

Your Algebra learners will explore what equations are functions or not functions and how to alter the domain to produce a possibility for the relations being a function with a limitted domain.

Learners write an example to show a function statement true and another to show it false in this short task that addresses some common student misconceptions. 

Sequences and series are traditionally thought of as topics for the pre-calculus or calculus class, when learners are figuring out how to develop limits. But this unit uses patterns and slopes of linear functions in unique ways...

This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), students generate the graphs of f(x + c), f(x) + c, and  cf(x) for...

Use the real-world cost of parking a car to demonstrate the properties of a function. The resource describes to learners how much it is to park in a certain lot. It is up to your number crunchers to complete a table of minutes...

Learners rewrite a general quadratic function by completing the square to see a new form of the function that more easily identifies the x-coordinate of the vertex and the two roots of the function.

Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...

Learners construct an exponential function from a graph, and two given points on the graph, as they analyze what makes up an exponential function.

Algebra learners explore, analyze and build an exponential equation given its form and a specific point that exists on the function in this task. The last question asks learners to apply their ideas to an exponential equation given two...

Learners explore the characteristics of logarithmic functions and their relationship to exponential functions. Using the subscriber website Explorelearning.com, pupils observe changes in the input variable and its effect on the graph of...

Here's a resource that models rising water levels with a linear function. The task contains three parts about the level of water in a cylinder in relationship to the number of golf balls placed in it. Class members analyze the data and...

Deep mathematical thinking is found with just a coin and a number line. Combining computing some probabilities in a discrete situation, and the interpretation of a function, this simple task gives learners a lot to think about on...

Your learners can approach this task algebraically, geometrically, or both. They analyze the building of a linear function given two points and expand the concrete approach to the abstract when they are asked to find the general form of...

Clarify the Common Core standards for your eighth grade mathematicians with this series of classroom displays. By rewriting each standard as an achievable "I can" statement, these posters give students clear goals to work toward...

Many phenomena in life are periodic in nature. A task-based lesson asks scholars to explore one of these phenomena. They collect data showing the sunrise time of a specific location over the period of a year. Using the data, they create...

The equations look different, but their graphs are the same. How can that be? This activity leads your mathematicians in an exploration of three different forms of the same quadratic function. After comparing the equations, their graphs,...

Turn your algebra learners into meteorologists. Students are given three graphs that contain information about the weather in Santa Rosa, California during the month of February, 2012. Graph one shows temperatures, graph two displays the...