The slider feature on Desmos excellently shows how graphs change based on different variable values. Learners look at two similar rational functions and compare and discuss what happens when the numbers go from positive to zero to...

Introduce your algebra learners to linear and quadratic functions. Learners compare the differences and relate them back to the equations and graphs. Lead your class to discussions on the properties of a function or a constant slope...

Can you solve an equation graphically? Absolutely! This Algebra II lesson makes the connection between solving an absolute value equation and graphing two functions. Graphing absolute value functions is presented through the process of...

A six-day unit for algebra II on exponential and logarithmic functions builds upon Chapter 12 of Merrill Algebra II with Trigonometry; Applications and Connections. The text provides assistance in the depth of instruction...

Your vegetable eaters will practice function notation statement interpretation in this short task. These few exercises will bring out misconceptions students may have about function notation as well.

Everyone needs to know how to eat well to stay healthy. Learners with mild disabilities log what they eat, discuss food choices, and review healthy foods. The lesson could be used to foster living skills in high-functioning individuals...

Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...

An Algebra II instructional activity 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...

Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...

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...

Forgive me, I regress. Building upon previous modeling activities, the class examines models using the regression function on a graphing calculator. They use the modeling process to interpret the context and to make predictions...

Linear or not linear — that is the question. The lesson plan has class members translate descriptions into algebraic expressions. They take the written expressions and determine whether they are linear or nonlinear based upon the...

Throw some logic into quadratics and see if learners can match a vague graph to multiple equations. Young mathematicians must look at quadrant location, vertices, and intercepts to best match the graph to one or more equations. 

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

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...

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...

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,...

Through discussions and journaling, classmates determine methods to associate types of functions with data presented in a table. Small groups then work with examples and exercises to refine their methods and find functions that work...

Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...

I got a different answer, are they both correct? While working through modeling problems interpreting graphs, the question of precision is brought into the discussion. Problems are presented in which a precise answer is needed and...

Financial literacy skills and exponential models are connected by the compound interest formula in this task centered on inflation calculations. Collaborative learners get experience collecting data from the given websites and exploring...

A baseball trajectory and a parabola seem to make the best pair in real-world quadratic applications. Here is a current baseball resource with questions, discussions, and explorations regarding a quadratic function and home run...

Paper folding, flu spreading in a school, bacteria growth, and continuously compounded interest all provide excellent models to study exponential functions. This is a comprehensive resource that looks at many different aspects of...

Learners are given a graph of a parabola on a coordinate system, but intercepts and vertex are not labeled. The task is to analyze eight given quadratic functions and determine which ones might possibly be represented by the graph. The...