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...

Extend the concept of exponents to irrational numbers. In the fifth installment of a 35-part module, individuals use calculators and rational exponents to estimate the values of 2^(sqrt(2)) and 2^(pi). The final goal is to show that the...

Work out to Algebra II with the 50-question worksheet that practices different types of functions. Multiple choice questions focus on topics such as rational, radical, and logarithmic functions. The resource comes with a printed answer...

Not all continuous functions are differentiable. Pupils find three types of functions that are defined everywhere but not differentiable for all values of x. Along with providing examples of each type of function, students...

Reflect upon the graphs of quadratic functions. Given a quadratic function to graph, pupils determine whether the graph after a horizontal and vertical reflection is still a function. The final two questions ask scholars to describe a...

The midline of the mathematical model of the number of hours of sunlight is not 12 hours. Pupils use the modeling cycle to determine a function that will model the number of hours of sunlight at a location of their choosing. Using...

Take a unique approach to study the graphing of trigonometric functions. Young scholars consider two sine functions and write three functions that will lie between the two given. They use a graphing utility to assist in their explorations.

It's time to check the mail! The task is to determine the most cost-effective way to mail a packet of information. Young scholars write an equation that models the amount of postage as a function of the number of sheets mailed and...

How many things does one transformation tell you? Learners compare and contrast the graphs of different parent functions with the same transformation. Using a rational and absolute value function, pupils identify key features of their...

Root for young mathematicians learning about functions. A set of two problems assesses understanding of polynomial functions and their roots. Scholars select values for a, b, and c, and then create two functions that meet given...

Here is a study guide that breaks graphing quadratic functions into three simple steps. Quadratic functions in vertex and intercept form are included. Use during a lesson or afterward for skills practice. Note: Make sure your class has...

Pupils must graph the location of a train using the time given a timetable. They analyze the different legs of the trip, graph the return trip, and compare the two graphs. The lesson ends with a discussion of similarities and...

That's the ticket! Pupils write and investigate two linear functions representing the cost of printing tickets. Individuals then determine which of two printing companies would be a better buy.

Just how durable could a hollow ball bearing be? Learners model the strength of the walls of a ball bearing as a function of the radius of its cavity. They use their models to make reasonable conclusions about the probability of failure...

Students are given a description of a scenario of Professor Fink searching for a group of children. When he finds them, he states that he can express their location as a function of his hand. Students analyze the scenario and determine...

Using this resource, scholars develop graphs that model situations by showing change over time. They answer 15 questions based on information from charts that show growth in weight. They extend the concepts to an assessment section of...

Represent the ups and downs of a bank account. The two-part task points out that some types of graphs may better show discrete functions than others. Pupils analyze a graph on how well it represents the situation. They develop their own...

Birthdays are a time for celebration, and now they're a time for calculation! An AP calculus lesson uniquely explores relationships between a polynomial function and its derivative. Learners create a cubic function based...

Writing a general rule to model a specific pattern is a high-level skill. Your classes practice the important skill as they write rules describing the solutions to a system of equations with variable coefficients. As an added challenge,...

Line up to learn about lines! Scholars discover how to express patterns as linear functions. The workbook then covers how to graph and write linear equations in slope-intercept form, as well as how to write equations of...

It all starts with arithmetic. An educational resource provides four items to use in summative assessments. The items reflect the basic skill level required by the standards in the domain and are designed to have...

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...