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...

In this function worksheet, students read word problems and write functions. They determine the instantaneous rate of change and identify intervals. This three-page worksheet contains approximately 20 problems.

Pupils draw the graph of a door opening and closing over time. They graph a given function on their calculators, create a table of values and interpret the results by telling if the door is opening or closing and evaluate the average...

In this calculus worksheet, students problem solve 8 word problems involving rates of change in association with high school students. Students work out each problem and give a short explanation of each answer.

Your class will be very interested in the results of this activity. How long does it take a MP3 and video game player to charge?  Sam only has an hour and the MP3 player only has 40% of its battery life left. Plus, his video player...

Your movie fans will be interested in this resource. They will compare video streaming plans. One plan charges a set rate per month and a reduced viewing fee, and the other has a flat rate per each video viewed. Unfortunately, learners...

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.

Students investigate speed. For this rate of change lesson, students complete a rate/time/distance table to determine the average m.p.h. of a given trip. They listen and follow along with the lecture and examples to determine the average...

In this successive approximations worksheet, students use the Babylonian algorithm to determine the roots of given numbers. They identify the limits of a function, and compute the rate of change in a linear function. This two-page...

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...

An inquiry-based algebra lesson explores real-world applications of linear functions. Scholars investigate four different situations that can be modeled by linear functions, identifying the rate of change, as well as the...

Context is the key to understanding slope. A real-world application of slope uses a weight loss scenario with a constant rate of change to introduce the concept of slope of a line, before it makes a connection to the ordered pairs...

Inquiry-based learning and investigations form the basis of a deep understanding of quadratic functions in a very thorough unit plan.  Learners develop recursive and closed methods for representing real-life situations,...

In this derivatives worksheet, learners identify the partial derivatives of a function, find the rate of change, and determine the maximum and minimum values of a function. This one-page worksheet contains 6 multi-step problems.

Middle-schoolers explore the concept linear equations. They use the internet to navigate through videos and problems. Pupils problem solve to determine rates of change, slope, and x and y-intercepts.

It seems like it should be about three. Pupils learn to get an estimate of the derivative of a function at a point by using the derivative functionality of their graphing calculators. They take that information to determine the equation...

Swimming is more fun with quantities. The short assessment task encompasses finding the volume of a trapezoidal prism using an understanding of quantities. Individuals make a connection to the rate of which the pool is filled with a...

Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...

How can you compare linear functions? The seventh installment of a 12-part module teaches learners how to compare linear functions whose representations are given in different ways. They use real-world functions and interpret features in...

Melting and burning might seem like opposites, but both exist as common examples of exothermic reactions. Scholars work with three different exothermic chemical reactions to determine the enthalpy changes. They measure and mix chemicals,...

This exercise is an opportunity for algebra learners to understand the connection between the slope of a line and points found on the line. Use similar triangles to explain why slope m is the same between any two points. Discuss with the...

How does an input affect an output? Assess your learners' ability to answer this question using this pre-test. Scholars answer questions about the basics of a function. Topics include determining if a table or statement represents a...

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...

Your class can become linear equations masters, as they calculate the rate of change of a function. They observe different types of coordinates as they relate to a graph, then use the Ti-navigator to move the line around and draw...