Simply find the slope to find the average rate of change. A short video provides the definition of the average rate of change. Using the definition, pupils calculate the average rate of change to solve problems that cover finding average...

Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.

Learners consider the rate of filling a cone in the 23rd installment of this lesson series. They analyze the volume of the cone at various heights and discover the rate of filling is not constant. The lesson ends with a...

The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson plan. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots...

Ramp up the average rate of change—instantly. Learners use their knowledge of the formula to find the average rate of change to find the instantaneous rate of change. The presenter shows pupils an interactive that demonstrates finding...

How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...

Pupils, with the assistance of their TI-84 Plus / TI-83 Plus calculators, distinguish meanings from right, left and symmetric difference quotients that include rate of change and graphical interpretations. They utilize symmetric...

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...

For 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.

Explore functions with non-constant rates of change. The first installment of a 12-part module teaches young mathematicians about the concept of a function. They investigate instances where functions do not have a constant rate of change.

Which is faster, a Ford or a Ferrari? The short assessment has pupils analyze graphs to determine the rates of change between the two. Individuals interpret the rates of change within the context of speeds of the cars and develop a map...

Students observe and calculate slopes. In this algebra lesson, students graph equations and determine the pace at which the slope is changing. They use the navigator to see the change as they graph the lines around.

It's shark week! In this problem, young mathematically minded marine biologists need to study the fish population by analyzing data over time. The emphasis is on understanding the average rate of change of the population and drawing...

Be instantly transfixed by the idea of instantaneous rates of change. Scholars watch an informative video that introduces the fathers of calculus, Newton and Leibniz. They then learn about instantaneous rates of change by first...

Students investigate speed. In 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...

Investigate patterns in the binomial theorem. Pupils begin by reviewing the coefficients from Pascal's triangle. They look at the individual terms, the sums of the coefficients on a row, and the alternating sum of each row. Individuals...

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.

For 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...

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...

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...

Scholars model the height of water in a container with an exponential function and apply average rates of change to this function. The main attraction of the lesson is the discovery of Euler's number. 

What variables change heart rate? Young scientists observe the beating heart in Daphnia to understand these variables. They make changes in temperature, chemicals, and other factors as they graph the heart rates. Analysis questions help...

Young scholars investigate the reaction rate of iodine and soluble starch. In this rates of chemical reactions lesson plan, students study the effects of varying concentrations of reactants and varying temperatures of reactants on the...