Use a hands-on approach to exploring the concepts of related rates in your AP Calculus class. Individuals explore the effect of the rate of change on a variable related to a variable they control. After analyzing the data they...

Help learners determine the rate of change for the temperature of sand. They will collect data on the temperature of wet and dry sand over time with a heat lamp overhead. Then make a scatter plot of the data and find a linear model to...

Students observe and calculate slopes. In this algebra lesson plan, 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.

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...

If mathematicians know the secret to compound interest, why aren't more of them rich? Young mathematicians explore compound interest with exponential functions in the twenty-seventh installment of a 35-part module. They calculate future...

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...

In this rate of change worksheet, students determine the rate of change at a prescribed rate. This one-page worksheet contains 1 multi-step problem.

Learners match a given velocity graph and sketch the corresponding position graph using a graphing calculator. After collecting data from their everyday life, students use specific functions on their calculators to create graphs and...

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...

Speed up your pupils' understanding of derivatives. Two cars travel in perpendicular distances to each other. With the aid of the interactive, learners visualize the situation. Pupils use the derivative to calculate the instantaneous...

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.

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...

Students investigate reaction rates.  In this seventh or eighth grade mathematics instructional activity, students collect, record, and analyze data regarding how the temperature of water affects the dissolving time of a sugar...

In this slope of a line activity, students read about line graphs and plotting the slope of a line. They read about the rate of change which is represented by the slope. Students practice finding the slope of lines.

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...

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...

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...

High schoolers 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...

In this Newton's Law of Cooling learning exercise, students complete an essay format write up of a convection model. They write the purpose and assumptions of their lab. Students complete three rate of change problems. They describe a...

Your young microbiologists will interpret and solve exponential equations in this real-world context task set in a hospital research scenario. Learners think in terms of the functions as well as their rates of change. 

Accumulate the content so far. Learners review the content from the first five lessons dealing with accumulation functions. The eight problems go over finding maximums, minimums, concavity, points of inflection, and intervals of increase...

Graph polynomials and identify the end behavior of each polynomial function. The class differentiates between linear, quadratic, and other polynomial equations.

How much do you spend on healthcare each year? Data shows the expenditures in the US rise significantly each year. Young scholars use the data to calculate a rate of change over a 30-year period and look for—as well as provide— possible...