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Rate of Change Teacher Resources
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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 conclusions about the behavior of the function.It is a great lesson that foreshadows concepts of rate of change and tangent lines to a specific point on a curve that will be explored in future years.
Twelfth graders explore the use of the derivative to determine the rate of change of one variable with respect to another. In this calculus lesson, 12th graders investigate the relationship between average and instantaneous velocity. Additionally, students examine the physical meaning of negative and positive rates of change.
Students apply the application of differentiation in an experiment with the inflation of a balloon in order to observe the relationship between the rate its volume is changing and the rate points on its surface are getting closer to each other. They then utilize the symbolic capacity of their calculator and calculus to determine the exact rate of change.
Twelfth graders investigate rate of change. In this calculus lesson, 12th graders use a balloon to observe the relationship between the rate its volume is changing and the rate at which points on its surface are getting closer together. Students use the symbolic capacity of the TI-89 calculator to determine the exact rate of change.
High schoolers investigate logistic models by making a scatter plot of internet phone users over 5 years. They find a logistic model that fits their data and then discuss what the instantaneous rate of change means in the context of the problem. Very relevant and applicable!
Learners build a SIR (Susceptible-Infected-Recovered) model for an epidemic moving through a population. They develop rate equations for the rate of change in the number of susceptible people with respect to time, the rate of change in the number of infected people with respect to time, and the rate of change in the number of recovered people with respect to time.
In this calculus worksheet, 12th graders differentiate and integrate basic trigonometric functions, calculate rates of change, and integrate by substitution and by parts. The twenty-two page worksheet contains explanation of the topic, numerous worked examples, and sixteen multi-part practice problems. Answers are not provided.
Students explore the concept of derivatives. In this derivatives lesson, students find the derivatives of the cosine function on the Ti-Nspire. Students use the definition of derivative to find the derivative of the cosine function as h approaches zero. Students compare their answer with the derivative through differentiation.
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 worksheet contains explanations, examples, and approximately ten problems.
Young scholars explore rates of change. In this cardiac output lesson, students measure the amount of blood being pumped by a heart. They explore the flow rate and complete an accumulation and concentration problem. They analyze data, flow rates, and concentration of a mexture.
Young scholars draw the graph of a door opening and closing over time. In this rate of change instructional activity, students graph a given function on their calculators. Young scholars create a table of values and interpret the results by telling if the door is opening or closing. They evaluate the average rates using time intervals.