Rate of Change Teacher Resources
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Working with Rates of Change
In this calculus activity, 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.
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.
Average Rate of Change
Math pupils calculate the average rate of change over a specific interval. They represent the average rate of change on a graph and examine the behavior of the graph for decreasing and increasing numerals.
Exploration 1: Instantaneous Rate of Change Function
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.
Rate of Change
Twelfth graders explore the use of the derivative to determine the rate of change of one variable with respect to another. In this calculus instructional activity, 12th graders investigate the relationship between average and instantaneous velocity. Additionally, students examine the physical meaning of negative and positive rates of change.
Rate of Change in Linear Functions
Third graders graph lines using slope and y-intercept. In this algebra lesson plan, 3rd graders define the rate of change and and discover how the rate of change in linear functions remains constant.
Rate of Change
Students calculate the rate of change using the derivative. In this algebra instructional activity, students identify the function over closed interval and identify the rate of change. They use correct notation and classify a function as increasing or decreasing.
Blowpop Rate of Change of Volume
Students explore the concept of rate of change. In this rate of change lesson, students record the rate of change of the radius of a blowpop as a students sucks on the blowpop. Students use derivatives to find the 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.
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.
Internet Phone Subscribers Soar
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!
Even More Calculus
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.
Derivatives: Instantaneous Rate of Change
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.
What Does Math Have to Do with Getting Sick?
Students 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.
The Babylonian Algorithm, Limits and Rates of Change
In this successive approximations activity, 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 activity contains explanations, examples, and approximately ten problems.
Average Rate of Change, Difference Quotients, and Approximate Instantaneous Rate of Change
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 difference quotients to approximate instantaneous rate of changes.
Exponential Decay Formula (can skip, involves Calculus)
Sal continues his discussion of decay by showing students the math involved in determining how much a substance is left after one half-life, two half-lives, and even three half-lives have gone by. He sets up a general function of time that can be used to determine the remaining amount of a substance after 10 minutes, or three billion years have elapsed!
Students solve problems using implicit differentiation. In this calculus lesson, students take the derivative to calculate the rate of change. They observe two robots and draw conclusion from the data collected on the two robots.
Rate of Change
In this calculus instructional activity, students calculate the rate of change in an isosceles trapezoid. They take the derivative to find their answer.
Cardiac Output, Rates of Change, and Accumulation
Learners 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.