Rate of Change Teacher Resources
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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.
In this function learning exercise, students read word problems and write functions. They determine the instantaneous rate of change and identify intervals. This three-page learning exercise contains approximately 20 problems.
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.
Students calculate the rate of change using the derivative. In this algebra lesson, 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.
Learners 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 learners sucks on the blowpop. Students use derivatives to find the rate of change.
Sal solves an example for finding the rate of change of the height of water in a cone at a specific point when it is being filled at a given rate. In this video, Sal reviews the volume of a cone and the chain rule and then, uses these to find the change in height with respect to time.
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.
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.
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!
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 worksheet contains explanations, examples, and approximately ten problems.
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.
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.
Learners explore the concept of Pick's Theorem. In this Pick's Theorem lesson, students use a spreadsheet to observe patterns over a large range of cells. Learners analyze perimeter pins and interior pins on a geoboard and a spreadsheet. Students discuss rate of change based on their analysis of the perimeter and interior pins.
Students explore rates of change. In this cardiac output instructional activity, 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.
For this calculus worksheet, students calculate the rate of change of an equation as it relates to a leaning ladder. There is an answer key to this word problem.
In this rate of change worksheet, learners determine the rate of change at a prescribed rate. This one-page worksheet contains 1 multi-step problem.
In this rate of change worksheet, learners estimate the rate of change over an interval of time. This two-page worksheet contains four multi-step problems.
In this functions worksheet, students use given functions to determine the volume of a container. They find the rate of change in the volume at a specified time. Students determine the constant of the proportionality. This one-page worksheet contains three multi-step problems.
Students investigate integral calculus. In this calculus lesson, students explore an application of integrations through a leaking hot tub problem. The activity emphasizes using the integral of a rate of change to give the accumulated change.
Third graders graph lines using slope and y-intercept. In this algebra lesson, 3rd graders define the rate of change and and discover how the rate of change in linear functions remains constant.