Continuous Function Teacher Resources
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New Review Using Function Notation II
Learners write an example to show a function statement true and another to show it false in this short task that addresses some common student misconceptions.
There are four fundamental theorems of mathematics: arithmetic, algebra, calculus, and linear algebra listed here. Each one is described on this poster or handout. The challenge for a student of math is to figure out why they are true.
Here is an activity that should catch the attention of your class! It focuses on the real-world problem of selecting the best cellular phone plan. This exercise would be especially good to use when introducing piecewise functions. Learners compare costs for various data plans, considering such features as unlimited talk and unlimited texts, to determine which plan is the most cost effective for different scenarios. The task requires giving graphical and numerical representations of the options and writing a justification for choosing a particular plan. The resource includes a detailed commentary for the teacher and three follow-up questions.
Learners investigate the intervals represented by a function in this calculus lesson plan. They decide what interval of the function will be positive, negative or zero. They are then given graphs of functions and asked to analyze it.
Pupils solve problems using the unit circle. In this precalculus lesson, students identify angles using the properties of the unit circle. They observe the trigonometric graphs and sine, cosine and tangent.
The highlight of this series is activitiy #4. Anatomy pupils examine slides of three unknown cells. With the function of the nervous system in mind, they consider the structure of each and try to guess which one is part of that system. In other activities, they examine the nervous system of earthworm and grasshopper specimens, or they study drawings of different animal nervous systems. The drawings unfortunately aren't included in this resource; however, they can be accessed through the National Science Teachers Association website.
By looking the expression (sin x)/x that is not defined at the limit value of 0, Sal uses the squeeze theorem to show that the function can by bound between two other functions that are defined at limit value so the limit can indeed be found.
Sal explores more complex limit problems including showing how to take the limit of an expression with a square root by using the conjugate and how to simplify trigonometric functions that are part of limit problems. Note: A mistake is made on the last step of first problem where multiplication should have been used instead of addition, resulting in the correct answer of 3/16.
Participate in a life science unit that examines the relationships of living organisms to each other and to their environment as well as the student's role in the cycle of life. Through hands-on activities, research, and scientific investigations they explore the problem of persistent pollutants and their harmful effects on both humans and ecosystems.
Here's a real-world instructional activity using a business simulation. Two business accounts are used to find slope and intercept functions. The class graphs and interprets the information to find a break even point. There are plenty of worksheets and assessments included in this instructional activity.
Students investigate limits and continuity of functions. In this limits and continuity of functions lesson, students find the limit as a function approaches a given value. Students find the domain of functions.
Investigate non-linear functions based upon the characteristics of the function or the representation of the function. The functions are displayed in multiple formats including as graphs, symbols, words, and tables. Learners use written reflection scored on a rubric to assess understanding.
Design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Middle schoolers graph and write an equation for a line of best fit. They use their derived equation to make predictions about the amount of water that whould be wasted from one leak over a long period of time or the amount wasted by serveral leaks during a specific time period.
If the flu outbreak continues, exams will have to be canceled. Investigate the properties of exponential and logarithmic functions. In this algebra instructional activity, students use the TI to examine and differentiate between exponential growth and decay. They relate math to the real world by creating models.
Ninth graders investigate the functional relationship of different environmental phenomena. In this math lesson, 9th graders create models of various natural disasters. They use logarithmic and exponential functions to interpret population growth.
In this functions worksheet, students identify the domain and range of a function. They find the slope of a line. Students determine the limits of an equation and note the discontinuous and continuous functions. This three-page worksheet contains 14 multiple-choice problems.
In this calculus worksheet, students answer 14 short-answer questions regarding Euler's Method, rate equations, initial conditions, and slope functions.
This Mean Value Theorem and Rolle's Theorem worksheet is very thorough in explaining the two Theorums and showing the formulas. There are six prractice problems for classwork, and eight additional problems for homework.
Ninth graders examine the different systems of government politics and power. As they study they'll record their reflections in their journals and in return share their insights with their classmates. For mastery, 9th graders prepare and perform a skit for their classmates.
Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The calculus controversy paper is not included but one can find a number of good resources on the Internet regarding the development of calculus and the role of Newton and Leibnez.