Difference Quotient Teacher Resources
Find Difference Quotient educational ideas and activities
Showing 1 - 20 of 27 resources
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.
Local Linearity, Differentiability, and Limits of Difference Quotients
Learners explore the local linearity of several functions at different points. They investigate the local linearity given a function and a point and then connect that notion with the function's differentiability at that point.
Functions and Derivatives
Learners derive functions given a limit. In this calculus instructional activity, student define the derivative of f at x=a, knowing the derivative is a point or just a number. This assignment requires students to work independently as much as possible.
The Definition of Deravitive
Twelfth graders investigate derivatives. In this Calculus lesson plan, 12th graders use the Ti-89 calculator to explore the difference quotient as the definition of the derivative.
Investigation the Derivatives of Some Common Functions
Students investigate the derivative of a function. In this calculus lesson, students explore the derivatives of sine, cosine, natural log, and natural exponential functions. The lesson promotes the idea of the derivative as a function and uses numerical and graphical investigations to form conjectures about common derivative formulas.
Mathematicians use a symmetric secant line to prove the derivative at a point. In this trigonometry lesson, students create secant lines on the navigator to analyze the derivative. They move the lines around and make observations.
Symbols in Algebra
Students name and sketch numerical expressions. In this order of operation instructional activity, students add, subtract, multiply and divide using the correct order of operation. They perform four specific calculations for their motivation instructional activity.
Motion of Related Objects - Introducing Related Rates
Students explore the concept of related rates. In this related rates lesson, students collect data about the position of a ball as it is dropped and the shadow of the ball. Students calculate the rates of the ball position v. time and shadow v. time. Students use proportions and derivatives in determining the related rates between position, time, and the shadow of the dropped ball.
Strategies for Solving Problems
Students develop strategies for solving problem situations. In this "actions" for problem situations lesson, students examine each operation (addition, subtraction, multiplication, and division) for further understanding. Then by using act it out, mental images, making models, and drawing pictures to represent "actions" in problem situations, students determine the operation needed for solution.
Functions and Velocity
Young scholars calculate the velocity of object as they land or take off. In this calculus instructional activity, students are taught how to find the velocity based on the derivative. They graph a picture the represent the scenario and solve for the velocity.
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!
Partial Derivatives for a Function of Two Variables
In this partial derivatives worksheet, students complete one word problem by finding the (x,y) coordinates of a point when it moves parallel to one axis. When given a function, they find six partial derivatives. Students solve four multivariable derivatives. They prove that partial differentiation can be easier than ordinary differentiation.
Graph And Their Derived Function
Students analyze graphs and determine their general shape. In this calculus instructional activity, students solve functions by taking the derivative, sketch tangent lines and estimate the slope of the line using the derivative. They graph and analyze their answers.
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.
In this algebra instructional activity, 9th graders rewrite word problems into algebraic sentences. They define sum, difference, quotient and factors. There are 5 word problems with an answer key.
Using Math Virtual Manipulatives
Virtual math manipulatives are tools designed to help pupils understand mathematical concepts. Sixth graders will use a manipulative called Laser Beams to practice estimating to find sums, differences, quotients, and products. This is fine as a way to practice a skill, but it is inadequate as a mode of teaching.
Beginning the Year with Local Linearity
Students investigate an article on local linearity. In this calculus lesson, students read about the application of math in the real world. They gain insight from the teachers view of how to teach and relate the topic to the real world.
Exploring the FTC using the TI
Learners use the Fundamental Theorem of Calculus to solve problems. In this calculus lesson, students use the TI to solve the graphing porting of the problem. They practice graphing functions and discuss their place in the real world.
Learners explore the slope of a line. In this Pre-Algebra/Algebra I lesson, students investigate the coordinates of points that are horizontal or vertical and the slope of the line going through those points. Learners also explore positive and negative slopes. Ti-nspire handheld required.
Strategies for Solving Problems
Fourth graders analyze and solve multi, 4th graders learn strategies for solving problem situations. First, students develop further understanding of each operation (addition, subtraction, multiplication and division) by thinking about the "action" of the operation (combining, separating or comparing).