Difference Quotient Teacher Resources
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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.
Students 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.
Young scholars derive functions given a limit. In this calculus lesson, 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.
Twelfth graders investigate derivatives. In this Calculus lesson, 12th graders use the Ti-89 calculator to explore the difference quotient as the definition of the derivative.
Here is one lesson on interpreting algebraic expressions. Pupils evaluate expressions given an input, play a game in cooperative groups, match algebraic expressions to their quantity in context, and participate in a group discussion. The plan concretely connects the abstract expressions of Algebra to real-life situations. Your class will be hooked with the mention of chocolate.
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.
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.
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.
Learners calculate the velocity of object as they land or take off. In this calculus lesson, 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.
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 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.
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.
Learners explore the concept of derivatives. For this derivatives lesson, students find the derivatives of the cosine function on the Ti-Nspire. Learners 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 learning exercise, 9th graders rewrite word problems into algebraic sentences. They define sum, difference, quotient and factors. There are 5 word problems with an answer key.
Students use the Fundamental Theorem of Calculus to solve problems. In this calculus activity, students use the TI to solve the graphing porting of the problem. They practice graphing functions and discuss their place in the real world.
Students name and sketch numerical expressions. In this order of operation lesson, students add, subtract, multiply and divide using the correct order of operation. They perform four specific calculations for their motivation lesson.
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.
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.
Students explore the slope of a line. In this Pre-Algebra/Algebra I activity, students investigate the coordinates of points that are horizontal or vertical and the slope of the line going through those points. Students also explore positive and negative slopes. Ti-nspire handheld required.