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Lesson Plan
EngageNY

Piecewise and Step Functions in Context

For Students 9th - 10th Standards
Looking for an application for step functions? This activity uses real data to examine piecewise step functions. Groups create a list of data from varying scenarios and create a model to use to make recommendations to increase revenue. 
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Lesson Plan
EngageNY

Modeling with Inverse Trigonometric Functions 2

For Teachers 11th - 12th Standards
Use inverse trigonometric functions to work with ramps, rabbits, and Talladega. The class models real-world situations with trigonometric functions and solves them using inverses in the 15th installment of a 16-part series. Pupils solve...
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Lesson Plan
EngageNY

Graphs of Functions and Equations

For Teachers 8th Standards
Explore the graphs of functions and equations with a resource that teaches scholars how to graph functions as a set of input-output points. They learn how the graph of a function is the graph of its associated equation.
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Lesson Plan
1
1
EngageNY

Structure in Graphs of Polynomial Functions

For Students 10th - 12th Standards
Don't allow those polynomial functions to misbehave! Understand the end behavior of a polynomial function based on the degree and leading coefficient. Learners examine the patterns of even and odd degree polynomials and apply them to...
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Lesson Plan
EngageNY

Graphs of Piecewise Linear Functions

For Students 9th - 10th Standards
Everybody loves video day! Grab your class's attention with this well-designed and engaging resource about graphing. The video introduces a scenario that will be graphed with a piecewise function, then makes a connection to domain...
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Unit Plan
Mathematics Vision Project

More Functions, More Features

For Teachers 10th - 12th Standards
Learners tackle a wide range of intimidating topics in this comprehensive unit that spans piecewise functions, absolute value of functions, and inverse functions (among other topics). Investigative group work alternates with more...
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AP Test Prep5:50
1
1
Flipped Math

Calculus AB/BC - Interpreting the Derivative in Context

For Students 10th - 12th
Put math in a real-life context to increase connections to the concept. Pupils view a short video that first reviews the connection between derivatives and rates of change. They learn how to interpret the derivative in contextual...
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AP Test Prep14:15
1
1
Flipped Math

Calculus AB/BC - Connecting a Function, Its First Derivative, and Its Second Derivative

For Students 10th - 12th
Uncover what the first and second derivatives reveal about the function. Pupils move beyond sketching graphs to determine what derivatives tell about the function itself. The video reminds learners about particle motion and how to...
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Interactive
CK-12 Foundation

Logarithmic Differentiation: Graphing the Derivative of a Logarithm

For Students 11th - Higher Ed
Log the values of the derivative of a logarithm. The interactive plots the derivative of the natural logarithm. Learners first determine the derivative of natural logarithm and the general logarithm. Using the formulas for the...
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AP Test Prep9:02
1
1
Flipped Math

Calculus AB/BC - Interpreting the Behavior of Accumulation Functions Involving Area

For Students 10th - 12th
Accumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...
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Lesson Plan
EngageNY

Exploring the Symmetry in Graphs of Quadratic Functions

For Students 9th - 10th Standards
Math is all about finding solutions and connections you didn't expect! Young mathematicians often first discover nonlinear patterns when graphing quadratic functions. The lesson begins with the vocabulary of a quadratic graph and uses...
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AP Test Prep2:19
1
1
Flipped Math

Calculus AB/BC - Selecting Procedures for Derivatives

For Students 10th - 12th
Don't get lost trying to memorize all those derivative rules. Scholars review the different methods at their disposal to determine derivatives from Units 2 and 3. They fill out a graphic organizer and then complete a set of practice...
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AP Test Prep11:54
1
1
Flipped Math

Calculus AB/BC - The Fundamental Theorem of Calculus and Accumulation Functions

For Students 10th - 12th
Connect integrals with differentiation. The beginning of the video introduces the definition of an accumulation function. Scholars learn about the relationship between integrals and derivatives. Using what is commonly known as Part Two...
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AP Test Prep12:50
1
1
Flipped Math

Calculus AB/BC - Using the Second Derivative Test to Determine Extrema

For Students 10th - 12th
Take a second look at extrema of functions. Pupils learn how to use the second derivative to determine whether a critical point is a maximum or a minimum. Learners use concavity to identify critical points as either a max or a min and...
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Lesson Plan
Curated OER

Worksheet 23 - Directional Derivative

For Teachers Higher Ed
In this function worksheet, students compute the directional derivative of a function and identify the xy-coordinates of the maximum and local minimum. This two page worksheet contains six multi-step problems.
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Lesson Plan
Curated OER

Worksheet 24 - Derivative

For Teachers Higher Ed
In this derivative worksheet, students identify second derivatives and find the directional derivative of a function. They also list the extremes and saddle points of a function. This one-page worksheet contains seven multi-step problems.
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Lesson Plan
Curated OER

Worksheet 12 - Differentiable Functions

For Teachers Higher Ed
For this differentiable function worksheet, pupils identify differentiable functions and calculate the derivative of a function. This two-page worksheet contains eight multi-step problems.
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Lesson Plan
Curated OER

Worksheet 20 - Derivatives

For Teachers Higher Ed
For this derivative worksheet, students solve functions, sketch the direction of the rate of change, and describe functions using polar coordinates. This two-page worksheet contains seven multi-step problems.
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AP Test Prep
College Board

Differentiability of Piecewise Defined Functions

For Teachers 10th - 12th
Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...
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Lesson Plan
Curated OER

Worksheet 27 - Functions

For Teachers Higher Ed
In this function worksheet, students sketch the graph of a nonzero function, estimate the value of an infinite sum, and determine the derivative and slope of functions. This one-page worksheet contains approximately 6 multi-step problems.
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Lesson Plan
Curated OER

Similarities and Differences in Properties of Different Families of Functions - An Investigation

For Teachers 9th - 12th Standards
Exploring families of functions allows students compare and contrast properties of functions.  Students discuss properties that include symmetry, max and min points, asymptotes, derivatives, etc.
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Worksheet
Curated OER

Senior Analysis: Graphing Rational Functions

For Students 10th - 12th
Budding mathematicians graph given functions, identify the asymptotes, graph absolute values, and write a table of points. This three-page activity contains 23 problems.
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Worksheet
Curated OER

Applications of Derivatives: Finding Maxima and Minima

For Students 12th - Higher Ed
In this calculus worksheet, students are given 10 short-answer problems regarding functions, derivatives, minima, maxima and extremes.
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Interactive
CK-12 Foundation

Derivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima

For Students 11th - Higher Ed
Rolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...