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Lesson Plan
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\n\"Stretching\n\n
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\nEngageNY\n
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\nStretching and Shrinking Graphs of Functions\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nWhy is that graph wider? Pupils learn about stretching and shrinking graphs of square root, absolute value, cubic, and quadratic functions. They study both vertical and horizontal stretches and shrinks in addition to reflections. \n
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Lesson Plan
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\n\"Revisiting\n\n
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\nEngageNY\n
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\nRevisiting the Graphs of the Trigonometric Functions\n

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\n\nFor Teachers\n\n11th - 12th\n\nStandards\n
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\nUse the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...\n
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\n\"Formal\n\n
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\nEngageNY\n
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\nFormal Definition of a Function\n

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\n\nFor Students\n\n8th\n\nStandards\n
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\nFormalize the notion of a function. Scholars continue their exploration of functions in the second lesson of the module. They consider functions as input-output machines and develop function rules for selected functions.\n
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\n\"Linear\n\n
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\nEngageNY\n
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\nLinear Functions and Proportionality\n

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\n\nFor Students\n\n8th\n\nStandards\n
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\nConnect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...\n
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\n\"Transforming\n\n
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\nEngageNY\n
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\nTransforming the Graph of the Sine Function\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nBuild a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function. \n
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\n\"Piecewise\n\n
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\nEngageNY\n
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\nPiecewise and Step Functions in Context\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nLooking 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...\n
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\n\"Modeling\n\n
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\nEngageNY\n
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\nModeling with Inverse Trigonometric Functions 2\n

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\nUse 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...\n
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\n\"Graphs\n\n
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\nEngageNY\n
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\nGraphs of Functions and Equations\n

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\n\nFor Teachers\n\n8th\n\nStandards\n
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\nExplore 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.\n
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\n\"Structure\n\n
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\nStructure in Graphs of Polynomial Functions\n

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\n\nFor Students\n\n10th - 12th\n\nStandards\n
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\nDon'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...\n
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Lesson Plan
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\n\"Graphs\n\n
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\nEngageNY\n
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\nGraphs of Piecewise Linear Functions\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nEverybody 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...\n
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Instructional Video5:21
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\n\"Power\n\n
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\nPower Rule for Derivatives\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nFind shortcuts to finding derivatives. The resource introduces the power rule for finding the derivatives of polynomial functions. The fourth video in a series of 31 starts by applying the rule to monomials and then shows how to combine...\n
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Instructional Video7:49
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\n\"Derivatives\n\n
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\nDerivatives\n

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\nInstantly find the rate of change at a point. The video presents an example illustrating how to find the rate of change at a point on a function. Using graphs, the presenter illustrates the method of approximating the slope of the...\n
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Unit Plan
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\n\"More\n\n
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\nMathematics Vision Project\n
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\nMore Functions, More Features\n

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\n\nFor Teachers\n\n10th - 12th\n\nStandards\n
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\nLearners 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...\n
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AP Test Prep5:50
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\n\"Calculus\n\n
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\nCalculus AB/BC - Interpreting the Derivative in Context\n

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\n\nFor Students\n\n10th - 12th\n
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\nPut 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...\n
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Instructional Video8:38
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\n\"Hydrocarbon\n\n
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\nCrash Course\n
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\nHydrocarbon Derivatives\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nThis comprehensive video focuses on functional groups including alcohols, hydroxyl groups, aldehydes, carboxylic acid, acetone, ethers, esters, and amines. \n
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Instructional Video8:00
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\n\"Equation\n\n
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\nKrista King Math\n
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\nEquation of the Tangent Line\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nGiven a function and a point on the function, the video shows how to determine the equation of the tangent line at that point. Using the function equation, the presenter determines the y-coordinate for the point. The 24th video in a...\n
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AP Test Prep14:15
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\n\"Calculus\n\n
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\nCalculus AB/BC - Connecting a Function, Its First Derivative, and Its Second Derivative\n

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\nUncover 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...\n
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Instructional Video13:50
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\n\"Derivatives\n\n
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\nDerivatives of Exponentials | Essence of Calculus, Chapter 5\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSee why exponential functions are special. Viewers learn how the derivatives of exponential functions are proportional to their original functions. They see that e^x is a special case where the constant of proportionality is one. \n
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Interactive
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\n\"Logarithmic\n\n
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\nCK-12 Foundation\n
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\nLogarithmic Differentiation: Graphing the Derivative of a Logarithm\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nLog 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...\n
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AP Test Prep9:02
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\n\"Calculus\n\n
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\nCalculus AB/BC - Interpreting the Behavior of Accumulation Functions Involving Area\n

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\n\nFor Students\n\n10th - 12th\n
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\nAccumulation 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...\n
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AP Test Prep2:19
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\n\"Calculus\n\n
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\nCalculus AB/BC - Selecting Procedures for Derivatives\n

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\n\nFor Students\n\n10th - 12th\n
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\nDon'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...\n
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AP Test Prep11:54
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\n\"Calculus\n\n
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\nCalculus AB/BC - The Fundamental Theorem of Calculus and Accumulation Functions\n

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\n\nFor Students\n\n10th - 12th\n
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\nConnect 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...\n
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Lesson Plan
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\n\"Exploring\n\n
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\nEngageNY\n
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\nExploring the Symmetry in Graphs of Quadratic Functions\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nMath 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...\n
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Instructional Video10:20
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\n\"How\n\n
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\nCurated OER\n
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\nHow was the Quadratic Formula Derived?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nIf you or your class members are interested in how the quadratic formula is derived, then take a look at this video! The tutorial takes you through each step necessary to derive the quadratic formula from the general form for a quadratic...\n
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