Calculus

  1. Limits and Local Linearization
    (limits, continuity, differentiability, average rates of change, limit definition of the derivative, tangent lines and differentials)

  2. Rates of Change
    (derivatives, higher order derivatives, product quotient and chain rules, concavity and inflection points, graph sketching, motion)

  3. Rates of Change Related to Other Things
    (optimization, related rates, exponential functions, trig functions, slope fields, differential equations)

  4. Accumulating Rates of Change
    (Riemann sums, defining the integral, average values)

  5. The Fundamental Theorem of Calculus
    (antiderivatives, definite integrals and initial conditions, functions defined by integrals)

  6. Area and Volume
    (area vs. integral, area between two graphs, volume of cross sectional solids, volumes of revolution)

  7. End of the Year Projects

  8. AP Specific Resources

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Limits and Local Linearization

Limits

Sam Shah’s awesome test question that uses a scratch off sticker to see if students understand the difference between a function value and a limit.

Continuity

Differentiability

Average Rates of Change

Limit Definition of the Derivative

Tangent Lines and Differentials

My visual way of solving tangent line problems.

My use of stock prices to introduce the equation for differentials.

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Rates of Change

Derivatives

Higher Order Derivatives

Product, Quotient and Chain Rule

Sam Shah’s box method to teach the chain rule [scroll down].

Shawn Cornally’s use of gears to visualize the chain rule.

My use of “Wannabe Math” to show that the derivative of a product isn’t the product of the derivatives.

Concavity and Inflection Points

My introduction of concavity using an infection spreading through class.

Shawn Cornally’s Superbowl Ad exploration to explore real inflection points.

Graph Sketching

My visual method of drawing first and second derivative number lines.

My project about country populations and

Motion

Dan Meyer’s Graphing Stories

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Rates of Change that are Related to Other Things

Optimization

Riley Lark on using programming to better motivate the concept of optimization.

Sam Shah’s packaging optimization project.

Related Rates

Shawn Cornally’s Gas Tank Exploration, an open ended attempt to figure out why the gas gauge doesn’t seem to go down at a constant rate.

Sam Shah’s Logger Pro Analysis of a Funnel Draining – a cool use of technology to demonstrate a great related rates problem, but show that they aren’t always so simple.

My Related Rates introduction using GeoGebra.

My post on illustrating Related Rates problems.

Exponential and Logarithmic Functions

My experiment where students model their memories.

Trig Functions

Slope Fields

Differential Equations

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Accumulating of Rates of Change

Riemann Sums

Sam Shah’s great way of setting up the Riemann Sum so that the notation gels with the physical situation.

Defining the Integral

Vi Hart’s math doodling on Appollonian Gaskets (drawing an infinite number of circles or triangles or elephants inside of a shape).

My activity relating a speedometer to an odometer.

Average Values

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Fundamental Theorem of Calculus

Antiderivatives

Maria Anderson’s Antiderivative Block game to practice integration rules.

My skills activities for practicing antiderivatives.

Definite Integrals and Initial Conditions

Functions Defined by Integrals

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Volume and Area

Area vs. Integral

Area Between Two Graphs

My drawing with GeoGebra project for setting up area integrals.

Volumes of Cross-Sectional Solids

My visual method of setting up volume integrals.

Volumes of Revolution

My reflections on teaching both solids of revolution and solids of known cross section.

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End of the Year Projects

My students’ end-of-the-year student project ideas from 2012 and same project ideas from 2011 .

My students’ projects: Twitter Followers Math, 3D Solid Modeling, Math of the Pilgrimage and Packaging Consultants.

Sam Shah’s packaging optimization project.

My reflections on project implementation (some great comments here).

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AP Specific Resources

Mr. Squires’s resources for AP Calculus AB, including tons of notes and old questions. I used this to help me with pacing and to make sure I was nailing all the right topics.

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  1. Hello. Would it be possible for you to send me you 5 minute drills for review?

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