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12th Grade Math

(10 Units, 104 Lessons)

Unit 3 - Formalizing Derivatives and Techniques for Differentiation(21 Lessons)

Sketching Derivative Functions (Part 1 of 2)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:We’ve developed the idea of the derivative as the slope of a tangent line. Today we use this idea to sketch graphs of derivative functions.

20 Resources

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20 Resources

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Sketching Derivative Functions (Part 2 of 2)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Visually estimating tangent slopes point-by-point to plot the derivative can be tedious. Today we look for ways to improve this process.

24 Resources

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24 Resources

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Sketching Antiderivative Graphs (Part 1 of 2)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:What does f ’ say about f ? By analyzing the process for sketching derivatives graphically, students will reverse this process to sketch f.

20 Resources

1 Favorites

20 Resources

1 Favorites

Sketching Antiderivative Graphs, In The Lab

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Got technology? Students will use an excellent online applet for using the graphical behavior of f ’ and f ” to sketch the antiderivative f.

18 Resources

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18 Resources

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Sketching Antiderivative Graphs (Part 2 of 2)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:What do f ’ and f ” say about f ? By reversing the process for sketching derivatives graphically, students will be able to sketch f.

22 Resources

1 Favorites

22 Resources

1 Favorites

Multiple Representations of Multiple Derivatives

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Graphs and Tables and Words, oh my! Using multiple representations to describe relationships among f, f’, and f” promotes understanding.

17 Resources

1 Favorites

17 Resources

1 Favorites

Introducing the Power Rule

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:I am SICK of using the difference quotient! Through strategically chosen functions, students form conjectures about the Power Rule.

15 Resources

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15 Resources

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The Product and Quotient Rules

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:(fg)’ = f ’g’ right? In this lesson we not only introduce the product and quotient rules, but disprove common errors students like to make.

20 Resources

2 Favorites

20 Resources

2 Favorites

Gettin' Triggy Wit It

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:With sketching derivative functions graphically and the quotient rule, students will discover the derivatives of the 6 trig functions.

21 Resources

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21 Resources

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The Chain Rule

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Something is missing. The derivative of (5x+1)^3 is not 3(5x+1)^2. With strategically chosen examples, students discover the Chain Rule.

19 Resources

3 Favorites

19 Resources

3 Favorites

Chain Rule Continued

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:How does the Chain Rule meld with other derivative rules? Students apply multiple rules simultaneously to differentiate functions.

20 Resources

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20 Resources

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Chain Chaaain Chaaaaaiin

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:It’s time to close the deal. Let’s make a lasting, memorable impression so students will always remember to use the Chain Rule.

18 Resources

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18 Resources

0 Favorites

Differentiation - The Next Level

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Why learn all these derivative rules? Today students engage with multi-step differentiation and use derivatives to identify critical points.

18 Resources

1 Favorites

18 Resources

1 Favorites

Finding Local and Absolute Extrema (Part 1 of 3)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Mount Everest or just a Bunny Hill? Today students use derivatives to identify local and absolute extrema on an interval.

21 Resources

0 Favorites

21 Resources

0 Favorites

Finding Local and Absolute Extrema (Part 2 of 3)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Continuing from yesterday, students will evaluate derivatives at given points then reverse that process to find critical points and extrema.

17 Resources

0 Favorites

17 Resources

0 Favorites

Finding Local and Absolute Extrema (Part 3 of 3)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Today we conclude using derivatives to find extrema on closed intervals, quiz on computing derivatives, and preview the 1st derivative test.

16 Resources

0 Favorites

16 Resources

0 Favorites

The First Derivative Test

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:We have used multiple derivative relationships to identify a function’s extrema graphically. Now, let’s develop an algebraic approach.

19 Resources

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19 Resources

0 Favorites

The First and Second Derivative Tests

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Our prior work with multiple derivatives is paying off; today students will develop the 2nd derivative test on their own.

17 Resources

1 Favorites

17 Resources

1 Favorites

Differentiation Practice and Review (Part 1 of 3)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:This unit was long and segmented. Today we start reassembling the pieces to create a coherent understanding of differentiation techniques.

19 Resources

0 Favorites

19 Resources

0 Favorites

Differentiation Practice and Review (Part 2 of 3)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:Connections are critical. Today we continue reassembling the pieces to create a coherent understanding of differentiation techniques.

15 Resources

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15 Resources

0 Favorites

Differentiation Practice and Review (Part 3 of 3)

12th Grade Math

» Unit:

Formalizing Derivatives and Techniques for Differentiation

Big Idea:We conclude the 3 synthesis days providing students much needed time to make meaningful connections among topics and retain their learning.

19 Resources

0 Favorites

19 Resources

0 Favorites