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
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.
Sketching Derivative Functions (Part 2 of 2)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Sketching Antiderivative Graphs (Part 1 of 2)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Sketching Antiderivative Graphs, In The Lab12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Sketching Antiderivative Graphs (Part 2 of 2)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Multiple Representations of Multiple Derivatives12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Introducing the Power Rule12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
The Product and Quotient Rules12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Gettin' Triggy Wit It12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
The Chain Rule12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Chain Rule Continued12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Chain Chaaain Chaaaaaiin12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Differentiation - The Next Level12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Finding Local and Absolute Extrema (Part 1 of 3)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Finding Local and Absolute Extrema (Part 2 of 3)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Finding Local and Absolute Extrema (Part 3 of 3)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
The First Derivative Test12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
The First and Second Derivative Tests12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Differentiation Practice and Review (Part 1 of 3)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Differentiation Practice and Review (Part 2 of 3)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
Differentiation Practice and Review (Part 3 of 3)12th Grade Math» Unit:Formalizing Derivatives and Techniques for Differentiation
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.
