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Integrals (31)
area (Integrals) (8)
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rectangle approximations (3)
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There are 31 results
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Easy as ABC - Areas Between Curves
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
What if the x- or y-axes do not bound the region? Today we compute areas between two functions as a natural extension of definite integrals.
Standards:
MP1
MP1
MP3
MP3
MP7
MP7
Favorites
(2)
Resources
(23)
Reflections
(1)
Volumes of Solids of Revolution (part 1 of 4)
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
What happens when you integrate an Area formula? You get a Volume formula! Today we delve into 3-dimensional calculus.
Standards:
MP1
MP1
MP4
MP4
MP7
MP7
Resources
(17)
Volumes of Cross-Sectional Solids (part 3 of 4)
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
Hard to visualize 3D solids? Let’s build some! Today students construct models and use them in computing volumes of cross-sectional solids.
Standards:
MP1
MP1
MP3
MP3
MP5
MP5
MP6
MP6
MP7
MP7
Favorites
(1)
Resources
(21)
Reflections
(1)
Applications and Problem Solving with Volumes of Solids (part 1 of 2)
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
When will I ever use this? Today we encounter applications and problem solving with volumes of solids familiar to students.
Standards:
MP1
MP1
MP4
MP4
MP5
MP5
MP7
MP7
Favorites
(2)
Resources
(23)
Reflections
(1)
Areas Between Curves - dx or dy?
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
For some regions, integrating with respect to x is more complicated. Integrating with respect to y can help.
Standards:
MP1
MP1
MP3
MP3
MP4
MP4
MP7
MP7
Resources
(21)
Wait, the Interval Width Varies?
12th Grade Math
»
Unit: Full Course Review via Motion
12th Grade Math
»
Unit: Full Course Review via Motion
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
How can we interpret integrals with function limits of integration? Tables & graphs supplement symbolic representations for understanding.
Standards:
MP2
MP2
MP4
MP4
MP6
MP6
Resources
(25)
Advanced Related Rates and the Mean Value Theorem (Part 2 of 4)
12th Grade Math
»
Unit: Applications of Differentiation, Part 2
12th Grade Math
»
Unit: Applications of Differentiation, Part 2
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
The Mean Value Theorem is one of the most important in all of calculus. Today we begin to make its importance obvious to students.
Standards:
MP1
MP1
MP2
MP2
MP3
MP3
MP4
MP4
MP6
MP6
MP7
MP7
MP8
MP8
Resources
(18)
u-Substitution (Part 1 of 2)
12th Grade Math
»
Unit: The Integral
12th Grade Math
»
Unit: The Integral
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
Integrate sin(x)cos(x). Double angle sine? Or treat cos(x) like the chain rule? Today we introduce u-substitution to “undo” the chain rule.
Standards:
MP1
MP1
MP2
MP2
MP5
MP5
MP7
MP7
Favorites
(2)
Resources
(17)
Variable Limits of Integration and the Fundamental Theorem of Calculus
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
An integral with a variable limit of integration equals another function. So what is the derivative of such an integral? Let’s investigate…
Standards:
MP1
MP1
MP3
MP3
MP5
MP5
MP7
MP7
Resources
(22)
Reflections
(1)
u-Substitution (Part 2 of 2)
12th Grade Math
»
Unit: The Integral
12th Grade Math
»
Unit: The Integral
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
Can there ever be several choices for u that work? Today we explore various options and considerations for productive choices for u.
Standards:
MP1
MP1
MP7
MP7
Resources
(23)
Reflections
(1)
Rectangular Approximation Methods
12th Grade Math
»
Unit: The Integral
12th Grade Math
»
Unit: The Integral
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
Computing area under linear functions is easy. But what about curvy functions? Summing an infinite number of rectangles offers a solution.
Standards:
MP1
MP1
MP2
MP2
MP3
MP3
MP6
MP6
Favorites
(2)
Resources
(22)
Volumes of Cross-Sectional Solids (part 1 of 4)
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
No matter how you slice it, computing volumes of cross-sectional solids is a blast! Today we introduce another application of integration.
Standards:
MP1
MP1
MP4
MP4
MP6
MP6
MP8
MP8
Favorites
(1)
Resources
(19)
Meet My Friend Riemann
12th Grade Math
»
Unit: Full Course Review via Motion
12th Grade Math
»
Unit: Full Course Review via Motion
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
Students reconsider the task of approximating areas under curvy functions, then improve their approximations to perfection. Hello integrals!
Standards:
MP2
MP2
MP6
MP6
Favorites
(1)
Resources
(25)
Volumes of Solids of Revolution (part 3 of 4)
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
Students reach mastery with solids of revolution at different times. Today we differentiate and extend this topic to challenge all students.
Standards:
MP1
MP1
MP2
MP2
MP4
MP4
MP7
MP7
Favorites
(1)
Resources
(17)
Volumes of Solids of Revolution (part 4 of 4)
12th Grade Math
»
Unit: Applications of Integration
12th Grade Math
»
Unit: Applications of Integration
Jason Slowbe
Temecula, CA
Environment: Suburban
Big Idea:
Why is a sphere’s volume 4/3 pi*r^3 ? Why is a cone’s volume 1/3 pi*r^2*h? How can we split a solid into thirds? Calculus has the answers.
Standards:
MP1
MP1
MP2
MP2
MP3
MP3
MP4
MP4
MP5
MP5
MP7
MP7
Resources
(16)
Reflections
(1)
Now showing
1 to 15
of 31 results
Page
of 3
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