12th Grade Math
(10 Units, 104 Lessons)
Unit 7 - Applications of Integration(14 Lessons)
Easy as ABC - Areas Between Curves12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
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.
Areas Between Curves - dx or dy?12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:For some regions, integrating with respect to x is more complicated. Integrating with respect to y can help.
Variable Limits of Integration and the Fundamental Theorem of Calculus12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
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…
Catch-up Day - ABC and FTC12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:Today we pause to digest our new learning and tie together loose ends with Areas Between Curves and the Fundamental Theorem of Calculus.
Volumes of Solids of Revolution (part 1 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:What happens when you integrate an Area formula? You get a Volume formula! Today we delve into 3-dimensional calculus.
Volumes of Solids of Revolution (part 2 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:Students will pursue mastery of volumes of solids through analyzing the structure of the integrals for several related solids of revolution.
Volumes of Solids of Revolution (part 3 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:Students reach mastery with solids of revolution at different times. Today we differentiate and extend this topic to challenge all students.
Volumes of Solids of Revolution (part 4 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
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.
Volumes of Cross-Sectional Solids (part 1 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:No matter how you slice it, computing volumes of cross-sectional solids is a blast! Today we introduce another application of integration.
Volumes of Cross-Sectional Solids (part 2 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:No matter how you slice it, finding volumes of cross-sectional solids is a blast! Today we continue with volumes of cross-sectional solids.
Volumes of Cross-Sectional Solids (part 3 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
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.
Volumes of Cross-Sectional Solids (part 4 of 4)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:We spent a full period building 3D models of cross-sectional solids. Today students analyze and correct other students’ models and work.
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
Big Idea:When will I ever use this? Today we encounter applications and problem solving with volumes of solids familiar to students.
Applications and Problem Solving with Volumes of Solids (part 2 of 2)12th Grade Math» Unit:Applications of Integration
12th Grade Math
» Unit:
Applications of Integration
Big Idea:Today we catch-up on yesterday’s modeling lesson, and prepare for one last check for understanding before concluding volumes of solids.
