Curriculum / Math / 10th Grade / Unit 6: Three-Dimensional Measurement and Application / Lesson 5
Math
Unit 6
10th Grade
Lesson 5 of 18
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Define a general cylinder and general cone. Identify two-dimensional shapes that when revolved will form a cylinder.
The core standards covered in this lesson
G.CO.A.1 — Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.GMD.B.4 — Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
The foundational standards covered in this lesson
7.G.A.3 — Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson covers key concepts in the unit to get students thinking about solids of revolution and the underpinnings of Cavalieri’s principle. It may be tempting to jump right into volume, but volume is better saved for the next lesson in order to focus solely on the key definitions of cylinder and cone in this lesson.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
What do the figures below have in common? How are they different?
Allison made several paper flags.
Which of these will make a cylinder when spun on the post of the flag? Explain your reasoning.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Is this a cylinder? Explain why or why not.
Geometry > Module 3 > Topic B > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 4
Lesson 6
Topic A: Area and Circumference of Circles
Describe and use the formulas for area and circumference of circles to solve problems.
A.SSE.A.1 G.GMD.A.1 N.Q.A.3
Calculate and justify composite area and circumference of circles.
N.Q.A.1 N.Q.A.2 N.Q.A.3
Solve multistep area and circumference of circles problems involving cost and other rates.
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Topic B: Three-Dimensional Concepts and General Volume
Describe the terms point, line, and plane. Define and classify polyhedrons, specifically prisms and pyramids.
G.CO.A.1
G.CO.A.1 G.GMD.B.4
Use volume concepts and formulas to analyze and solve multistep problems with cylinders and prisms.
G.GMD.A.1 G.GMD.A.3
Define and calculate the volume of pyramids and cones. Describe the relationship between general cylinders and general cones with the same base area.
Use the Pythagorean Theorem to find missing measurements and calculate volume of pyramids, prisms, and compound shapes comprised of pyramids and prisms.
G.GMD.A.3 G.GMD.B.4 G.SRT.C.8
Topic C: Cavalieri's Principle, Spheres, and Composite Volume
Describe the cross-sections of prisms and cylinders and make conjectures about volume from the cross-sections.
G.GMD.A.3 G.GMD.B.4
Describe Cavalieri’s principle relating equal area cross-sections and volume, and how this relates to the formulas for volume. Derive the volume of a sphere using Cavalieri’s principle.
G.GMD.A.1 G.GMD.A.2
Identify cross-sections of pyramids and use the relationships between the cross-sections to determine the volume of truncated cones and pyramids.
G.GMD.A.2 G.GMD.A.3
Calculate the volume of a sphere and use this in the solution of problems.
G.GMD.A.1 G.GMD.A.2 G.GMD.A.3 N.Q.A.3
Calculate the volume of compound objects and those with subtracted solids. Determine how the volume will be affected by scaling one or more dimensions.
G.GMD.A.3 G.GMD.B.4 N.Q.A.3
Topic D: Surface Area, Scaling, and Modeling with Geometry
Use lateral surface area formulas to solve problems.
N.Q.A.2
Use the surface area and volume to solve application problems.
G.GMD.A.3 G.GMD.B.4 G.MG.A.1 G.MG.A.3
Solve multistep volume and surface area problems with rates and unit conversions.
G.GMD.A.3 N.Q.A.2 N.Q.A.3
Apply density concepts to surface area and volume problems.
G.GMD.A.3 G.MG.A.2 N.Q.A.2 N.Q.A.3
Apply constraints on volume, surface area, or cost to solve design problems with three-dimensional figures.
G.GMD.A.3 G.MG.A.2 G.MG.A.3 N.Q.A.2 N.Q.A.3
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