Curriculum / Math / 10th Grade / Unit 6: Three-Dimensional Measurement and Application / Lesson 13
Math
Unit 6
10th Grade
Lesson 13 of 18
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Lesson Notes
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Calculate the volume of compound objects and those with subtracted solids. Determine how the volume will be affected by scaling one or more dimensions.
The core standards covered in this lesson
G.GMD.A.3 — Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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.
N.Q.A.3 — Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
The foundational standards covered in this lesson
8.G.C.9 — Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
In terms of pacing, this lesson could be spread out over the course of two days due to the amount of content it contains and in order to accomplish all necessary applications.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Figure A shows the water level before the rock is put in the water. Figure B shows the water level after the rock is put in the water. What is the volume of the rock?
Below is a two-dimensional pattern that will be spun on an axis to create a three-dimensional shape.
Module 5: Modeling with Geometry in Secondary Mathematics Three: Integrated Pathway CCSS made available by Mathematics Vision Project et al. in partnership with the Utah State Office of Education under the CC BY-NC-SA 3.0 license. © 2014 Utah State Office of Education. Accessed June 8, 2017, 1:18 p.m..
Given the right square prism below:
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A right circular cylinder with a radius of 1 centimeter has been cut from the center of the right rectangular prism below. Find the volume.
Two cylindrical containers have the same capacity. A designer wants to increase the volume so that each container could still hold the same amount. He doubles the height of one container and doubles the radius of the other. Will scaling each container as described result in the same volume? Why or why not?
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.
Next
Use lateral surface area formulas to solve problems.
Topic A: Area and Circumference of Circles
Describe and use the formulas for area and circumference of circles to solve problems.
Standards
A.SSE.A.1G.GMD.A.1N.Q.A.3
Calculate and justify composite area and circumference of circles.
N.Q.A.1N.Q.A.2N.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
Define a general cylinder and general cone. Identify two-dimensional shapes that when revolved will form a cylinder.
G.CO.A.1G.GMD.B.4
Use volume concepts and formulas to analyze and solve multistep problems with cylinders and prisms.
G.GMD.A.1G.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.3G.GMD.B.4G.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.3G.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.1G.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.2G.GMD.A.3
Calculate the volume of a sphere and use this in the solution of problems.
G.GMD.A.1G.GMD.A.2G.GMD.A.3N.Q.A.3
G.GMD.A.3G.GMD.B.4N.Q.A.3
Topic D: Surface Area, Scaling, and Modeling with Geometry
N.Q.A.2
Use the surface area and volume to solve application problems.
G.GMD.A.3G.GMD.B.4G.MG.A.1G.MG.A.3
Solve multistep volume and surface area problems with rates and unit conversions.
G.GMD.A.3N.Q.A.2N.Q.A.3
Apply density concepts to surface area and volume problems.
G.GMD.A.3G.MG.A.2N.Q.A.2N.Q.A.3
Apply constraints on volume, surface area, or cost to solve design problems with three-dimensional figures.
G.GMD.A.3G.MG.A.2G.MG.A.3N.Q.A.2N.Q.A.3
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