Curriculum / Math / 10th Grade / Unit 6: Three-Dimensional Measurement and Application / Lesson 3
Math
Unit 6
10th Grade
Lesson 3 of 18
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Solve multistep area and circumference of circles problems involving cost and other rates.
The core standards covered in this lesson
N.Q.A.1 — Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
N.Q.A.2 — Define appropriate quantities for the purpose of descriptive modeling.
N.Q.A.3 — Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
The foundational standards covered in this lesson
7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
The students in Mr. Rivera’s art class are designing a stained-glass window to hang in the school entryway. The window will be 2 feet tall and 5 feet wide. They have drawn the design below:
They have raised $100 to spend on the materials for the project. The colored glass costs $5 per square foot and the clear glass costs $3 per square foot. The materials they need to join the pieces of glass together cost $0.10 per square foot and the frame costs $4 per foot.
Do they have enough money to cover the costs of the materials they will need to make the window? Explain your reasoning.
Stained Glass, accessed on May 19, 2017, 11:19 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Watch the video, “Pokémon Go Cheat,” by Dan Meyer.
How long will that fan have to spin until the 5 km egg hatches?
Pokémon Go Cheat by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed Sept. 18, 2018, 11:12 a.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
A basketball court is being painted, represented by the shaded regions below: the two semicircles at the top of the free throw line and part of the center court circle. A can of paint costs $15.97 and covers 3 square feet.
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 2
Lesson 4
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
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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.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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