Three-Dimensional Measurement and Application

Lesson 16

Math

Unit 6

10th Grade

Lesson 16 of 18

Objective


Solve multistep volume and surface area problems with rates and unit conversions.

Common Core Standards


Core Standards

  • G.GMD.A.3 — Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
  • 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.

Criteria for Success


  1. Convert units using dimensional analysis to solve volume and surface area problems. 
  2. Identify a general plan for the solution of problems and revise this plan as necessary throughout.
  3. Describe the level of precision necessary at different stages of the problem to determine the most accurate answer.
  4. Identify information that is necessary to determine an accurate solution.
  5. Describe how you will assess whether your solution is reasonable or not.
  6. Justify the solution and process of solving the problem. 

Tips for Teachers


  • The criteria for success are generally repeated in Lessons 16–18, which all focus on modeling. In lesson 16, we are focusing on applications of volume and surface area with rates and unit conversions. 
  • There is no Target Task and little Problem Set Guidance in this lesson due to the level of work and explanation required for the two Anchor Problems. During the lesson, be sure to mix in plenty of independent work time and feedback cycles to ensure adequate thinking and processing time. 
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Anchor Problems


Problem 1

How long will it take to fill the tank?

Guiding Questions

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References

Dan Meyer's Three-Act Math Water Tank

Water Tank by Dan Meyer is licensed under the CC BY 3.0 license. Accessed June 2, 2017, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Jared is scheduled for some tests at his doctor’s office tomorrow. His doctor has instructed him to drink 3 liters of water today to clear out his system before the tests. Unfortunately, Jared forgot to bring his water bottle to work and was left in the unfortunate position of having to use the annoying paper cone cups that are provided by the water dispenser at his workplace. He measures one of these cones and finds it to have a diameter of 7 centimeters and a slant height of 9.1 centimeters. 

  1. How many of these cones of water must Jared drink if he typically fills the cone to within 1 centimeter of the top and he wants to compete this drinking during the work day?
  2. Suppose that Jared instead only manages to drink 25 cones of water during the day. When he gets home he measures one of his cylindrical drinking glasses and finds it to have a diameter of 7 centimeters and a height of 15 centimeters. If he typically fills his glasses to 2 centimeters from the top, about how many glasses of water must he drink before going to bed?

Guiding Questions

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References

Illustrative Mathematics Doctor's Appointment

Doctor's Appointment, accessed on June 8, 2017, 2:15 p.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.

Additional Practice


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.

  • Include shorter problems that focus on procedural fluency of rates and unit conversations.
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Lesson 15

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Lesson 17

Lesson Map

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Topic A: Area and Circumference of Circles

Topic B: Three-Dimensional Concepts and General Volume

Topic C: Cavalieri's Principle, Spheres, and Composite Volume

Topic D: Surface Area, Scaling, and Modeling with Geometry

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