Curriculum  /  Math  /  6th Grade  /  Unit 7: Geometry  /  Lesson 12

Geometry

Lesson 12

Math

Unit 7

6th Grade

Lesson 12 of 17

Objective

Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.

Common Core Standards

Core Standards

  • 6.G.A.2 — Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Foundational Standards

  • 6.EE.B.7
  • 5.MD.C.5.B
  • 5.NF.B.6
  • 6.NS.A.1

Criteria for Success

  1. Use the formulas for volume to determine missing measurements of rectangular prisms.
  2. Solve real-world problems using volume formulas and concepts.

Tips for Teachers

  • As the problems become more difficult, it will be increasingly important to model for students strategies to organize their workspace and record the information they know and don’t know.
  • In this lesson, students use their skills from 6.EE.7 as they write and solve equations in the form $$px=q$$.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

A storage box has a volume of 56 cubic inches, and the base of the box is 4 inches by 4 inches. 

a.   What is the height of the box?

b.   A teacher uses the box to store a set of cubes with an edge length of $$\frac{1}{2}$$ inch. If the box is completely full, how many cubes are in the set?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Open Up Resources Grade 6 Unit 4 Lesson 15 — 15.4: Storage Box

Grade 6 Unit 4 Lesson 15 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 20, 2018, 1:05 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

A rectangular tank is $${50}$$ cm wide and $${60}$$ cm long. It can hold up to $${126}$$ liters of water when full. If Amy fills $${{2\over3}}$$ of the tank as shown, find the height of the water in centimeters. (Recall that $$1$$ liter = $$1,000$$ cm$${^3}$$.)

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics Computing Volume Progression 3

Computing Volume Progression 3, accessed on March 20, 2018, 1:11 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.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

A tank that measures $$1\frac{1}{2}$$ feet across, $$2\frac{1}{3}$$ feet wide, and $$1\frac{1}{2}$$ feet tall, is filled halfway with water, as shown below. To fill the tank to the very top with water, how many cubic feet of water need to be added?

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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.

  • Examples where students are given various information about volume and must problem solve to determine new measurements; some examples (be sure to include fractional lengths): 
    • Given the volume of a tank, some water is splashed out and there is a new height of the water. Find the volume of the water remaining. 
    • Given the measurements of a tank partially filled with water, find the new volume if am amount of water is added.
    • Find the volume of cereal in a box before and after eating breakfast.
    • Given the volume of a box that is filled with smaller boxes, find the dimensions of each smaller box.

Next

Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.

Lesson 13
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Topic B: Polygons in the Coordinate Plane

Topic C: Volume of Rectangular Prisms

Topic D: Nets and Surface Area

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free