Geometry

Lesson 10

Math

Unit 7

6th Grade

Lesson 10 of 17

Objective


Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes. 

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

  • 5.MD.C.5
  • 5.NF.B.4

Criteria for Success


  1. Pack a rectangular prism with unit cubes and with fractional unit cubes.
  2. Find the volume of a rectangular prism by packing it with fractional unit cubes and multiplying the number of cubes it takes to fill the prism by the volume of one fractional unit cube. 
  3. Understand that the volume of a prism with fractional side lengths can be found by multiplying the length, width, and height of the prism.

Tips for Teachers


  • In fifth grade, students learned how to find the volume of rectangular prisms with whole number side lengths. They packed prisms with unit cubes, and also applied the formulas $$V=l \times w \times h$$ and $$V=B\times h$$. Anchor Problem 1 reviews volume with whole number values, and Anchor Problems 2 and 3 extend on this idea to involve prisms with fractional side lengths.
  • In the Fishtank curriuclum, the use of cubic unit notation with the exponent 3 (i.e. units$$^3$$) is new for students in 6th grade. In fifth grade, students described the units as cubic units or cubic yards or cubic inches, etc.
  • The following two resources are helpful if students need additional support grasping the concept of packing unit cubes and packing unit cubes with fractional side lengths. 
    • EngageNY includes an additional resource at the end of Grade 6 Module 5 Lesson 11 that includes scaffolding to understand 2-D and 3-D packing of squares and cubes with fractional edges.
    • Illustrative Mathematics task “6.G Volumes with Fractional Edge Lengths” walks students through a hands-on activity of building prisms with snap cube pieces that represent fractional unit cubes.
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Anchor Problems


Problem 1

Two rectangular prisms are shown below.

Which prism holds more $$1\times1\times1$$ in. cubes? How many more cubes does that prism hold than the other one?

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic C > Lesson 11Opening Exercise

Grade 6 Mathematics > Module 5 > Topic C > Lesson 11 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..

Modified by Fishtank Learning, Inc.

Problem 2

Instead of using $$1$$ in. unit cubes, you fill the rectangular prism shown below with cubes that measure $${1\over 2} \times {1\over 2} \times {{{1\over2}}}$$ in.

a.   How many $${{1\over2}}$$ in. cubes will fill the prism? 

b.   What is the volume of each $${{1\over2}}$$ in. cube?

c.   What is the volume of all the cubes that fill the prism? 

Guiding Questions

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Problem 3

A number of $${{{{{{{{1\over4}}}}}}}}$$ in. cubes are used to fill the prism below.

a.   How many $${{{{{{{{1\over4}}}}}}}}$$ in. cubes does it take to fill the prism? 

b.   Find the volume of the prism by packing it with $${{{{{{{{1\over4}}}}}}}}$$ in. cubes.

c.   Find the volume of the prism by multiplying the values for length, width, and height, and show it is the same answer you got by packing the prism with $${{{{{{{{1\over4}}}}}}}}$$ in. cubes. 

Guiding Questions

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Problem Set

Fishtank Plus Content

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

Target Task


A $${{{{{{{{1\over3}}}}}}}}$$ in. cube is used to fill the prism below. 

a.   How many $${{{{{{{{1\over3}}}}}}}}$$ in. cubes does it take to fill the prism?

b.   Find the volume of the prism by packing it with $${{{{{{{{1\over3}}}}}}}}$$ in. cubes.

c.   Find the volume of the prism by multiplying the values for length, width, and height, and show it is the same answer you got by packing the prism with $${{{{{{{{1\over3}}}}}}}}$$ in. cubes.

Student Response

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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.

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Lesson 9

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Lesson 11

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

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