Geometry

Lesson 11

Math

Unit 7

6th Grade

Lesson 11 of 17

Objective


Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.

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.A.1
  • 5.MD.C.5.B
  • 5.NF.B.6

Criteria for Success


  1. Understand that the volume of any rectangular prism can be found by multiplying the length, width, and height of the prism.
  2. Understand that the volume of any rectangular prism can also be found by multiplying the area of the base times the height of the prism, regardless of which rectangular face is used as the base. 
  3. Solve for volume of rectangular prisms using either formula depending on the information given.

Tips for Teachers


  • In 5th grade, students applied the formulas $$V=l \times w \times h$$ and $$V=B\times h$$ to rectangular prisms with whole number side lengths. In this lesson, students recall these formulas, demonstrate their equivalence, and extend their work to include rectangular prisms with fractional side lengths. 
  • Students again re-engage with 6.EE.2 and 6.EE.3 as they evaluate and manipulate the volume of rectangular prisms using the formulas. 
  • A visual demonstration or image may be helpful to show students the effect of layering and filling the prism with layers of the base, for example, like the image in Task 3 of Grade 7 Unit 4 Lesson 11 on OERCommons.org.
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Anchor Problems


Problem 1

A small box measures 5 in. across, 8 in. deep, and 6 in. tall. A book that measures 5 $$\times$$ 8 $$\times$$ 1 in. fits perfectly into the bottom of the box. 

a.   What is the volume of one book? How many books will fit into the box? What is the volume of all of the books that will fit into the box?

b.   What is the volume of the box? How is this related to the volume of one book?

c.   A medium box measures 12 inches tall. A different book with dimensions 8 $$\times$$ 10 $$\times$$ 1 in. fits perfectly into the bottom of the medium box. What is the volume of the medium box?

Guiding Questions

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Problem 2

The same rectangular prism is positioned in two different ways, as shown below. For each prism, use the rectangular face that the prism is “sitting on” as the base of the prism. 

For each prism, find the area of the base and multiply by the height. Show that this is the same volume as when all three dimensions are multiplied together. 

Guiding Questions

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Problem 3

A rectangular prism has a base area of $${4{3\over8}}$$ inches$${^2}$$, a width of $$1 \frac{1}{4}$$ inches, and a height of $${6 {1\over2}}$$ inches. Kirby writes the equation $$V=4\frac{3}{8}\times1\frac{1}{4}\times6\frac{1}{2}$$ to represent the volume of the prism. 

Do you agree with Kirby's equation? Explain and find the volume of the prism. 

Guiding Questions

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Problem Set

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Target Task


Find the volume of the rectangular prism below.

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 10

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Lesson 12

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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