Lesson 13 | Geometry | 6th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Geometry

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

The foundational standards covered in this lesson

5.MD.C.5.C

Measurement and Data

5.MD.C.5.C — Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
5.NF.B.6

Number and Operations—Fractions

5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Understand that a three-dimensional figure can be decomposed into separate shapes, just like a two-dimensional figure, and that volume is additive.
Find the volume of composite three-dimensional figures composed of rectangular prisms.
Solve real-world problems using volume formulas and concepts.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In fifth grade, students learned that volume is additive and found the volume of 3D figures composed of non-overlapping rectangular prisms with whole number side lengths. In this lesson, students extend on that idea to solve real-world problems with composite shapes with fractional side lengths.
With multiple parts and partial volumes, it will be important for students to stay organized in order to understand their work and to check their answers. Students can use numerical expressions as one way to organize their work.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Some moving trucks include an additional storage space called a “Mom’s Attic.” It is located above the driver and passenger seats.

The dimensions of the truck’s storage space are shown below in feet. How many cubic feet of space does the truck hold?

Guiding Questions

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Problem 2

A special-order sandbox has been created for children to use as an archeological digging area at the zoo. Determine the volume of the sandbox. (Figure not drawn to scale.)

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic D > Lesson 14 — Example 2

Grade 6 Mathematics > Module 5 > Topic D > Lesson 14 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..

Problem Set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

A smaller cube sits on top of a larger cube. The combined height of both cubes is 4 inches and the larger cube has a side length of $$2\frac{1}{2}$$ inches. Find the combined volume of both cubes.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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.

Include examples such as
- Two differently sized boxes stacked on top of one another—find the volume of both
- A swimming pool with a deep end and a shallow end
- A mix of problems where students are given the area of the base(s)

MARS Formative Assessment Lessons for Grade 6 Using Space Efficiently: Packing a Truck
Illustrative Mathematics Computing Volume Progression 4
EngageNY Mathematics Grade 6 Mathematics > Module 5 > Topic D > Lesson 14 — Exercises and Problem Set (Use all the problems you did not use for Lesson 12)
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Lesson 12

Lesson 14

Lesson Map

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Find the area of parallelograms.

6.G.A.1

Find the area of right triangles.

6.G.A.1

Find the area of acute triangles using height and base.

6.G.A.1

Find the area of any triangle using height and base.

6.G.A.1

Find the area of polygons using composition and decomposition.

6.G.A.1

Solve real-world and mathematical problems involving area of polygons.

6.G.A.1

Topic B: Polygons in the Coordinate Plane

Draw polygons in the coordinate plane and find area and perimeter (Part 1).

6.G.A.3

Draw polygons in the coordinate plane and find area and perimeter (Part 2).

6.G.A.3

Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.

6.G.A.1 6.G.A.3

Topic C: Volume of Rectangular Prisms

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

6.G.A.2

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

6.G.A.2

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

6.G.A.2

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

6.G.A.2

Topic D: Nets and Surface Area

Describe features of and identify nets that match prisms and pyramids.

6.G.A.4

Create nets and use them to find surface area of three-dimensional figures.

6.G.A.4

Find the surface area of three-dimensional figures with and without nets.

6.G.A.4

Find surface area and volume in real-world problems.

6.G.A.2 6.G.A.4

Geometry

Objective

Common Core Standards

Core Standards

Geometry

Foundational Standards

Measurement and Data

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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