Measurement
Focus: Proportional Reasoning
The student will
a) describe volume and surface area of cylinders;
b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and
c) describe how changing one measured attribute of a rectangular prism affects its volume and surface area. 


Essential Knowledge and Skills 
 Determine if a practical problem involving a rectangular prism or cylinder represents the application of volume or surface area.
 Find the surface area of a rectangular prism.
 Solve practical problems that require finding the surface area of a rectangular prism.
 Find the surface area of a cylinder.
 Solve practical problems that require finding the surface area of a cylinder.
 Find the volume of a rectangular prism.
 Solve practical problems that require finding the volume of a rectangular prism.
 Find the volume of a cylinder.
 Solve practical problems that require finding the volume of a cylinder.
 Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to changing attributes by scale factors only.
 Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to changing attributes by scale factors only.

Essential Understandings 
 How are volume and surface area related?
Volume is a measure of the amount a container holds while surface area is the sum of the areas of the surfaces on the container.
 How does the volume of a rectangular prism change when one of the attributes is increased? There is a direct relationship between the volume of a rectangular prism increasing when the length of one of the attributes of the prism is changed by a scale factor.


Vertical Articulation 
 SOL 5.8abcde  a) find perimeter/area/volume; b) differentiate among
perimeter/area/ volume, ID which
measure is appropriate; c) ID equiv
measurements within metric
system; d) estimate/measure U.S.
Cust/metric; e) choose appropriate
unit of measure w/ U.S. Cust/ metric
 SOL 6.9  make ballpark comparisons
between U.S. Cust/metric system
 SOL 8.7ab  a) investigate/solve practical problems involving volume/surface
area of prisms, cylinders, cones,
pyramids; b) describe how changes
in measured attribute affects
volume/surface area

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Surface Area of a Rectangular Prism (PDF)  Determining the surface area of a rectangular prism (Word)
 VDOE Enhanced Scope and Sequence Lesson: Attributes of a Rectangular Prism (PDF)  Exploring how changing an attribute of a rectangular prism affects its volume and surface area (Word)
 VDOE Enhanced Scope and Seuqence Lesson: Surface Area and Volume of a Cylinder (PDF)  Determining the surface area and volume of a cylinder (Word)
 VDOE Enhanced Scope and Sequence Lesson: Volume of a Rectangular Prism (PDF)  Determining the volume of a rectangular prism (Word)
 Notes: Understanding Volume and Surface Area of 3D Shapes (flipchart)
 Notes: Surface Area and Volume (ppt)
 Notes: Volume and Surface Area of Prisms (flipchart)
 Guided Notes: Surface Area and Volume (doc)
 Activity: Rectangular Prisms and Cylinders (doc)
 Activity: Out of the Box  Surface Area (doc)
 VDOE Algebra Readiness Curriculum Companion: 3D Geometry (pdf)

Real World Lessons 
 Dan Meyer: Popcorn Picker  Which container will hold more popcorn?
 Dan Meyer: You Pour, I Choose  Which glass contains more soda?
 Mathalicious: 1600 Pennsylvania  How much would it cost to paint and heat the home of the president?

Practice 
 Worksheet: Volume and Surface Area 
Rectangular Prisms and Cylinders (doc)
 Worksheet: Rectangular Prisms (pdf)
 Worksheet: Volume and Surface Area (pdf)
 Worksheet: Surface Area and Volume Word Problems (doc)
 Worksheet: Surface Area and Volume Word Problems #2 (doc)
 Worksheet: Changing Attributes Word Problems (doc)
 Worksheet: Changing Attributes (doc)
 Worksheet: What's the Measure (doc)

SOL Mini Quiz 
 SOL 7.5 Mini Quiz: Volume and Surface Area (pdf)  (doc)

Skills 
 Mathematics Assessment Project:
 A03:Funsize Cans  Apprentice  In this task, you must design a cylindrical drink can that uses the least aluminum for a given volume of drink. (This task is very similar to Bestsize Cans, but with more stepbystep guidance.)
 E10:Sports Bag  Expert  In this task, you must figure out how to cut out the material to make a cylindrical sports bag.
 E12:Bestsize Cans  Expert  In this task, you must design a cylindrical drink can that uses the least aluminum for a given volume of drink. (This task is very similar to Funsize Cans, but with less stepbystep guidance.)
 Surface Area: Painting Dilemma (doc)
 Surface Area: Wrapping Presents (doc)

Videos 
 YouTube:
How to Find the Volume and Surface Area of a Rectangular Prism
 YouTube:
How to Find the Volume and Surface Area of a Cylinder
 YouTube: Changing Attributes
 PH: Finding surface areas of prisms using a formula
 PH: Finding the volumes of prisms
 PH: Finding the volumes of cylinders
 PH: Finding surface areas of prisms using a net
 PH: Finding surface areas of cylinders using a formula

Explore
Learning 
 Prisms and Cylinders  Activity A: Vary the height and baseedge or radius length of a prism or cylinder and examine how its threedimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder.
 Surface and Lateral Area of Prisms and Cylinders: Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid.

Websites 
 WisWeb applets: Building with Blocks  Choose the Building Freely option
 BrainingCamp: Interactive Real World Math
 Shodor: Surface Area and Volume

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Exploring 3D Geometry  The lessons focus on the geometry and measurement of threedimensional figures
including surface area and volume of prisms, cylinders, cones and pyramids. Students will investigate and
describe how changing the measure of one attribute affects the volume and surface area.(pdf)

Common Core
Standards 
6.G.4 
7.G.6 
NQ.1 
NQ.2 
NQ.3 
