Course 2 Online!
Henrico County Public Schools, Virginia
7.5 - Volume & Surface Area
Number, Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
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
  1. VDOE Enhanced Scope and Sequence Lesson: Surface Area of a Rectangular Prism (PDF) - Determining the surface area of a rectangular prism (Word)
  2. 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)
  3. VDOE Enhanced Scope and Seuqence Lesson: Surface Area and Volume of a Cylinder (PDF) - Determining the surface area and volume of a cylinder (Word)
  4. VDOE Enhanced Scope and Sequence Lesson: Volume of a Rectangular Prism (PDF) - Determining the volume of a rectangular prism (Word)
  5. Notes: Understanding Volume and Surface Area of 3-D Shapes (flipchart)
  6. Notes: Surface Area and Volume (ppt)
  7. Notes: Volume and Surface Area of Prisms (flipchart)
  8. Guided Notes: Surface Area and Volume (doc)
  9. Activity: Rectangular Prisms and Cylinders (doc)
  10. Activity: Out of the Box - Surface Area (doc)
  11. VDOE Algebra Readiness Curriculum Companion: 3-D Geometry (pdf)
Real World Lessons
  1. Dan Meyer: Popcorn Picker - Which container will hold more popcorn?
  2. Dan Meyer: You Pour, I Choose - Which glass contains more soda?
  3. Mathalicious: 1600 Pennsylvania - How much would it cost to paint and heat the home of the president?
Practice
  1. Worksheet: Volume and Surface Area - Rectangular Prisms and Cylinders (doc)
  2. Worksheet: Rectangular Prisms (pdf)
  3. Worksheet: Volume and Surface Area (pdf)
  4. Worksheet: Surface Area and Volume Word Problems (doc)
  5. Worksheet: Surface Area and Volume Word Problems #2 (doc)
  6. Worksheet: Changing Attributes Word Problems (doc)
  7. Worksheet: Changing Attributes (doc)
  8. Worksheet: What's the Measure (doc)
SOL Mini Quiz
  1. SOL 7.5 Mini Quiz: Volume and Surface Area (pdf) | (doc)
Skills
  1. 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 step-by-step 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 step-by-step guidance.)
  2. Surface Area: Painting Dilemma (doc)
  3. Surface Area: Wrapping Presents (doc)
Videos
  1. YouTube: How to Find the Volume and Surface Area of a Rectangular Prism
  2. YouTube: How to Find the Volume and Surface Area of a Cylinder
  3. YouTube: Changing Attributes
  4. PH: Finding surface areas of prisms using a formula
  5. PH: Finding the volumes of prisms
  6. PH: Finding the volumes of cylinders
  7. PH: Finding surface areas of prisms using a net
  8. PH: Finding surface areas of cylinders using a formula
Explore Learning
  1. Prisms and Cylinders - Activity A: Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional 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.
  2. 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
  1. WisWeb applets: Building with Blocks - Choose the Building Freely option
  2. BrainingCamp: Interactive Real World Math
  3. Shodor: Surface Area and Volume
VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Exploring 3-D Geometry - The lessons focus on the geometry and measurement of three-dimensional 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
N-Q.1
N-Q.2
N-Q.3