Number and Number Sense, Computation and Estimation 

Measurement and Geometry 

Probability, Statistics, Patterns, Functions, and Algebra 

SOL Review Materials 




Measurement
Focus: Problem Solving
The student will
a) investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and
b) describe how changing one measured attribute of a figure affects the volume and surface area. 


Essential Knowledge and Skills 
 Distinguish between situations that are applications of surface area and those that are applications of volume.
 Investigate and compute the surface area of a square or triangular pyramid by finding the sum of the areas of the triangular faces and the base using concrete objects, nets, diagrams and formulas.
 Investigate and compute the surface area of a cone by calculating the sum of the areas of the side and the base, using concrete objects, nets, diagrams and formulas.
 Investigate and compute the surface area of a right cylinder using concrete objects, nets, diagrams and formulas.
 Investigate and compute the surface area of a rectangular prism using concrete objects, nets, diagrams and formulas.
 Investigate and compute the volume of prisms, cylinders, cones, and pyramids, using concrete objects, nets, diagrams, and formulas.
 Solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids.
 Compare and contrast the volume and surface area of a prism with a given set of attributes with the volume of a prism where one of the attributes has been increased by a factor of 2, 3, 5 or 10.
 Describe the twodimensional figures that result from slicing threedimensional figures parallel to the base (e.g., as in plane sections of right rectangular prisms and right rectangular pyramids).†Revised March 2011

Essential Understandings 
 How does the volume of a threedimensional figure differ from its surface area? Volume is the amount a container holds.
Surface area of a figure is the sum of the area on surfaces of the figure.
 How are the formulas for the volume of prisms and cylinders similar? For both formulas you are finding the area of the base and multiplying that by the height.
 How are the formulas for the volume of cones and pyramids similar? For cones you are finding 1/3 of the volume of the cylinder with the same size base and height.
For pyramids you are finding 1/3 of the volume of the prism with the same size base and height.
 In general what effect does changing one attribute of a prism by a scale factor have on the volume of the prism? When you increase or decrease the length, width or height of a prism by a factor greater than 1, the volume of the prism is also increased by that factor.


Vertical Articulation 
 SOL 6.9  make ballpark comparisons between U.S.
Cust/metric system
 SOL 7.5abc  a) describe volume/surface area of
cylinders; b) solve practical problems
involving volume/surface area of rect. prims
and cylinders; c) describe how changes in
measured attribute affects volume/surface
area

Instructional Materials 
 Enhanced Scope and Sequence Lesson: Volume and Surface Area (PDF)  Solving problems involving volume and surface area (Word)
 Notes: Surface Area and Volume (ppt)
 Notes: Surface Area and Volume #2 (ppt)
 Activity: Changing Attributes  Surface Area and Volume (pdf)
 VDOE Algebra Readiness Curriculum Companion: 3D Geometry (pdf)

Real World Lessons 
 Dan Meyer: You Pour, I Choose  Which glass contains more soda?
 Dan Meyer: Ticket to Ride  How many tickets are on the roll?
 Dan Meyer: Ditch Diggers  Guess whether or not the two ditch diggers will meet.

Practice 
 Worksheet: Surface Area and Volume Word Problems #1 (doc)
 Worksheet: Surface Area and Volume Word Problems #2 (doc)
 Worksheet: Surface Area and Volume Word Problems #3 (doc)
 Worksheet: Surface Area and Volume Practice #1 (doc)
 Worksheet: Surface Area and Volume Practice #2 (doc)
 Worksheet: Surface Area and Volume Review (doc)
 Worksheet: Surface Area Practice (pdf)
 Quiz: Volume and Surface Area of 3D Figures (doc)

SelfAssessments 
 SOL 8.7a MiniQuiz: Volume and Surface Area
 SOL 8.7b MiniQuiz: Changes in Attributes

Skills 
 Mathematics Assessment Project:
 A18:Matchsticks  Apprentice  How many matchsticks can be made from a tree with a trunk with a base radius of 1 foot and a height of 80 feet?
 E16:Propane Tanks  Expert  In this task, you must work out how much you need to change the radius of a propane gas tank in order to double its capacity.
 Practical Problem: Postal Expenses (doc)

Videos 

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.
 Pyramids and Cones  Activity A: Vary the height and base‑edge or radius length of a pyramid or cone and examine how its three‑dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone.
 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.
 Surface and Lateral Area of Pyramids and Cones: Vary the dimensions of a pyramid or cone 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 
 Learn Alberta: Exploring Surface Area, Volume, and Nets (Object Interactive)

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)
 VDOE Algebra Readiness Curriculum Companion: – Investigating Patterns, Functions, and Algebra  (SOL 8.7a) The lessons focus on algebraic reasoning. Students explore the relationships found in
number patterns through arithmetic and geometric sequences using variables expressions. They use modeling to collect data, and they learn to record data so that they can see the
relationship that exists among tables, graphs, words, and equations. (pdf)

Common Core
Standards 
7.G.3 
8.G.9 
GGMD.1 
GGMD.3 
GGMD.4 
GMG.1 
GMG.2 
GMG.3 

