Number and Number Sense 

Computation and Estimation 

Measurement and Geometry 

Probability, Statistics, Patterns, Functions, and Algebra 

SOL Review Materials 




Measurement
Focus: Problem Solving with Area, Perimeter, Volume, and Surface Area
The student will
c) solve practical problems involving area and perimeter; and
d) describe and determine the volume and surface area of a rectangular prism. 


Essential Knowledge and Skills 
 Apply formulas to solve practical problems involving area and perimeter of triangles and rectangles.
 Create and solve problems that involve finding the circumference and area of a circle when given the diameter or radius.
 Solve problems that require finding the surface area of a rectangular prism, given a diagram of the prism with the necessary dimensions labeled.
 Solve problems that require finding the volume of a rectangular prism given a diagram of the prism with the necessary dimensions labeled.

Essential Understandings 
 What is the difference between area and perimeter? Perimeter is the distance around the outside of a figure while area is the measure of the amount of space enclosed by the perimeter.
 What is the relationship between area and surface area? Surface area is calculated for a threedimensional figure. It is the sum of the areas of the twodimensional surfaces that make up the threedimensional figure.


Vertical Articulation 
 SOL 4.7ab  a) estimate/measure length,
describe result in metric/U.S. Cust
units; b) ID equivmeasurements
between units within the U.S. Cust
system and between units within the
metric system
 SOL
5.9  identify/describe
diameter/radius/chord/
circumference of circle
 SOL 8.11  solve practical area/perimeter
problems involving composite plane
figures

Instructional Materials 
 Enhanced Scope and Sequence Lesson: Out of the Box (PDF)  Applying formulas to measure attributes of shapes (Word)
 Notes: Perimeter, Circumference, and Area (flipchart)  76 slides: notes, multiple choice, interactive practice
 Notes: Perimeter and Area (flipchart)
 Activity: Area and Perimeter Stations with QR codes (doc)  4 stations practicing perimeter and area
 Activity: Tissue Box (doc)  activity to understand surface area and volume
 Stations: Area, Perimeter, and Circumference (doc)  4 stations practicing perimeter, area and circumference
 VDOE Algebra Readiness Curriculum Companion: 3D Geometry (pdf)

Real World Lessons 
 Dan Meyer  Coke v Sprite  Which glass now contains more of its original soda?

Practice 
 Worksheet: Area and Perimeter Review (doc)  16 practice problems including word problems
 Worksheet: Area and Perimeter Review #2 (doc)  8 practice problems including word problems
 Worksheet: Area and Perimeter Problem Solving (pdf)  6 practice word problems
 Worksheet: Surface Area and Volume (doc)  8 practice problems solving for both surface area and volume
 Worksheet: Formula Practice (doc)  12 multiple choice practice problems

SOL Mini Quiz 
 SOL 6.10cd Mini Quiz: Perimeter, Surface Area, and Volume (pdf)

Skills 
 Mathematics Assessment Project:
 E01:Security Camera  Expert  A shop owner wants to prevent shoplifting. He decides to install a security camera on the ceiling of his shop. Your task is to decide on the best place to put the camera.
 E01:Candle Box  Expert  In this task, you will design a hexagonal gift box made from card.
 E08:Smoothie Box  Expert  In this task, you must figure out how to make a cardboard box just big enough for 12 bottles.
 E03:Fruit Boxes  Expert  A grocer wants to sell boxes of fruit. What is the largest volume box he can make using a 36 inch square of card?
 Perimeter and Area (doc)
 Problem Solving: Bathroom Tiles (doc)

Videos 
 Math Game Time: Surface Area of a Cube
 PH: Finding perimeter and area of a rectangle
 PH: Finding areas of triangles

Explore
Learning 
 Circle: Circumference and Area: Resize a circle and compare its radius, circumference, and area.
 Measuring Trees: Measure the height, diameter, and circumference of trees in a forest. Count growth rings to determine the age of each tree. Grow the trees for several years and investigate how growth is affected by precipitation.
 Fido's Flower Bed (Perimeter and Area): Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with prebuilt gardens made of 36 squares each to compare perimeters of shapes with equal areas.
 Minimize Perimeter: Minimize the perimeter of a rectangle with a given area. Vary the perimeter, base, and height of the rectangle and examine changes to the graph of the area.
 Perimeter, Circumference, and Area  Activity B: Resize a rectangle, circle, or square and find its perimeter or circumference and area.
 Rectangle: Perimeter and Area: Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). NOTE: The title of this Gizmo was changed on 1/4/13. The title was formerly "Rectangles: Perimeter and Area."
 Balancing Blocks (Volume): This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model.
 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 
 Everything You Wanted To Know About Area And Volume
 Learner: Surface Area Interactives
 WisWeb applets: Building with Blocks  Choose the Building Freely option
 BrainGenie: Area of a Triangle
 BrainGenie: Area and Perimeter of a Square and Rectangle
 BrainGenie: Volume and Surface Area of Cubes and Cuboids

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Exploring 3D Geometry  (SOL 6.10d) 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 
4.MD.3 
5.MD.5a 
5.MD.5b 
5.MD.5c 
6.G.1 
6.G.2 
6.G.4 
7.G.4 
7.G.6 

