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
a) define π (pi) as the ratio of the circumference of a circle to its diameter;
b) solve practical problems involving circumference and area of a circle, given the diameter or radius.



Essential Knowledge and Skills 
 Derive an approximation for pi (3.14 or 22/7) by gathering data and comparing the circumference to the diameter of various circles, using concrete materials or computer models.
 Find the circumference of a circle by substituting a value for the diameter or the radius into the formula C = pd or C = 2pr.
 Find the area of a circle by using the formula A = π r^2.

Essential Understandings 
 What is the relationship between the circumference and diameter of a circle? The circumference of a circle is about 3 times the measure of the diameter.


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: Going the Distance (PDF)  Applying formulas to measure attributes of shapes (Word)
 Notes: Perimeter, Circumference, and Area (flipchart)  76 slides: notes, multiple choice, interactive practice
 Notes: Circles (flipchart)  14 slides: notes, videos, interactive website and multiple choice questions to understand area and circumference of circles
 Notes: Circles (ppt)  powerpoint version of the above flipchart
 Activity: Area and Circumference Match (pdf)  14 questions matching the questions to the answers.
 Activity: Measuring Circles (pdf)  fill in chart to learn how to find pi by measuring different circles
 Activity: Origami  Finding the Circumference of a Circle (pdf)  fortune teller activity to practice solving circumference
 Activity: Finding the Circumference of a Circle Game (pdf)  board game to practice finding circumference of circles
 Activity: Bubble Mania (pdf)  students make bubbles and fill in a chart finding the circumference
 Activity: Pi and Area Investigations (pdf)  fill in chart to help with vocabulary of circles, investigation to find and understand circumference and area of circles
 Song: Circle Song (flv)  sound file
 VDOE Algebra Readiness Curriculum Companion: Exploring Circles (pdf)

Real World Lessons 
 Dan Meyer  Penny Circle  How many pennies will the big circle will hold?
 Dan Meyer  Coin Carpet  If you were going to carpet the room with a single kind of coin, which would be the cheapest option?
 Dan Meyer  Brita  How many times would all the water bottles used in the US in a year wrap around the world?
 Mathalicious: Pizza Pi  Pizza Hut pizzas come in three sizes: large, medium and personal. Which size is the best deal, and is it ever a good idea to buy the personal?
 Mathalicious: As The World Turns  How fast is the world spinning, and is it the same everywhere?

Practice 
 Worksheet: Area and Circumference Review (doc)  14 practice problems finding area and circumference
 Worksheet: Circle Patterns (doc)  measure 7 circles (not provided) to understand the relationship and patterns between circumference and diameter

SOL Mini Quiz 
 SOL 6.10ab Mini Quiz: Circumference and Area (pdf)

Skills 
 Mathematics Assessment Project: A13: Historic Bicycle  Apprentice  In this task, you will figure out some problems about a strange old bicycle.

Videos 
 Math Rap  Don't Let Pi Make Ya Cry! (mp4)
 Math Playground: Circumference
 PH: Finding circumference

Explore
Learning 

Websites 
 Sadlier: Circumference :
 Quia: Circumference and Area of a Circle
 Learn Alberta: Select Shape and Space  Circles
 BrainGenie: Area and Circumference of Circle
 Illuminations: Circle Tool

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Exploring Circles  (SOL 6.10ab) The lessons focus on exploring the relationships among the radius, diameter, center,
circumference, chord, and area of a circle and on using formulas involving pi. (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 

