Number and Number Sense, Computation and Estimation 

Measurement and Geometry 

Probability, Statistics, Patterns, Functions, and Algebra 

SOL Review Materials 




Computation and Estimation
Focus: Practical Applications of Operations with Real Numbers
The student will
a) determine whether a given number is a perfect square; and
b) find the two consecutive whole numbers between which a square root lies. 


Essential Knowledge and Skills 
 Identify the perfect squares from 0 to 400.
 Identify the two consecutive whole numbers between which the square root of a given whole number from 0 to 400 lies (e.g.,square root of 57 lies between 7 and 8 since 72 = 49 and 82 = 64).
 Define a perfect square.
 Find the positive or positive and negative square roots of a given whole number from 0 to 400. (See Curriculum Guide or Framework for symbols).

Essential Understandings 
 How does the area of a square relate to the square of a number?
The area determines the perfect square number. If it is not a perfect square, the area provides a means for estimation.
 Why do numbers have both positive and negative roots?
The square root of a number is any number which when multiplied by itself equals the number. A product, when multiplying two positive factors, is always the same as the product when multiplying their opposites (e.g., 7 ∙ 7 = 49 and 7 ∙ 7 = 49).


Vertical Articulation 
 SOL 6.5  investigate/describe positive exponents,
perfect squares
 SOL 7.1a  investigate/describe negative
exponents for the powers of 10
 SOL 7.1d  determine square roots

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Perfect Squares and Square Roots (PDF)  Working with perfect squares and square roots (Word)
 Notes: Square Roots and Perfect Squares (flipchart)
 Notes: Square Roots and Perfect Squares (doc)
 Notes: Estimating Square Roots with Practice (pdf)
 Guided Notes: Squares and Square Roots (doc)
 Activity: Square Roots Number Line (doc)
 VDOE Algebra Readiness Curriculum Companion: Exploring Whole Numbers (pdf)

Real World Lessons 

Practice 
 Quiz: Squares and Square Roots (doc)
 Worksheet: Square Root Word Problems (doc)
 Worksheet: Square Roots Practice (doc)

SelfAssessments 
 SOL 8.5 MiniQuiz: Square Roots

Skills 
 Mathematics Assessment Project
 A06:Sidewalk Patterns  Apprentice  In Prague some sidewalks are made of small square blocks of stone. The blocks are in different shades to make patterns that are in various sizes. In this task, you will look for rules which let you work out how many blocks of different colors are needed to make different sized patterns. (This task is very similar to Sidewalk Stones, but offers more stepbystep guidance.)
 E13:Sidewalk Stones  Expert  This task is very similar to Sidewalk Patterns, but offers less stepbystep guidance.

Videos 
 Khan Academy: Approximating Square Roots
 LearnAlberta: Exploring Square Roots Video (Video Interactive)
 PH: Simplifying square roots

Explore
Learning 
 None

Websites 

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Exploring Whole Numbers  The lessons focus on solving problems that use whole number operations, prime and
composite numbers, odd and even numbers, perfect squares and square roots. (pdf)

Common Core
Standards 

