Number and Number Sense, Computation and Estimation 

Measurement and Geometry 

Probability, Statistics, Patterns, Functions, and Algebra 

SOL Review Materials 




Number and Number Sense
Focus: Relationships within the Real Number System
The student will
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and properties of operations with real numbers; and
b) compare and order decimals, fractions, percents, and numbers written in scientific notation. 


Essential Knowledge and Skills 
 Simplify numerical expressions containing: 1) exponents (where the base is a rational number and the exponent is a positive whole number); 2) fractions, decimals, integers and square roots of perfect squares; and 3) grouping symbols (no more than 2 embedded grouping symbols). Order of operations and properties of operations with real numbers should be used.
 Compare and order no more than five fractions, decimals, percents, and numbers written in scientific notation using positive and negative exponents. Ordering may be in ascending or descending order.

Essential Understandings 
 What is the role of the order of operations when simplifying numerical expressions? The order of operations prescribes the order to use to simplify a numerical expression.
 How does the different ways rational numbers can be represented help us compare and order rational numbers? Numbers can be represented as decimals, fractions, percents, and in scientific notation. It is often useful to convert numbers to be compared and/or ordered to one representation (e.g., fractions, decimals or percents).
 What is a rational number? A rational number is any number that can be written in fraction form.
 When are numbers written in scientific notation? Scientific notation is used to represent very large and very small numbers.


Vertical Articulation 
 SOL 6.2ab  a) frac/dec/%  describe as ratios; b) identify
from representation;
 SOL 6.2cd  c) equiv relationships;
d) compare/order
 SOL 6.8  evaluate whole number expressions
using order of operations
 SOL 7.1bc  b) determine scientific notation for
numbers > zero; c) compare/order
fract/dec/%, and scientific notation
 SOL 7.1e 
ID/describe absolute value for rational
numbers
 SOL 7.13ab  a) write verbal expressions as algebraic
expressions and sentences as equations and
vice versa; b) evaluate algebraic expressions
 SOL A.1  represent verbal quantitative situations
algebraically/evaluate expressions for given
replacement values of variables

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Order of Operations (PDF)  Following the order of operations (Word)
 VDOE Enhanced Scope and Sequence Lesson: Ordering Numbers (PDF)  Comparing and ordering numbers (Word)
 Guided Notes: Order of Operations (doc)
 Group Activity: Order of Operations/Properties (doc)
 Stations Activity: Order of Operations/Justification (doc)
 Activity: Order of Operations with Dice (doc)
 Notes: Exponents with Negative Bases (doc)
 Notes: Comparing Rational Numbers (pdf)
 Notes: Scientific Notation (pdf)
 Activity: Ordering War Cards (pdf)
 Activity: Around the Room Review (doc)
 Project: Equivalency Masterpiece (doc)  Demonstrate fraction, decimal, and percent equivalency through art.
 VDOE Algebra Readiness Curriculum Companion: Comparing and Ordering (pdf)

Real World Lessons 

Practice 
 Worksheet: Order of Operations #1 (doc)
 Worksheet: Order of Operations #2 (doc)
 Worksheet: Order of Operations with Justifications (doc)
 Quiz: Exponents (doc)
 Worksheet: Comparing Rational Numbers (pdf)
 Review: Ordering Fractions, Decimals, Percents (flipchart)
 Worksheet: Scientific Notation (pdf)

SelfAssessments 
 SOL 8.1a MiniQuiz: Simplifying Expressions
 SOL 8.1b MiniQuiz: Fractions, Decimals, Percents, and Scientific Notation

Skills 
 Mathematics Assessment Project
 E02:Cross Totals  Expert  In this task, you investigate a number puzzle.
 E04:Hot Under The Collar  Expert  In this task you will compare two methods of converting temperature measurements from Celsius to Fahrenheit.
 E06:“Ponzi” Pyramid Schemes  Expert  Do you want to get rich quick? Your task is to find the fatal catch in this surefire money making scheme.
 Real Number Operations: Pay Scales (doc)

Videos 
 Math Vids: Howto Videos on Order of Operations

Explore
Learning 
 Order of Operations: Select and evaluate the operations in an expression following the correct order of operations.
 Comparing and Ordering Decimals: Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line.
 Comparing and Ordering Fractions: Use area models to compare and order fractions. Also see a visual representation of the least common denominator of two fractions. With the visual representation of the LCD, this Gizmo can be an introduction to adding and subtracting fractions with unlike denominators.
 Comparing and Ordering Rational Numbers: Compare and order two rational numbers using an area model.
 Ordering Percents, Fractions and Decimals: Compare and order numbers represented as percents, fractions, and decimals using area grids and a number line.
 Ordering Percents, Fractions and Decimals Greater Than 1: Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals.
 Percents and Proportions: Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.

Websites 
 Game: Changing Fractions and Decimals into Percents  Millionaire style
 Notes/Practice: Order of Operations
 Interactive Activity: Order of Operations
 Student Notes: Conversions
 Concentration Game: Equivalent Relationships
 Game: Order of Operations with Multiplication, Addition, Subtraction
 Game: Operation Order  3 levels
 Notes: Order of Operations (math.com)
 Notes: Order of Operations (purplemath.com)

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Using Order of Operations and Exploring Properties  (SOL 8.1a) The lessons focus on order of operations and evaluating numerical expressions. Students
will also investigate and recognize properties of real numbers used to solve an equation. (pdf)
 VDOE Algebra Readiness Curriculum Companion: Comparing and Ordering  (SOL 8.1b) The lessons focus on comparing and ordering fractions, decimals, percents and numbers
written in scientific notation. (pdf)
 VDOE Algebra Readiness Curriculum Companion: Working With Percents  (SOL 8.1b) The lessons in this section focus on relating percents to decimals and fractions, comparing and ordering,
solving multistep practical problems and determining the percent of increase or decrease for a give situation. (pdf)

Common Core
Standards 

