Course 3 Online!
Henrico County Public Schools, Virginia
Important News: Effective August 15, 2018, this site will be realigning to the 2016 SOL.
As a result, many of the instructional notes, activities, and worksheets will be removed. Please download any files you wish to keep for future use.
8.1 - Expressions and Operations
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
  1. SOL 6.2ab - a) frac/dec/% - describe as ratios; b) identify from representation;
  2. SOL 6.2cd - c) equiv relationships; d) compare/order
  3. SOL 6.8 - evaluate whole number expressions using order of operations
  4. SOL 7.1bc - b) determine scientific notation for numbers > zero; c) compare/order fract/dec/%, and scientific notation
  5. SOL 7.1e - ID/describe absolute value for rational numbers
  6. SOL 7.13ab - a) write verbal expressions as algebraic expressions and sentences as equations and vice versa; b) evaluate algebraic expressions
  7. SOL A.1 - represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of variables
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Order of Operations (PDF) - Following the order of operations (Word)
  2. VDOE Enhanced Scope and Sequence Lesson: Ordering Numbers (PDF) - Comparing and ordering numbers (Word)
  3. Guided Notes: Order of Operations (doc)
  4. Group Activity: Order of Operations/Properties (doc)
  5. Stations Activity: Order of Operations/Justification (doc)
  6. Activity: Order of Operations with Dice (doc)
  7. Notes: Exponents with Negative Bases (doc)
  8. Notes: Comparing Rational Numbers (pdf)
  9. Notes: Scientific Notation (pdf)
  10. Activity: Ordering War Cards (pdf)
  11. Activity: Around the Room Review (doc)
  12. Project: Equivalency Masterpiece (doc) -  Demonstrate fraction, decimal, and percent equivalency through art.
  13. VDOE Algebra Readiness Curriculum Companion: Comparing and Ordering (pdf)
Real World Lessons


  1. Worksheet: Order of Operations #1 (doc)
  2. Worksheet: Order of Operations #2 (doc)
  3. Worksheet: Order of Operations with Justifications (doc)
  4. Quiz: Exponents (doc)
  5. Worksheet: Comparing Rational Numbers (pdf)
  6. Review: Ordering Fractions, Decimals, Percents (flipchart)
  7. Worksheet: Scientific Notation (pdf)
  1. SOL 8.1a Mini-Quiz: Simplifying Expressions
  2. SOL 8.1b Mini-Quiz: Fractions, Decimals, Percents, and Scientific Notation
  1. 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 sure-fire money making scheme.
  2. Real Number Operations: Pay Scales (doc)
  1. Math Vids: How-to Videos on Order of Operations
Explore Learning
  1. Order of Operations: Select and evaluate the operations in an expression following the correct order of operations.
  2. Comparing and Ordering Decimals: Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line.
  3. 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.
  4. Comparing and Ordering Rational Numbers: Compare and order two rational numbers using an area model.
  5. Ordering Percents, Fractions and Decimals: Compare and order numbers represented as percents, fractions, and decimals using area grids and a number line.
  6. 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.
  7. 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.
  1. Game: Changing Fractions and Decimals into Percents - Millionaire style
  2. Notes/Practice: Order of Operations
  3. Interactive Activity: Order of Operations
  4. Student Notes: Conversions
  5. Concentration Game: Equivalent Relationships
  6. Game: Order of Operations with Multiplication, Addition, Subtraction
  7. Game: Operation Order - 3 levels
  8. Notes: Order of Operations (
  9. Notes: Order of Operations (
VDOE Interventions
  1. 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)
  2. 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)
  3. 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