Order of Operations

Order of Operations "Levels"

This is how I understand order of operations from a "power" perspective.

Level 1 Operations: Addition & Subtraction

• Addition: just combining 2 quantities.

• Subtraction: just splitting (finding the difference between) 2 amounts.

Level 2 Operations: Multiplication & Division

• Multiplication: repeated addition (doing a Level 1 Operation several times).

  • Example: 5*3 = 5 + 5 + 5

or

• • Example: 5*3 = 3 + 3 + 3 + 3 + 3

• Division: repeatedly making groups (taking away multiple times)

  • Example: 15 / 3 = 5

    • 15 divided into 3 groups ends up with 5 per group

or

• • Example: 15 / 5 = 3

    • 15 divided into 5 groups ends up with 3 per group

• Bonus video: Why Do People Say that Repeated Addition is Multiplication? (Art of Problem Solving)

Level 3 Operation: Exponents

• Exponents are repeated multiplication (doing a Level 2 operation several times).

  • Example: 5^3 = 5 * 5 * 5

Level 4 Operation: Grouping Symbols

• Grouping symbols are like an "override" function and must be done before anything else.

• These include anything inside of

  • parentheses ( )

  • brackets [ ]

  • braces { }

  • absolute value |2|

  • radicals (square root symbols)

• For fraction bars: complete any possible operations in the numerator and/or the denominator before dividing them.

IXL Topics (order, solve, evaluate)

• 6th grade

  • 6.D.5 exponents with decimal bases

  • 6.O.3 evaluate numerical expressions (whole numbers)

  • 6.O.4 identify mistakes for order of operations

  • 6.O.7 evaluate numerical expressions (decimals)

  • 6.O.10 evaluate numerical expressions (fractions)

  • 6.O.12 evaluate numerical expressions (integers)

• 7th grade

  • 7.C.24 evaluate numerical expressions (integers)

  • 7.E.11 evaluate numerical expressions (decimals)

  • 7.G.18 evaluate numerical expressions (fractions)

  • 7.I.2 evaluate exponents

  • 7.I.5 exponents with decimal & fraction bases

  • 7.I.7 evaluate numerical expressions (exponents)

  • 7.R.4 evaluate expressions (variables)

  • 7.R.5 evaluate multi-variable expressions

  • 7.R.6 evaluate expressions (absolute value)

  • 7.R.7 evaluate expressions (variables w/ exponents)

• 8th grade

  • 8.C.8 evaluate numerical expressions (integers)

  • 8.E.9 evaluate numerical expressions (rational numbers)

  • 8.F.2 evaluate exponents

  • 8.V.5 evaluate expressions (variables)

  • 8.V.6 evaluate expressions (multiple variables)

  • 8.V.7 evaluate expressions (absolute value)

  • 8.V.8 evaluate expressions (square roots)

  • 8.V.9 evaluate expressions (rational numbers)

• Algebra I

  • A.B.1-7 operations

  • A.GG.9 evaluate rational expressions

  • A.I.8 solve equations using order of operations

Addition Resources (Videos)

• BrainPop: Order of Operations

• Virtual Nerd:

  • What's the Order of Operations?

  • How do You Use the Order of Operations?

  • Simplifying Expressions Using Order of Operations

  • Solving a Multi-Step Equation Using Reverse Order of Operations

  • Solving a Multi-Step Equations with Fractions Using Reverse Order of Operations

  • Solving a Multi-Step Inequality using Reverse Order of Operations