Teacher Guide: Order of Operations (PEMDAS)
Learn the correct order to solve math problems with multiple operations using PEMDAS.
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Class quiz
10 questions on Basic Operations. Students join with a name, you see everyone's score.
For Teachers
- Students will correctly apply the order of operations (PEMDAS) to evaluate expressions with multiple operations
- Students will explain why the order of operations is necessary for consistent mathematical results
- Students will identify and correct common errors in order of operations
- Students will solve expressions containing parentheses, exponents, and all four basic operations
- • Understanding of addition, subtraction, multiplication, and division
- • Familiarity with basic exponents (squares)
- • Ability to recognize mathematical symbols
- 1. Why do you think mathematicians needed to agree on a specific order for operations?
- 2. What would happen if everyone solved math problems in different orders?
- 3. Can you think of a real-life situation where the order of steps matters?
- 4. How does your calculator know which operation to do first?
- 5. What would happen if we didnt have parentheses?
Multiplication always comes before division
Remediation: Show examples like 12 ÷ 3 × 2 and demonstrate working left to right. Have students practice with expressions where division comes first.
PEMDAS means do operations in that exact letter order
Remediation: Emphasize that M/D are equal priority and A/S are equal priority. Use visual groupings: P → E → (M and D) → (A and S)
Parentheses only mean grouping
Remediation: Explain that parentheses also indicate multiplication in cases like 2(3) and ensure students understand implicit multiplication
For Struggling Students:
- • Provide a PEMDAS checklist to reference
- • Use color-coding for different operation types
- • Start with expressions that only have 2 operations
- • Use manipulatives to visualize grouping
For On-Level Students:
- • Practice with standard 3-4 operation expressions
- • Include expressions with parentheses and exponents
- • Challenge with word problems requiring PEMDAS
For Advanced Students:
- • Include nested parentheses
- • Introduce expressions with variables
- • Have students create expressions that equal specific values
- • Explore order of operations in programming
- 5.OA.A.1 (CCSS.MATH.CONTENT.5.OA.A.1)
Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols
- 6.EE.A.2.C (CCSS.MATH.CONTENT.6.EE.A.2.C)
Evaluate expressions at specific values of their variables, including expressions that arise from formulas
- materialWhiteboard or Projector
For demonstrating worked examples step by step
- materialPEMDAS Anchor Chart
Visual reference showing the order of operations
- worksheetPractice Worksheets
Graduated difficulty problems for student practice
- manipulativeCalculator
For checking answers and exploring patterns
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
- P = Parentheses (do these first)
- E = Exponents (powers and roots)
- M/D = Multiplication and Division (left to right)
- A/S = Addition and Subtraction (left to right)
Worked Examples
Solve:
Look for Parentheses
No parentheses → Move to next step
Look for Exponents
No exponents → Move to next step
Do Multiplication first
→
Do Addition
→
Answer:
Common Mistakes
Adding before multiplying
Why it's wrong: Students often work left to right, doing before the multiplication in
Correct: Always do multiplication and division before addition and subtraction. The answer is , not
Thinking M comes before D
Why it's wrong: PEMDAS lists M before D, making students think multiplication always comes first
Correct: Multiplication and Division have EQUAL priority. Work left to right. In , do first, then
Forgetting to work inside parentheses completely
Why it's wrong: Students may only do part of what is inside parentheses
Correct: Solve EVERYTHING inside parentheses before moving on. In , you must do first, then
Ignoring exponents
Why it's wrong: Students sometimes treat exponents like regular multiplication
Correct: Exponents come before multiplication. In , first calculate , then
Why It Matters
- Science - calculating formulas correctly
- Programming - computers follow strict operation orders
- Finance - calculating interest, taxes, and budgets
- Engineering - designing safe structures and systems
Real World Applications
Shopping Discounts
When shopping, you often need to calculate final prices after discounts and additional costs. The order in which you apply these calculations matters!
Example:
A 50 dollar shirt is 20% off, then you add 5 dollar shipping. Calculate: dollars
You want to buy a video game that costs 60 dollars. The store has a 25% off sale, and there is a 4 dollar tax added at the end.
What is the final price you will pay?
Step 1: Write the mathematical expression
Write the mathematical expression using the numbers from the problem:
Cooking & Recipes
When scaling recipes or combining ingredients, the order of operations ensures you get the right amounts.
Example:
A recipe needs cups total (2 cups flour + 1 cup sugar, tripled)
You are making cookies. The recipe calls for 2 cups of flour plus 1 cup of sugar, and you want to make 4 batches.
How many total cups of dry ingredients do you need?
Step 1: Write the mathematical expression
Write the expression using parentheses to group what goes in one batch:
Video Game Scoring
Video games use mathematical formulas to calculate damage, scores, and rewards. Understanding order of operations helps you predict outcomes.
Example:
Damage = base × multiplier + bonus: damage
In a game, your base attack is 15, you have a 3× critical hit multiplier, and a +10 bonus from your weapon.
How much total damage do you deal?
Step 1: Write the mathematical expression
Write the damage formula (base × multiplier + bonus):
Key Takeaways
- 1PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
- 2Always solve inside Parentheses first, starting with the innermost
- 3Exponents (powers) come after parentheses
- 4Multiplication and Division have equal priority - work left to right
- 5Addition and Subtraction have equal priority - work left to right
- 6When in doubt, use parentheses to make your intention clear
- 7BODMAS and PEMDAS are the same thing - different regions use different names
Frequently Asked Questions
What does PEMDAS stand for?
Why does multiplication come before addition?
What is the difference between PEMDAS and BODMAS?
Do I always multiply before dividing?
What if there are no parentheses?
How do I handle nested parentheses?
Glossary
- Order of Operations
- A set of rules that determines which calculations are performed first in an expression
- PEMDAS
- An acronym to remember the order: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
- BODMAS
- British version of PEMDAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction
- Expression
- A mathematical phrase containing numbers and operations, like 3 + 4 × 2
- Parentheses
- Symbols ( ) used to group parts of an expression that should be calculated first
- Exponent
- A number that shows how many times to multiply a base by itself, written as a superscript
Formula Card
PEMDAS Order
The order to follow: Parentheses, Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right)