Add a student-friendly definition in the Binder Page editor.
Order of Operations (PEMDAS)
Students learn to evaluate numerical expressions accurately by following the order of operations. This lesson explains grouping symbols, exponents, multiplication, division, addition, and subtraction while emphasizing left-to-right reasoning and clear written work.
Find It. Learn It. Master It.
Intermediate
15–20 minutes
The Number System
The Number System
Page 4 of 5
Inside Cover
Order of Operations (PEMDAS)
At a Glance
Binder SectionThe Number System
DifficultyIntermediate
Estimated Time15–20 minutes
PrerequisitesWhole-number operations and exponents
Why does the order in which we perform operations matter?
Build Understanding
The order of operations is a set of rules that tells us which parts of a numerical expression to calculate first. Following the same rules ensures that everyone evaluates an expression in the same way.nnThe acronym PEMDAS can help you remember the order:nnP: Parentheses and other grouping symbolsnE: ExponentsnM and D: Multiplication and division from left to rightnA and S: Addition and subtraction from left to rightnnBegin with operations inside parentheses or other grouping symbols. For example, in 4 x (7 - 2), subtract inside the parentheses first: 7 - 2 = 5. Then multiply: 4 x 5 = 20.nnNext, evaluate exponents. An exponent tells how many times a base is used as a factor. For example, 3 squared means 3 x 3, which equals 9. In the expression 2 + 3 squared, evaluate the exponent first: 3 squared = 9. Then add: 2 + 9 = 11.nnAfter parentheses and exponents, perform multiplication and division in the order they appear from left to right. Multiplication does not always come before division. For example, evaluate 24 divided by 6 x 2 from left to right. First, 24 divided by 6 = 4. Then 4 x 2 = 8.nnFinally, perform addition and subtraction in the order they appear from left to right. Addition does not always come before subtraction. For example, evaluate 15 - 6 + 2 from left to right. First, 15 - 6 = 9. Then 9 + 2 = 11.nnFor a multi-step example, evaluate 5 + 3 x (10 - 6) squared. First, calculate inside the parentheses: 10 - 6 = 4. Next, evaluate the exponent: 4 squared = 16. Then multiply: 3 x 16 = 48. Finally, add: 5 + 48 = 53.nnIt is helpful to rewrite the expression after completing each step. This keeps the remaining numbers and operations organized and reduces errors.nnCommon misconceptions and corrections: Students may complete operations only from left to right without considering PEMDAS, assume multiplication always comes before division, or assume addition always comes before subtraction. Remember that multiplication and division have equal priority and are completed from left to right. Addition and subtraction also have equal priority and are completed from left to right.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Evaluate expressions inside parentheses or other grouping symbols first.
- Evaluate exponents after completing the operations inside grouping symbols.
- Complete multiplication and division from left to right.
- Complete addition and subtraction from left to right.
- Rewrite the expression after each step to keep your work organized.
- Estimate the answer to determine whether your result is reasonable.
Click each word
Interactive Vocabulary
Add a student-friendly definition in the Binder Page editor.
Add a student-friendly definition in the Binder Page editor.
Reveal one step at a time
Worked Examples
Example 1
Worked Example 1
1
18 ÷ 3 × 2 = 6 × 2 = 12.
Example 2
Worked Example 2
1
4 + 3² × 2 = 4 + 9 × 2 = 22.
Example 3
Worked Example 3
1
Evaluate inside grouping symbols first.
Ask and explain
Common Questions
What does PEMDAS stand for? It stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Does multiplication always come before division? No. Multiplication and division have equal priority, so complete them from left to right.
Does addition always come before subtraction? No. Addition and subtraction have equal priority, so complete them from left to right.
What should I do when an expression contains more than one set of grouping symbols? Begin with the innermost grouping symbols and work outward.
Why should I rewrite the expression after every step? Rewriting helps you focus on one operation at a time while preserving the parts that have not yet been evaluated.
Notice and correct
Common Misconceptions
Reading PEMDAS as six separate priority levels.
Review the example and compare the digit’s place with its value.
Adding before multiplying.
Review the example and compare the digit’s place with its value.
Multiplying the base and exponent.
Review the example and compare the digit’s place with its value.
Learn Through Video
Watch, pause, and explain
Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
Not Started
Build Your Skills
Practice until you can explain it
Move from a quick warm-up to guided practice, independent work, and deeper challenges.
0%
0 of 4 stages complete
Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
Evaluate 6 + 4 × 3.
2
We Do
Guided Practice
Evaluate: 6 + 4 x 3. Answer: 18.
Evaluate: (6 + 4) x 3. Answer: 30.
Evaluate: 20 divided by 5 x 2. Answer: 8.
Evaluate: 18 - 7 + 4. Answer: 15.
Evaluate: 2 + 3 squared x 4. Answer: 38.
Evaluate: 5 x (9 - 3) + 2. Answer: 32.
Evaluate: 36 divided by (4 + 2) x 3. Answer: 18.
Evaluate: 8 + 2 x (7 - 4) squared. Answer: 26.
3
You Do
Independent Practice
Evaluate 30 ÷ 5 × 4.
Evaluate 7 + 2(6 − 1).
Evaluate 20 − 8 + 3.
4
Stretch Your Thinking
Challenge & Real-World Practice
Insert grouping symbols into 8 + 4 × 3 − 2 to make two different values. Show each evaluation.
Write an expression using all four operations that has a value of 20, then prove it.
Practice Complete
Continue to My Math Journal →
Nice work!
You completed the Practice It learning path.
IXL
Evaluate Numerical Expressions
Open resourceOrder of Operations
Open resourceKhan Academy
Intro to Order of Operations
Open resourceOrder of Operations Practice
Open resourceDeltaMath
DeltaMath Student Login
Open resource
BUILD YOUR PERSONAL MATH LIBRARY
Save today’s lesson and grow your MathBinder
Collect lesson resources, revisit recent pages, build review packets, and watch your binder grow over time.
My Binder
0
Saved Items in My Binder
Start your collection
Today’s Lesson
0 resources collected
Printable Resources
Available Now
Choose a Printable ↓
Interactive Notebook Printables
Choose any notebook page below and select Print Blank Copy to complete it by hand.
- Lesson-specific pages
- Clean print layout
- Add to a physical binder
Your Collection
Recently Added
Your saved items will appear here.Build a binder you can use all year.
Binder Preview
My MathBinder
MathBinder
Find It. Learn It. Master It.
0 saved items
Number SystemRatiosAlgebraGeometry
Study Tools
Build a Review Packet
My Collected Lessons
Create a printable list of the lessons saved in this browser.
Favorite This Lesson
Save this page for quick access from your MathBinder dashboard.
Continue Learning
Move to another published lesson in this Binder Section.
Open Place Value →Milestones
Your Binder Achievements
Finish Strong
Go to My Math Journal →
Learned. Watched. Practiced. Saved.
Now capture the most important idea in My Math Journal.
Parent Tip
Spend five minutes reviewing one saved lesson together each week. Ask your child to explain one example aloud.
MY PRIVATE MATH SPACE
My Math Journal
Capture your thinking, questions, and reflections. Everything is saved automatically on this device.
Saved on this device
Ready
Confidence Check
How confident do you feel?
Awesome! You’re ready to teach someone else!
Quick Reflection
Complete the thought
My Math Notes
0 words
What do you want to remember?
Learning Record
0 entries
My Journal History
Revisit reflections saved from other MathBinder lessons on this device.
Your journal history will grow as you reflect.
Complete this lesson’s journal to begin your learning record.
Your Math Journal is automatically saved on this device.
Clearing your browser data will erase your saved journal entries.
Show What You Know
Can you do this on your own?
Complete each question without hints. Your result is saved privately on this device.
5–8
Minutes
0 of 5 answered
0%
Before you begin, I can…
- I can evaluate an expression in the correct order.
- I can explain left-to-right rules.
- I can find and correct an order-of-operations error.
1
Question 1
Evaluate 18 ÷ 3 × 2.
2
Question 2
Evaluate 4 + 3² × 2.
3
Question 3
What should be completed first in 5(8 − 3)?
4
Question 4
Does multiplication always come before division?
5
Question 5
Evaluate 24 − 6 ÷ 2.
Confidence Check
How confident do you feel?
Mastery Result
0%
Your Results
Recommended Next Step
Review and try again
Badge EarnedOrder of Operations (PEMDAS) Master
Related Binder Pages
Lesson Complete
Great job on Order of Operations (PEMDAS)!
You reviewed the lesson, practiced the skill, and completed the mastery check.