Estimated Time: 10–15 minutes
Goal: Learn how to translate real-world situations into mathematical expressions and solve them using the correct order of operations
Flipping Flashcards First
Flip through flashcards first before reading and after you complete this guide.
📖 Step 1 — READ (3–5 minutes)
Translating Words Into Operations
Before you can use PEMDAS, you first have to translate the story into math.
Look for these common keyword clues:
Operation | Common Clues |
➕ Addition | deposit, gain, total, combined, increase |
➖ Subtraction | withdrawal, fee, loss, decrease, below zero, difference |
✖️ Multiplication | each, per, times, double, of |
➗ Division | split, shared equally, divided into, unit cost |
Parentheses Change the Story
Sometimes the story requires you to combine numbers first before multiplying or dividing.
That's when parentheses are needed.
Example 1 — Flat Rate
A landscaping company charges a $15 equipment fee plus $10 per hour for work. They work for 3 hours.
Expression:
15+10×3
Solve:
- 10×3=30
- 15 + 30=45
Total Cost: $45
Example 2 — Group Purchase
Three friends each buy a $15 concert ticket and a $10 T-shirt.
Expression:
3(15+10)
Solve:
Total Cost: $75
Notice: The ticket and shirt belong together for each person, so they must be added before multiplying.
Tracking Negative Situations (The Bank Account Trap)
Negative numbers usually represent debt, loss, or values below zero.
Example
Your bank balance is
−$12
Then a $5 subscription fee is charged.
Expression:
−12−5
Solve:
=−17
You moved farther into debt.
⭐ Remember
As you read the problem:
- Read one sentence at a time.
- Pull out the numbers.
- Decide which operation each sentence represents.
- Build the expression.
- Only then solve using PEMDAS.
🎥 Step 2 — WATCH (5–10 minutes)
Watch:
- Math with Mr. J — Writing Expressions from Word Problems
- Math with Mr. J — Solving Percent Word Problems
✍️ Step 3 — TRY IT YOURSELF
Write the mathematical expression first, then solve it.
1. The Temperature Drop
The temperature at midnight in Arlington was −4°F.
Over the next 6 hours, the temperature dropped 3°F each hour.
What was the final temperature?
Expression
Answer
2. The Shared Discount
Four friends go to a movie in Reston.
Each ticket costs $12, but a group coupon takes $3 off each ticket.
What was the total cost?
Expression
Answer
3. The Construction Split
A construction worker has a board 50 inches long.
He cuts off 14 inches, then divides the remaining board into 4 equal pieces.
How long is each piece?
Expression
Answer
🧠 Word Problem Strategy
Whenever you solve a word problem, follow this checklist:
✅ 1. Bracket the Question
Figure out exactly what the problem wants you to find.
✅ 2. Circle the Action Words
Look for clues like:
- each
- per
- split
- dropped
- increased
- fee
- total
- shared
These tell you which operation to use.
✅ 3. Ask Yourself:
"Do any numbers need to be combined before multiplying or dividing?"
If yes, use parentheses.
✅ 4. Compute Layer by Layer
After you've built the expression, solve it using PEMDAS.
🎒 Come Prepared
Bring your scratch paper to our next session.
Be ready to explain:
- Why some problems required parentheses.
- Where the negative-number traps appeared.
- How you decided which operation each sentence represented.