5.OA.2 • Expressions Numerical Expressions
1 / 27

Numerical Expressions

How do we translate between words and math expressions?

📚
Standard
OA.2
📅
Grade
5th
⏱️
Duration
60m

📋 Standards & Objectives

📐Standard
5.OA.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
🎯SWBAT
  • Translate word phrases into numerical expressions
  • Translate numerical expressions into word phrases
  • Identify key vocabulary: sum, difference, product, quotient
  • Use parentheses to show grouping in expressions

💭 Math Has Its Own Language!

Just like we translate between English and other languages, we can translate between words and math expressions!

🛒Shopping

"I bought 3 packs of pencils with 12 in each pack, then gave away 5."
In math: (3 × 12) − 5

🍕Pizza Party

"We ordered 4 pizzas with 8 slices each, shared equally among 16 people."
In math: (4 × 8) ÷ 16

💰Saving Money

"I had $50 and earned $15 more, then spent $20."
In math: (50 + 15) − 20

📖 Key Vocabulary

These words tell us which operation to use!

➕
Sum
The answer to an addition problem.
"The sum of 4 and 6" → 4 + 6
➖
Difference
The answer to a subtraction problem.
"The difference of 10 and 3" → 10 − 3
✖️
Product
The answer to a multiplication problem.
"The product of 5 and 7" → 5 × 7
➗
Quotient
The answer to a division problem.
"The quotient of 20 and 4" → 20 ÷ 4

✨ Words → Expressions

Key words in a phrase tell us which operation and which numbers to use. Parentheses show what to do first!

The sum of 4 and 6 multiplied by 5
→
(4 + 6) × 5
8 less than the quotient of 60 and 3
→
(60 ÷ 3) − 8
The product of 12 and 3 divided by the difference of 11 and 2
→
(12 × 3) ÷ (11 − 2)

📌 How to Translate

3 Steps to Write an Expression
🔍
Step 1
Find the key words
sum, difference, product, quotient, more than, less than, times, divided by
🔢
Step 2
Write the operation
Match each key word to +, −, ×, or ÷ and identify the numbers
( )
Step 3
Add parentheses
Group the part that should be done first with parentheses
⚠️Watch Out!

"Less than" and "subtracted from" flip the order! "8 less than 20" means 20 − 8, NOT 8 − 20.

✏️ Problem 1

👨‍🏫 I Do • Words → Expression
The sum of 4 and 6 multiplied by 5
Write a numerical expression
💡 Step-by-Step Translation
1 Find the key words: "sum" means addition (+). "multiplied by" means multiplication (×).
2 The sum of 4 and 6 is done first → put it in parentheses: (4 + 6). Then multiply by 5.
✓ Expression
(4 + 6) × 5

✏️ Problem 2

👨‍🏫 I Do • Words → Expression
8 less than the quotient of 60 and 3
Write a numerical expression
💡 Step-by-Step Translation
1 Find the key words: "quotient" means division (÷). "less than" means subtraction (−) and flips the order!
2 "8 less than" means we subtract 8 FROM the quotient. The quotient of 60 and 3 → (60 ÷ 3). Then subtract 8.
✓ Expression
(60 ÷ 3) − 8

✏️ Problem 3

👥 We Do • Words → Expression
10 more than the product of 9 and 4
Write a numerical expression
💡 Step-by-Step Translation
1 Find the key words: "product" means multiplication (×). "more than" means addition (+).
2 The product of 9 and 4 → (9 × 4). Then add 10 more: (9 × 4) + 10.
✓ Expression
(9 × 4) + 10

✏️ Problem 4

👥 We Do • Words → Expression
The sum of 15 and 12 divided by 9
Write a numerical expression
💡 Step-by-Step Translation
1 Find the key words: "sum" means addition (+). "divided by" means division (÷).
2 The sum of 15 and 12 is computed first → (15 + 12). Then divide the whole thing by 9.
✓ Expression
(15 + 12) ÷ 9

✏️ Problem 5

💪 You Do • Words → Expression
The product of 7 and 3 added to 15
Write a numerical expression
💡 Step-by-Step Translation
1 "Product" → multiplication. "Added to" → addition. The product of 7 and 3 comes first.
2 Product of 7 and 3 → (7 × 3). Then add it to 15 → (7 × 3) + 15.
✓ Expression
(7 × 3) + 15

✏️ Problem 6

💪 You Do • Words → Expression
Subtract 20 from the quotient of 72 and 8
Write a numerical expression
💡 Step-by-Step Translation
1 "Quotient" → division. "Subtract...from" → subtraction. "Subtract 20 FROM" means the quotient comes first.
2 Quotient of 72 and 8 → (72 ÷ 8). Subtract 20 from it → (72 ÷ 8) − 20.
✓ Expression
(72 ÷ 8) − 20

💬 Turn & Talk

🤔Discussion

1. What is the difference between these two expressions?

(8 + 2) × 5
8 + (2 × 5)

2. Why do parentheses matter? What happens if we move them?

3. Can you think of a real-world situation that matches each expression?

✨ Expressions → Words

Now we go the other direction! Read a numerical expression and write it as words.

(5 + 9) × 4
→
The sum of 5 and 9 multiplied by 4
(30 ÷ 3) − 8
→
The quotient of 30 and 3 subtracted by 8

There are often multiple correct ways to write it in words!

📌 How to Read Expressions

3 Steps to Write in Words
👀
Step 1
Read the operations
+ → sum/add, − → difference/subtract, × → product/multiply, ÷ → quotient/divide
( )
Step 2
Start inside parentheses
Describe the grouped part first, then describe what happens to it
✍️
Step 3
Write it out
Use vocabulary words to describe each operation in order

✏️ Problem 7

👨‍🏫 I Do • Expression → Words
(50 − 10) + 6
Write as a word phrase
💡 Step-by-Step Reading
1 Inside the parentheses: 50 − 10. The minus sign means difference. → "The difference of 50 and 10"
2 Outside: + 6. The plus sign means added to. → "added to 6" or "plus 6"
✓ Word Phrase
The difference of 50 and 10, added to 6

✏️ Problem 8

👨‍🏫 I Do • Expression → Words
9 × (23 − 12)
Write as a word phrase
💡 Step-by-Step Reading
1 Inside the parentheses: 23 − 12. → "the difference of 23 and 12"
2 Outside: 9 ×. The multiplication sign means times. → "9 times the difference of 23 and 12"
✓ Word Phrase
9 times the difference of 23 and 12

✏️ Problem 9

👥 We Do • Expression → Words
(15 + 13) ÷ 4
Write as a word phrase
💡 Step-by-Step Reading
1 Inside the parentheses: 15 + 13. → "the sum of 15 and 13"
2 Outside: ÷ 4. → "divided by 4". Full phrase: "The sum of 15 and 13 divided by 4"
✓ Word Phrase
The sum of 15 and 13 divided by 4

✏️ Problem 10

👥 We Do • Expression → Words
(8 + 4) × 7
Write as a word phrase
💡 Step-by-Step Reading
1 Inside the parentheses: 8 + 4. → "the sum of 8 and 4"
2 Outside: × 7. → "multiplied by 7". Full phrase: "The sum of 8 and 4 multiplied by 7"
✓ Word Phrase
The sum of 8 and 4 multiplied by 7

✏️ Problem 11

💪 You Do • Expression → Words
(36 − 9) × 5
Write as a word phrase
💡 Step-by-Step Reading
1 Inside: 36 − 9 → "the difference of 36 and 9"
2 Outside: × 5 → "multiplied by 5"
✓ Word Phrase
The difference of 36 and 9 multiplied by 5

✏️ Problem 12

💪 You Do • Expression → Words
48 ÷ (12 + 4)
Write as a word phrase
💡 Step-by-Step Reading
1 Inside: 12 + 4 → "the sum of 12 and 4"
2 Outside: 48 ÷ → "48 divided by". Full: "48 divided by the sum of 12 and 4"
✓ Word Phrase
48 divided by the sum of 12 and 4

🏆 Matching Challenge

🏆 Challenge • Match Them Up!

Which expression matches each word phrase? Think carefully about the parentheses!

1️⃣Word Phrase

6 less than the product of 12 and 4

A.  6 − (12 × 4) B.  (12 − 6) × 4 C.  (12 × 4) − 6

C. (12 × 4) − 6
"Less than" flips the order!

2️⃣Word Phrase

The sum of 18 and 6 divided by 3

A.  (18 + 6) ÷ 3 B.  18 + 6 ÷ 3 C.  (18 × 6) ÷ 3

A. (18 + 6) ÷ 3
"The sum of" needs parentheses first!

3️⃣Word Phrase

The difference between 10 and 2 multiplied by the sum of 8 and 4

A.  (10 − 2) × (8 ÷ 4) B.  (10 − 2) × (8 × 4) C.  (10 − 2) × (8 + 4)

C. (10 − 2) × (8 + 4)
Two groups: difference AND sum!

4️⃣Expression

9 added to the quotient of 24 and 6

A.  9 + (24 × 6) B.  9 + (24 ÷ 6) C.  (9 + 24) ÷ 6

B. 9 + (24 ÷ 6)
"Quotient" means division, then add 9!

🏆 Word Problem Challenge

🏆 Challenge • Real-World Problem
The Williams family bought 3 tubes of toothpaste. Each tube contained 9 ounces. If the family has used a total of 12 ounces, how many ounces of toothpaste does the Williams family have left?
Write a numerical expression (don't solve!)
💡 Step-by-Step Translation
1 3 tubes × 9 ounces each = total toothpaste bought → 3 × 9
2 Used 12 ounces, need to subtract from total → (3 × 9) − 12
✓ Expression
(3 × 9) − 12

💬 Turn & Talk

🤔Discussion

1. Can you write two different word phrases for this expression?

(40 ÷ 8) + 16

2. Why is it important to know how to translate between words and expressions?

3. Create your own word problem that matches this expression: (25 − 10) × 3

📝 Key Takeaways

📖 Know Your Vocabulary
Sum → addition, Difference → subtraction, Product → multiplication, Quotient → division. These words are your translation guide!
( ) Parentheses Show Order
Use parentheses to group the part of the expression that should be done first. They change the meaning of the expression!
⚠️ Watch for Tricky Words
"Less than" and "subtracted from" flip the order. "8 less than 20" = 20 − 8, not 8 − 20!
↔️ Two-Way Translation
You can go words → expression AND expression → words. Both skills help you understand math problems better!

🎫 Exit Ticket

Show what you learned! Write your answers on your whiteboard.

1️⃣Words → Expression

The product of 6 and 8 subtracted from 50

"Subtracted from" flips the order!
50 − (6 × 8)

2️⃣Expression → Words

(42 ÷ 7) + 15

The quotient of 42 and 7 added to 15
or "15 more than the quotient of 42 and 7"

3️⃣Word Problem

Mia has 4 bags with 8 marbles in each. She gives away 10 marbles. Write an expression for marbles she has left.

4 bags × 8 each, then subtract 10
(4 × 8) − 10

Great Work! 🎉

You can now translate between words and math expressions!

⭐
Remember
Words ↔ Expressions
Vocabulary is the key!