To find a fraction of a whole number:
1️⃣ Draw a bar = the whole number.
2️⃣ Split it into equal parts (use the denominator).
3️⃣ Divide to find ONE part.
4️⃣ Multiply by the numerator to take the parts you need.
Shortcut (algorithm): ab of n = (a × n) ÷ b
⚠️ Self-check: Your answer should ALWAYS be smaller than the whole.
Fraction of a Whole Number
Solving Word Problems with Bar Models
📚
Subject
Math · Grade 5
⏱️
Duration
45–50 min
🎯
Standard
5.NF.B.4a
📋 Standards & Objectives
📜Standards
5.NF.B.4aInterpret the product ab × q as a parts of a partition of q into b equal parts.
5.NF.B.6Solve real-world problems involving multiplication of fractions and mixed numbers.
5.NF.A.1Add and subtract fractions with unlike denominators (spiral review).
🎯SWBAT
- Find a fraction of a whole number using a bar model.
- Solve real-world word problems using the "fraction of" method.
- Identify and fix common fraction-of-whole errors.
- Underline what a word problem is asking before solving.
📖 Key Vocabulary
Click a card to see examples
📝Fraction Of
A phrase that means "take part of a whole group." "Fraction of" is the same as multiplication.
½ of 10 = 5 (half of 10 is 5)
¼ of 20 = 5 (one-fourth of 20 is 5)
"3/5 of the class" means 3 parts out of 5 equal groups of students.
📝Bar Model
A drawing (also called a tape diagram) that shows a whole amount split into equal parts.
A bar model for 28 split into 4 equal parts shows four boxes, each worth 7.
┌────┬────┬────┬────┬────┐
│ 5 │ 5 │ 5 │ 5 │ 5 │
└────┴────┴────┴────┴────┘
👆 A bar model showing 25 split into 5 equal parts.
│ 5 │ 5 │ 5 │ 5 │ 5 │
└────┴────┴────┴────┴────┘
👆 A bar model showing 25 split into 5 equal parts.
📝Numerator
The top number in a fraction. It tells you how many parts you take.
In 35, the numerator is 3 — you take 3 parts.
In 47, the numerator tells you to grab 4 of the 7 equal pieces.
📝Denominator
The bottom number in a fraction. It tells you how many equal parts to split the whole into.
In 35, the denominator is 5 — split the whole into 5 equal parts.
In 47, the denominator tells you to divide the whole into 7 equal groups.
📝Distractor
Extra info in a word problem that is not needed to solve it. SBA tests love these!
"There are 35 fish. 10 are red, 8 are blue, and 3/7 are goldfish. How many goldfish?" → The "10 red" and "8 blue" are distractors.
On SBA, watch out for distractors — they're put there to trick you into using the wrong numbers.
🔄 Spiral Warm-Up
Fraction subtraction with unlike denominators
Before we start today's lesson...
Let's warm up with 2 fraction subtraction problems.
Remember: when the denominators are different, we need to find a common denominator first.
📓 Try each one in your notebook before clicking the answer!
🔄 Warm-Up #1
5.NF.A.1 · Fraction subtraction
Solve:
78 − 13 = ?
Step 1: Common denominator of 8 and 3 → 24
Step 2: 78 = 2124 · 13 = 824
Step 3: 2124 − 824 = 1324
🔄 Warm-Up #2
5.NF.A.1 · Fraction subtraction
Solve:
45 − 210 = ?
Step 1: Common denominator → 10 (10 is already a multiple of 5!)
Step 2: 45 = 810
Step 3: 810 − 210 = 610 = 35
(Always simplify when you can!)
🍕 Hook: Pizza Party!
Your class just earned it — but how much do you actually get?
The Situation 🎉
Your class earned a pizza party! There are 4 pizzas, and your table gets 38 of the total.
🤔 How much pizza does your table get?
🍕
🍕
🍕
🍕
That's 4 pizzas total. Your table takes 3/8 of them. 🍕🍕🍕🍕 → ?
❓ Today's Big Question
How do we find a FRACTION OF a whole number?
(Because "3/8 of 4 pizzas" is a totally real-world thing!)
👉 By the end of today, you'll know two ways to solve these problems: a bar model and an algorithm.
⭐ SBA Tip #2
Underline what the question is asking for
⭐ SBA Test-Taking Tip #2
Word problems on SBA often give EXTRA information. The real question is usually at the very end. Underline it before you start solving so you answer the right question.
📝Example — Spot the Real Question
There are 35 fish in the tank. 10 are red, 8 are blue, and 3/7 are goldfish. HOW MANY GOLDFISH ARE IN THE TANK?
💡 The "10 red" and "8 blue" are distractors — you don't need them! The underlined question only asks about goldfish. Use 35 and 3/7 only.
👉 Every word problem today: UNDERLINE THE QUESTION FIRST.
👨🏫 What Does "Fraction Of" Mean?
I Do · Direct Instruction
When you see the phrase "_____ of a number", you are taking part of the whole.
Key Idea 🔑
"Fraction of" = multiply. The word "of" is a secret math clue — it means "times."
½ of 10
= 5
¼ of 20
= 5
⅓ of 12
= 4
You already know some of these! Today we'll learn a method for the trickier ones.
📊 The 4-Step Bar Model Strategy
Our go-to tool for "fraction of" problems
1Draw the Whole
Draw one bar that represents the total amount. Label it with the whole number.
2Split Into Equal Parts
The denominator tells you how many equal parts to split the bar into.
3Find One Part
Divide the total by the denominator to find the value of ONE part.
4Take the Parts You Need
The numerator tells you how many of those parts to take. Multiply!
📓 Write these 4 steps in your notebook!
🤖 Model Problem: Laura's Robots
I Do · Using the bar model
47 of Laura's 28 robots make noise. How many make noise?
Whole: 28 robots
4
4
4
4
4
4
4
7 equal parts (denominator) · Take 4 parts (numerator)
Step 1: Bar = 28 robots.
Step 2: Split into 7 equal parts (denominator).
Step 3: 28 ÷ 7 = 4 robots per part.
Step 4: Take 4 parts → 4 × 4 = 16 robots make noise ✓
🧮 Laura's Robots — The Algorithm
The same answer, using multiplication
We can also write this as multiplication. Remember: "of" = ×.
47 of 28 = 47 × 28
Multiply the numerator by the whole, then divide by the denominator:
(4 × 28) ÷ 7 = 112 ÷ 7 = 16
✅ Same answer as the bar model: 16 robots
🔍 Bar Model vs. Algorithm
Two tools, same answer
📊 Bar Model Way
1️⃣ Draw bar = 28
2️⃣ Split into 7 equal parts
3️⃣ 28 ÷ 7 = 4 per part
4️⃣ Take 4 parts → 4 × 4 = 16
🧮 Algorithm Way
47 × 28
= (4 × 28) ÷ 7
= 112 ÷ 7
= 16
✅ Both ways give 16 robots. Use whichever one helps YOU understand the problem best!
👨🏫 Model Problem 2: 3/5 of 25 Students
I Do · Second worked example
35 of the 25 students are boys. How many boys are there?
Whole: 25 students
5
5
5
5
5
Split 25 into 5 equal parts · Take 3 parts
1. Bar = 25 · 2. Split into 5 parts · 3. 25 ÷ 5 = 5 per part · 4. Take 3 → 3 × 5 = 15 boys
Algorithm: 35 × 25 = (3 × 25) ÷ 5 = 75 ÷ 5 = 15 ✓
⚠️ Marcus vs. Tina
Who's right? (And what did the other kid mess up?)
Problem: What is 25 of 30 students?
😬 Marcus says: 75
Marcus multiplied 2 × 30 = 60, then added 15? Or wrote 2 × 30 ÷ ? = 75. He forgot to DIVIDE by the denominator (5).
⚠️ Problem: 75 is BIGGER than the whole (30). That's impossible when finding a fraction-of-whole!
😎 Tina says: 12
Tina used the bar model: 30 ÷ 5 = 6 per part. Then 2 parts → 2 × 6 = 12 ✓
Algorithm: 25 × 30 = (2 × 30) ÷ 5 = 60 ÷ 5 = 12 ✓
🚨 The Big Rule: If your answer is BIGGER than the whole when finding a fraction-of-whole... you messed up. Stop and check!
📓 Write This Down!
The Fraction-of-a-Whole Method
Key Terms
Fraction of = ×
Bar Model
Denominator → ÷
Numerator → ×
Notes — The 4-Step Method
👥 We Do #1: Cupcakes
Let's solve this together
23 of the 24 cupcakes have sprinkles. How many have sprinkles?
Whole: 24 cupcakes · Split into 3 equal parts · Take 2 parts
8
8
8
24 ÷ 3 = 8 per part → 2 × 8 = 16 cupcakes 🧁
Check: 16 < 24 ✓
👥 We Do #2: Bus Riders
Bigger numbers, same method
A school has 150 students. 310 of them ride the bus. How many ride the bus?
Think it through together:
• Whole = 150 · Denominator = 10 → split into 10 equal parts
• One part = 150 ÷ 10 = 15
• Take 3 parts → 3 × 15 = ?
3 × 15 = 45 students ride the bus 🚌
Algorithm: (3 × 150) ÷ 10 = 450 ÷ 10 = 45 ✓
👥 We Do #3: Crayons
👀 Careful — read it slowly!
There are 36 crayons in the box. 56 of them are NOT broken. How many are not broken?
⚠️ The question says "NOT broken" — that means you're finding the 5/6 that are good, not the broken ones!
36 crayons ÷ 6 parts = 6 per part
6
6
6
6
6
6
Take 5 parts → 5 × 6 = 30 crayons not broken 🖍️
🤝 Turn & Talk
30 seconds with your partner
🤔Discuss with Your Partner
Marcus says 25 of 30 is 75. Is he right? How do you know — without doing the whole problem?
Sentence starter: "Marcus is not right because my answer should always be ___ than ___."
Marcus is wrong because 75 is bigger than 30. When you find a fraction of a whole, the answer is always smaller than the whole. The correct answer is 12 (because 30 ÷ 5 = 6, and 2 × 6 = 12).
🔍 You Try — Directions
4 problems · Try on your own first!
Your Turn 💪
- Read each problem carefully.
- Underline what the question is asking.
- Draw a bar model in your notebook.
- Solve it. Check: is your answer smaller than the whole?
- When we reveal the answer, see if you got it!
🔍 You Try #1: Blue Marbles
78 of the 32 marbles are blue. How many are blue?
4
4
4
4
4
4
4
4
Whole: 32 · split into 8 equal parts · take 7
32 ÷ 8 = 4 per part → 7 × 4 = 28 blue marbles 🔵
🔍 You Try #2: Brown Cows
A farmer has 45 cows. 29 of them are brown. How many are brown?
Split 45 into 9 parts · take 2
5
5
5
5
5
5
5
5
5
45 ÷ 9 = 5 per part → 2 × 5 = 10 brown cows 🐄
🔍 You Try #3: Mystery Books (2 steps!)
The library has 120 books. 34 are fiction, and 13 of the fiction books are mysteries. How many mystery books are there?
⚠️ This one has TWO steps. Find fiction first, THEN find mysteries from that.
Step 1: Find fiction books
34 of 120 → 120 ÷ 4 = 30 per part → 3 × 30 = 90 fiction books
Step 2: Find mysteries (1/3 of the fiction books)
13 of 90 → 90 ÷ 3 = 30 mystery books 📚
🔍 You Try #4: Tina's Test
There are 40 questions on a test. Tina answered 45 of them correctly. How many did she get right? How many did she get wrong?
⚠️ Two questions! Answer BOTH.
45 of 40 → 40 ÷ 5 = 8 per part → 4 × 8 = 32 right ✅
Wrong = 40 − 32 = 8 wrong ❌
(Or: the other 1/5 is wrong → 1 × 8 = 8.)
🎯 SBA Spotlight · Multiple Choice
Watch Out for Distractors!
A school has 150 students. 310 of them ride the bus. How many ride the bus?
A) 15
B) 45
C) 50
D) 450
A) 15 ❌ Divided 150÷10 but forgot to × 3. Only did part of the work.
B) 45 ✅ 150÷10=15, then 15×3=45. CORRECT!
C) 50 ❌ Used 1/3 instead of 3/10. Read the fraction wrong.
D) 450 ❌ Multiplied 3×150 without dividing by 10. Huge distractor!
💡 The test WANTS you to pick A, C, or D if you're not careful. Always divide by the denominator first!
🎯 SBA Spotlight · Constructed Response
Show Your Work AND Explain
A library has 120 books. 34 are fiction, and 13 of the fiction books are mysteries. How many mystery books are there?
Show your work with a model AND explain how you got your answer.
✅ ANSWER
30 mystery books
📐 MATH
Step 1: 34 of 120
120÷4=30, 30×3=90 fiction
Step 2: 13 of 90
90÷3=30 mysteries
💬 EXPLANATION
"First I took 34 of 120 to find the number of fiction books, which was 90. Then I took 13 of 90 to find the mysteries. The answer is 30 mystery books."
⚠️ Two-step problem! You must find 3/4 of 120 FIRST, then take 1/3 of that result.
📝 Wrap-Up
What We Learned Today
🧠 Big Ideas
- "Fraction OF a number" means multiply.
- 4-Step Bar Model: Draw the bar → divide by denominator → multiply by numerator → label your answer.
- Algorithm shortcut: Divide the whole by the denominator, then multiply by the numerator.
- SBA Tip: Underline what the question is asking. Watch for distractors!
- Two-step problems: Finish step 1 before starting step 2.
🎟️ Exit Ticket
Show What You Know
1. Fish Tank
There are 35 fish in the tank. 37 of them are goldfish. How many goldfish are in the tank?
2. Bakery
A bakery made 48 cookies. 58 of them are chocolate chip. How many are chocolate chip?
3. Who's Right? (SBA Format)
Jamal and Priya both solve What is 34 of 24? Jamal says 18. Priya says 32. Who is correct, and what mistake did the other student make?
4. Spiral Review
Solve: 56 − 14 = ?
(Find a common denominator first!)