Teacher Guide: Dividing Fractions

@ Learning Objective 5-10 min lesson

Students will: Divide a unit fraction by a whole number and divide a whole number by a unit fraction using visual models, number lines, and the relationship between multiplication and division.

Why this matters for FAST: Dividing fractions is a critical Grade 5 skill. Students must understand both types of division (unit fraction / whole number AND whole number / unit fraction) and recognize when each applies in word problems.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Fraction strips or tiles
Paper strips for folding
Number line printout
Colored pencils

! Common Misconceptions to Address

Misconception #1: Division Always Makes Smaller

Students think 4 / 1/2 should be less than 4 because "division makes things smaller."

How to Address:

"When you divide by a fraction less than 1, you're asking 'How many halves fit in 4?' Think about cutting each whole into halves - you get MORE pieces, not fewer! 4 / 1/2 = 8."

Misconception #2: Confusing the Two Types of Division

Students mix up 1/3 / 4 and 4 / 1/3, not understanding they represent different situations.

How to Address:

"1/3 / 4 means: I have 1/3 of something and I'm splitting it among 4 people. Each person gets a SMALLER piece (1/12). But 4 / 1/3 means: I have 4 wholes and I'm cutting each into thirds. How many thirds total? (12)"

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Review: "What does 12 / 4 mean?" (How many groups of 4 in 12, OR 12 split into 4 equal groups). Establish that division can mean either "how many groups" or "splitting equally."

2

Type 1: Unit Fraction / Whole Number (3 min)

SAY THIS:

"If I have 1/2 of a pizza and I need to share it equally among 4 friends, how much does each friend get? I'm taking something SMALL and making it even SMALLER."

12 / 4 = ?

Draw a bar, shade 1/2. Then divide that shaded part into 4 equal pieces.

Each piece is 1/8 of the whole bar.

12 / 4 = 18

Rule: 1a / b = 1a x b

3

Type 2: Whole Number / Unit Fraction (3 min)

SAY THIS:

"Now flip it! If I have 4 whole pizzas and each serving is 1/2 pizza, how many servings can I make? I'm asking how many halves fit in 4 wholes."

4 / 12 = ?

Draw 4 rectangles. Divide each into halves.

Count: 2 + 2 + 2 + 2 = 8 halves total

4 / 12 = 8

Rule: a / 1b = a x b

4

Connect to Number Lines (2 min)

Show 3 / 1/4 on a number line: Start at 0, make jumps of 1/4. How many jumps to reach 3? (12 jumps) So 3 / 1/4 = 12.

5

Guided Practice (2 min)

Work through together:

1/4 / 3 = ? (1/12 - splitting a fourth among 3)
5 / 1/3 = ? (15 - how many thirds in 5 wholes)
Word problem: "A recipe needs 1/4 cup of sugar. You have 2 cups. How many batches can you make?" (8)

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"Which expression has the greatest value?"

A) 1/2 / 5 B) 5 / 1/2 C) 1/5 / 2 D) 2 / 1/5

Correct answer: B) 5 / 1/2 = 10 (A=1/10, C=1/10, D=10, but B and D tie - discuss that 5/1/2 and 2/1/5 are equal!)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Divide unit fractions by whole numbers Divide whole numbers by unit fractions Divide fractions: word problems Divide fractions with models

^ Differentiation & Extension

For struggling students: Use paper folding. Fold a strip in half (1/2), then fold that into 4 parts. What fraction of the whole is one part? (1/8). This makes 1/2 / 4 = 1/8 concrete.

For advanced students: Challenge: "Is a / 1/b always equal to b / 1/a? Give examples to prove or disprove." (No - 4 / 1/2 = 8, but 2 / 1/4 = 8. Sometimes equal, sometimes not!)

For home: Send Parent Activity sheet. Families can explore with ribbon cutting and pizza sharing scenarios.