Dividing Fractions

Teacher Guide | Grade 6 Mathematics | FAST Success Kit
Florida B.E.S.T. Standards: MA.6.NSO.2.1, MA.6.NSO.2.2
@ Learning Objective 5-10 min lesson
Students will: Divide fractions by fractions (including mixed numbers) using the "Keep, Change, Flip" method with procedural fluency, and apply this skill to solve real-world problems.

Why this matters for FAST: Dividing fractions is a critical Grade 6 skill tested extensively on FAST. Students must understand that dividing by a fraction is the same as multiplying by its reciprocal, and be able to apply this to word problems.

% Materials Needed
! Common Misconceptions to Address

Misconception #1: Flipping the Wrong Fraction

Students flip the first fraction instead of the second: 2/3 / 4/5 becomes 3/2 x 4/5 (WRONG!)

How to Address:

"KEEP the first fraction exactly the same. Only FLIP the second fraction (the divisor). The first fraction stays put - it's the one being divided!"

Misconception #2: Forgetting to Change Division to Multiplication

Students flip the second fraction but keep the division sign, getting the wrong answer.

How to Address:

"All three steps happen together: KEEP the first, CHANGE division to multiplication, FLIP the second. Remember: when you flip a fraction, you're finding its reciprocal, and dividing is the same as multiplying by the reciprocal!"

Misconception #3: Not Converting Mixed Numbers First

Students try to use KCF on mixed numbers without converting to improper fractions first.

How to Address:

"Before using Keep-Change-Flip, always convert any mixed numbers to improper fractions first. 2 1/2 becomes 5/2, then you can divide!"

The Keep-Change-Flip Method

K
KEEP the first fraction
C
CHANGE / to x
F
FLIP the second fraction
$ Lesson Steps
1

Activate Prior Knowledge (1 min)

Review: "What is 2/3 x 4/5?" (8/15) "Great! Today we're going to learn how dividing fractions is really just multiplying in disguise!"

2

Introduce the Concept of Reciprocals (1 min)

SAY THIS:

"A reciprocal is what you get when you flip a fraction upside down. The reciprocal of 2/3 is 3/2. The reciprocal of 5 (or 5/1) is 1/5. When you multiply a number by its reciprocal, you always get 1!"

3

Teach Keep-Change-Flip (3 min)

Example: 2/3 / 4/5 = ?

23 / 45

KEEP: 2/3 stays the same

CHANGE: / becomes x

FLIP: 4/5 becomes 5/4

23 x 54 = 1012 = 56

4

Practice with Mixed Numbers (2 min)

Example: 1 1/2 / 3/4 = ?

Step 1: Convert 1 1/2 to improper: 3/2

32 / 34

Step 2: Keep-Change-Flip:

32 x 43 = 126 = 2

5

Apply to Word Problems (2 min)

EXAMPLE PROBLEM:

"You have 3/4 of a pizza and want to divide it into servings of 1/8 pizza each. How many servings can you make?"

Set up: 3/4 / 1/8 = 3/4 x 8/1 = 24/4 = 6 servings

Key insight: Division answers "how many groups of [divisor] fit into [dividend]?"

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"What is 3/5 / 2/3?"

A) 6/15   B) 2/5   C) 9/10   D) 10/9

Correct answer: C) 9/10

Work: 3/5 / 2/3 = 3/5 x 3/2 = 9/10

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Divide fractions Divide fractions and mixed numbers Divide fractions: word problems Reciprocals Multiply and divide fractions: word problems
^ Differentiation & Extension

For struggling students: Use visual models showing how many times a smaller fraction fits into a larger one. Start with unit fractions (1/2 / 1/4 = 2, because two 1/4s fit in 1/2).

For advanced students: Challenge with multi-step problems or problems involving three fractions. Introduce division of decimals by fractions.

For home: Send Parent Activity sheet. Families can practice with cooking (dividing 3/4 cup into 1/8 cup servings).

FAST Success Kit | Grade 6 | Dividing Fractions Standards: MA.6.NSO.2.1, MA.6.NSO.2.2