Teacher Guide: Multiplying Fractions

@ Learning Objective 5-10 min lesson

Students will: Multiply a fraction by a fraction (and by whole numbers) using the standard algorithm (multiply numerators, multiply denominators), use visual models to understand the concept, and simplify their answers.

Why this matters for FAST: Multiplying fractions is a key Grade 5 skill tested on FAST. Students must understand that multiplying by a fraction less than 1 produces a smaller product, interpret area models, and calculate with procedural fluency.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Grid paper for area models
Colored pencils
Paper for folding (optional)
Fraction tiles (optional)

! Common Misconceptions to Address

Misconception #1: Finding Common Denominators to Multiply

Students think they need common denominators for multiplication because they learned this for addition/subtraction.

How to Address:

"For multiplication, we DON'T need common denominators! Just multiply straight across: numerator times numerator, denominator times denominator. It's actually easier than adding fractions!"

Misconception #2: Thinking the Product Will Be Larger

Students expect 1/2 x 1/3 to be bigger than 1/2 because "multiplication makes things bigger."

How to Address:

"When you multiply by a fraction LESS than 1, you're taking a PART of something, so the answer is SMALLER. 1/2 x 1/3 means 'half of a third' - that's a smaller piece than what you started with!"

Misconception #3: Forgetting to Simplify

Students get 4/12 but don't simplify to 1/3.

How to Address:

"Always check: Can I simplify? Look for common factors. You can simplify BEFORE multiplying (cross-canceling) or after - either works!"

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Ask: "What is 1/2 of 6? (3) How did you figure that out? (6 x 1/2 or 6 / 2)" Connect to the idea that "of" means multiply.

2

Introduce the Algorithm (2 min)

SAY THIS:

"To multiply fractions, multiply the numerators together and multiply the denominators together. No common denominators needed!"

Example: 23 x 34 = ?

Numerators: 2 x 3 = 6

Denominators: 3 x 4 = 12

23 x 34 = 612 = 12

3

Visual Model: Area Model (2 min)

Draw a rectangle, divide it into 3 columns (for thirds), then divide into 4 rows (for fourths). Shade 2/3 one way, 3/4 the other way. The overlap shows 6/12 = 1/2.

SAY THIS:

"The area model shows why we multiply denominators: 3 columns x 4 rows = 12 small rectangles. The overlap (2 x 3 = 6 rectangles) is our numerator."

4

Multiplying Fractions by Whole Numbers (2 min)

Show that whole numbers can be written as fractions: 4 = 4/1

Example: 4 x 25 = 41 x 25 = 85 = 135

5

Guided Practice (2-3 min)

Work through these together:

1/2 x 1/4 = ? (1/8)
3/4 x 2/5 = ? (6/20 = 3/10)
6 x 2/3 = ? (12/3 = 4)

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"What is 1/3 x 3/4?"

A) 4/7 B) 3/12 C) 1/4 D) 4/12

Correct answer: C) 1/4 (1x3=3, 3x4=12, so 3/12 = 1/4)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Multiply two fractions Multiply fractions by whole numbers Multiply fractions: word problems Multiply mixed numbers Fraction multiplication and area

^ Differentiation & Extension

For struggling students: Use paper folding. Fold paper in half, then fold that in thirds. Ask: "What fraction of the whole paper is one section?" (1/6 = 1/2 x 1/3)

For advanced students: Introduce cross-canceling before multiplying. Example: 2/3 x 3/4 - the 3s cancel, leaving 2/4 = 1/2.

For home: Send Parent Activity sheet. Families can scale recipes (halving or doubling) using fraction multiplication.