Teacher Guide: Multi-digit Multiplication

🎯 Learning Objective 20-25 min lesson

Students will: Multiply multi-digit numbers using area models, partial products, and the standard algorithm. They will demonstrate procedural reliability and understand WHY each method works based on place value.

Key Understanding: All multiplication methods are based on the distributive property. When we multiply 23 x 45, we're really computing (20 + 3) x (40 + 5) = 20x40 + 20x5 + 3x40 + 3x5.

📦 Materials Needed

Base-ten blocks (for concrete understanding)
Grid paper for area models
Place value charts
Student worksheets
Calculators (for checking work only)

⚠ Common Misconceptions to Address

Misconception #1: Forgetting to Multiply All Parts

In 2-digit by 2-digit multiplication, students multiply only the ones or only the tens, missing partial products.

How to Address:

Use the area model to show all 4 parts visually. For 23 x 45, there are 4 rectangles to fill: 20x40, 20x5, 3x40, and 3x5. No parts can be skipped!

Misconception #2: Place Value Errors in Standard Algorithm

When multiplying by tens, students forget to add a zero (or shift over), writing 23 x 40 = 92 instead of 920.

How to Address:

Connect to place value: "You're multiplying by 4 TENS, not 4 ones. The answer must be in the tens place!" Some teachers use a placeholder zero; others teach shifting.

Misconception #3: Regrouping Errors

Students add the regrouped digit at the wrong time or forget it entirely.

How to Address:

Write regrouped numbers SMALL above the correct place. Cross them out after using. Practice: "Multiply first, THEN add the regrouped number."

📋 Strategy Progression

1. Area Model (Most Concrete)

Students draw a rectangle and decompose factors by place value. Best for building understanding.

23 x 45 using Area Model

	40	5
20	800	100
3	120	15

800 + 100 + 120 + 15 = 1,035

2. Partial Products (Bridge Strategy)

Write out each multiplication separately, then add. Shows what's happening in the algorithm.

23
x 45
----
15 (3 x 5)
100 (20 x 5)
120 (3 x 40)
800 (20 x 40)
----
1,035

3. Standard Algorithm (Most Efficient)

Traditional method with regrouping. Teach AFTER conceptual understanding is established.

📝 Lesson Steps

1

Connect to Prior Knowledge (3 min)

Review single-digit multiplication facts and multiplying by 10s.

SAY THIS:

"What's 6 x 7? (42) What's 6 x 70? (420) How did you know? Right - multiplying by 70 is like multiplying by 7, then by 10!"

2

Introduce Area Model for 2x2 (6 min)

Model 23 x 45 using a rectangle divided into 4 parts.

Draw rectangle, label sides (20 + 3) and (40 + 5)
Fill in each partial product
Add all four parts

3

Connect to Partial Products (4 min)

Show how the same four products appear in the partial products method.

SAY THIS:

"Notice the area model gave us 800, 100, 120, and 15. These are the SAME numbers we get with partial products! The methods are connected."

4

Teach Standard Algorithm (6 min)

Demonstrate the standard algorithm, connecting each step to the partial products.

Multiply by ones first (23 x 5 = 115)
Multiply by tens next (23 x 40 = 920) - note the zero!
Add the products (115 + 920 = 1,035)

5

Practice 4-digit by 1-digit (4 min)

Work through 2,456 x 7 together using partial products or standard algorithm.

6

Independent Practice

Distribute worksheets. Allow students to choose their preferred method, but require showing work.

💻 IXL Skills to Assign

Recommended IXL Practice:

Multiply 2-digit by 1-digit Multiply 3-digit by 1-digit Multiply 2-digit by 2-digit using area models Multiply 2-digit by 2-digit Multiplication word problems

🏠 Differentiation

For struggling students: Start with 2-digit x 1-digit. Use grid paper for area models. Allow calculators to check (not solve).

For advanced students: Extend to 3-digit x 2-digit. Challenge with estimation before calculating. Explore mental math strategies.

For home: Practice with prices (cost of 23 items at $45 each), distances, and packaging problems.