In fourth grade, students deepen their understanding of multiplication by progressing through three main stages: area model, partial products, and standard algorithm. Each step builds a strong foundation for the next, helping students truly understand how multiplication works—not just memorize steps.

1. Area Model: Building Conceptual Understanding

What it is:
The area model uses rectangles to visually represent the distributive property of multiplication. A two-digit number is broken into tens and ones, and each part is multiplied separately, then combined.

Example:
To solve 23 × 15:

Break into parts:

• 20 × 10 = 200

• 20 × 5 = 100

• 3 × 10 = 30

• 3 × 5 = 15

Then add:
200 + 100 + 30 + 15 = 345

Why it's important:
Students see what multiplication means and how numbers are broken apart and recombined. This builds a strong conceptual foundation.

2. Partial Products: Transitioning to Abstract Thinking

What it is:
This step removes the visual rectangle but keeps the structure of breaking numbers apart. Students write out each multiplication step as a partial product.

Same problem (23 × 15):

• 20 × 10 = 200

• 20 × 5 = 100

• 3 × 10 = 30

• 3 × 5 = 15

Add them:
200 + 100 + 30 + 15 = 345

Why it's important:
It bridges the gap between visual models and symbolic algorithms, keeping the math meaningful while increasing fluency.

3. Standard Algorithm: Efficient Computation

What it is:
The standard algorithm is the traditional method many adults learned: stack the numbers and multiply digit by digit, carrying as needed.

Why it's important:
It’s fast and efficient, but now students understand why it works thanks to the earlier models.