Using Place Value To Find The Product

Using Place Value to Find the Product: A Step‑by‑Step Guide

Multiplication is more than memorizing facts; it is a powerful tool that becomes easier when students understand the place value system. In a recent video, Center Grove Elementary 4th‑grade teacher Susan Campbell demonstrates how to use place value to find the product of numbers, especially those that are multiples of 10. This article breaks down the strategy, explains why it builds procedural fluency, and shows how it applies to both whole numbers and decimals.

Why Place Value Matters in Multiplication

Every digit in a number represents a specific value based on its position. When we multiply, we are essentially adding groups of these values together. Recognizing that a “3” in the hundreds place means 300, not just 3, helps students:

• Visualize the size of each group they are adding.
• Separate complex problems into simpler, manageable parts.
• Reduce errors caused by overlooking zeros.

By linking multiplication to the familiar concept of place value, learners develop a conceptual understanding that supports long‑term confidence.

Core Strategy from Susan Campbell’s Video

In the video, Susan Campbell shares a clear, repeatable method for multiplying numbers that end in zero. The steps are:

1. Identify the non‑zero digits. Strip away the trailing zeros and note the remaining numbers.
2. Multiply the non‑zero digits. Use any preferred multiplication fact or strategy (e.g., arrays, partial products).
3. Count the total zeros. Add together the zeros removed from each factor.
4. Attach the zeros to the product. Place the combined zeros at the end of the result from step 2.

This approach works for any pair of numbers that are multiples of 10, such as 30 × 40, 200 × 500, or 7,000 × 60.

Example: Multiplying Whole Numbers

Let’s apply the four steps to 30 × 40:

1. Non‑zero digits: 3 and 4.
2. Multiply: 3 × 4 = 12.
3. Total zeros: 1 (from 30) + 1 (from 40) = 2.
4. Attach zeros: 12 followed by two zeros = 1,200.

The product is 1,200. Notice how the method eliminates the need to perform a lengthy column multiplication, saving time and reducing mistakes.

Extending the Method to Larger Numbers

Consider 200 × 500:

1. Non‑zero digits: 2 and 5.
2. Multiply: 2 × 5 = 10.
3. Total zeros: 2 (from 200) + 2 (from 500) = 4.
4. Attach zeros: 10 followed by four zeros = 100,000.

The result, 100,000, demonstrates how the strategy scales effortlessly, even when the numbers contain several zeros.

Applying Place Value to Decimal Multiplication

After mastering whole numbers, Susan Campbell encourages students to “get confident multiplying decimals.” The same principle applies; the key is to treat the decimal as a whole number, perform the multiplication, then reposition the decimal point in the product.

Example: 0.3 × 0.4

1. Ignore the decimal points temporarily: 3 × 4 = 12.
2. Count total decimal places: 1 (from 0.3) + 1 (from 0.4) = 2.
3. Place the decimal point two places from the right: 0.12.

For numbers that also end in zero, combine the two ideas. Multiply the non‑zero digits, count both the zeros and decimal places, then attach the appropriate number of zeros and position the decimal point.

Benefits of Using Place Value to Find the Product

When students consistently use this technique, they experience several measurable gains:

• Procedural fluency: Repeating the four‑step process builds speed and accuracy.
• Conceptual clarity: Understanding why zeros are added reinforces the base‑10 system.
• Transferability: The method works for whole numbers, large multiples of ten, and decimal products.
• Confidence: As Susan Campbell notes, learners finish the video feeling ready to solve “ANY problem where you …”—a testament to the strategy’s versatility.

Practice Problems for Classroom or Home Use

Below are sample problems that follow the same pattern. Encourage students to write each step on paper before checking the answer.

1. 50 × 70
2. 300 × 90
3. 0.6 × 0.8
4. 4,000 × 250
5. 0.05 × 0.2

Answers: 3,500; 27,000; 0.48; 1,000,000; 0.01.

Integrating the Strategy into Daily Math Routines

Teachers can embed the place‑value method into warm‑up activities, math centers, or online quizzes. A quick “product of the day” challenge—where students must determine the product of two multiples of ten within 30 seconds—reinforces speed and accuracy. For remote learners, a short video recap (similar to Susan Campbell’s) paired with a digital worksheet provides the same reinforcement.

Conclusion

Using place value to find the product transforms multiplication from a memorization task into a logical, step‑by‑step process. By focusing on the non‑zero digits, counting zeros, and correctly positioning the decimal point, students develop both procedural fluency and deep conceptual understanding. Whether they are multiplying 30 × 40, 200 × 500, or 0.3 × 0.4, the strategy remains reliable and easy to teach.

Implement this approach in your classroom or at home, and watch confidence grow—just as the students in Susan Campbell’s video become ready to tackle any multiplication problem that comes their way.