Multiply by Two-Digit Numbers

When you multiply by the tens digit, you're actually multiplying by 10, 20, 30, etc. Shifting one place to the left is a way of showing that these numbers represent tens, not ones. For example, when you multiply 34 × 23, the second partial product (34 × 20) should be recorded as 680, which means 68 tens. Shifting left visually shows this place value difference.

This often happens because of careless mistakes in basic multiplication facts or errors in addition when combining partial products. Have your student slow down and check their work step-by-step: First, verify the ones multiplication (e.g., 4 × 3), then the tens multiplication (e.g., 4 × 20), then add the partial products carefully. Using a different color pen for each step can help them track their work.

While repeated addition shows understanding of multiplication, Grade 3 is the year to transition toward the standard algorithm. Repeated addition becomes very slow and error-prone with larger numbers like 34 × 23. Encourage the standard partial products method as a bridge between conceptual understanding and efficiency. You can still use repeated addition to check answers!

Your student likely understands basic multiplication but hasn't yet mastered the place value concepts needed for two-digit work. Review tens and ones frequently, use manipulatives like base-ten blocks to show what 23 × 4 looks like physically, and practice writing numbers in expanded form (e.g., 23 = 20 + 3). Once place value clicks, the algorithm becomes much easier.