Multiplying a two-digit number by a one-digit number can be done by decomposing the two-digit number into tens and ones, multiplying each part, and adding: 24 × 3 = (20 × 3) + (4 × 3) = 60 + 12 = 72. Arrays and area models support this understanding.
You know your multiplication facts up to 10 × 10. Now the question is: how do you multiply when one of the numbers is bigger than 10? The answer is to use place value to break the bigger number apart, multiply each piece using facts you already know, and add the results back together.
Take 24 × 3. You can think of 24 as 20 + 4. Multiplying each part by 3: 20 × 3 = 60, and 4 × 3 = 12. Then add: 60 + 12 = 72. This strategy is called decomposing the two-digit number into its tens and ones. You're not doing anything new — just applying your existing multiplication facts to smaller pieces.
The area model makes this visual. Draw a rectangle that is 24 units wide and 3 units tall. Split the width into two sections: 20 and 4. Now you have two smaller rectangles. The first is 20 × 3 = 60. The second is 4 × 3 = 12. The total area — the total product — is 60 + 12 = 72. This is the same calculation, just drawn as a picture. The area model works because area itself is multiplication (length × width), which is why your soft prerequisite connects here.
This decomposition strategy is the foundation of all multi-digit multiplication. In later grades, you'll use it to multiply two-digit numbers by two-digit numbers, or even larger. Every time, the idea is the same: break numbers into place-value parts, multiply each part, add up the partial products. Learning it well now — including understanding *why* it works, not just *how* to do it — will make all future multiplication much more approachable.
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