Lesson 2: Multiplying by One-Digit Numbers

Property

An area model represents a multiplication problem, such as $a \times N$, as the area of a rectangle.
The multi-digit number $N$ is decomposed into its expanded form (e.g., $123 = 100 + 20 + 3$).
The total area (product) is the sum of the smaller rectangular areas, which are the partial products.
For $a \times (b + c + d)$, the total product is $(a \times b) + (a \times c) + (a \times d)$.

Examples

• To model $6 \times 347$, you draw a rectangle with side lengths $6$ and $347$. Decompose $347$ into $300 + 40 + 7$. The partial products are the areas of the smaller rectangles: $6 \times 300 = 1800$, $6 \times 40 = 240$, and $6 \times 7 = 42$.

• To model $9 \times 4,582$, you draw a rectangle with side lengths $9$ and $4,582$. Decompose $4,582$ into $4000 + 500 + 80 + 2$. The partial products are the areas of the smaller rectangles: $9 \times 4000 = 36,000$, $9 \times 500 = 4,500$, $9 \times 80 = 720$, and $9 \times 2 = 18$.

Property

The standard algorithm for multiplication is a procedure where you multiply numbers vertically.
You multiply the single-digit multiplier by each digit of the multi-digit number, starting from the ones place and moving left.
When the product in any place value is 10 or more, you regroup (or 'carry') the tens digit to the next place value column to the left.

Examples