Multiplication - Multiplication Tables 2 to 10

Multiplication is the process of Repeated Addition. For example, $3 \times 4$ means adding $4$ three times: $4 + 4 + 4 = 12$. Visually, this can be seen as $3$ rows of $4$ dots each forming a rectangular grid totaling $12$ dots.

Terminology: In a multiplication sentence like $5 \times 2 = 10$, the number being multiplied ($5$) is the Multiplicand, the number of times it is multiplied ($2$) is the Multiplier, and the result ($10$) is the Product.

Order Property (Commutative Property): Changing the order of the numbers does not change the product. For example, $4 \times 5 = 20$ and $5 \times 4 = 20$. Visually, a grid of $4$ rows and $5$ columns is simply a rotated version of a grid with $5$ rows and $4$ columns.

The Identity Property of One: Any number multiplied by $1$ stays the same ($6 \times 1 = 6$). Visually, this is like having one single group containing $6$ items.

The Zero Property: Any number multiplied by $0$ results in $0$ ($9 \times 0 = 0$). Visually, this represents having multiple groups (like $9$ boxes) but with nothing inside them, resulting in a total of zero.

Multiplication on a Number Line: Multiplication can be visualized as taking equal-sized jumps. To solve $3 \times 2$, you start at $0$ and take $3$ jumps of $2$ units each, landing on $2, 4,$ and finally $6$.

Patterns in Tables: Specific tables have recognizable patterns. For example, the table of $5$ always ends in the digits $0$ or $5$ ($5, 10, 15, 20...$), and the table of $10$ always ends in $0$ ($10, 20, 30...$).

Doubling and Halving: Knowing the table of $2$ helps with the table of $4$. Since $4$ is double of $2$, the results in the table of $4$ are double the results in the table of $2$. For example, $2 \times 3 = 6$, so $4 \times 3 = 12$.