Number - Multiplication and Division Facts

Multiplication as Repeated Addition: Multiplication is a shortcut for adding the same number multiple times. Imagine a picture of 3 baskets, each containing 4 apples; this can be seen as $4 + 4 + 4$, which is written as $3 \times 4 = 12$.

Understanding Arrays: An array is a visual arrangement of objects in equal rows and columns. For example, a grid of dots with 2 horizontal rows and 5 vertical columns represents $2 \times 5 = 10$. This helps us see that the total count is the product of the rows and columns.

Division as Equal Sharing: Division is the process of splitting a large group into smaller, equal parts. If you have 15 stickers and share them equally among 3 friends, you can visualize 3 circles with 5 stickers inside each circle, representing $15 \div 3 = 5$.

Division as Equal Grouping: This involves finding how many groups of a certain size can be made from a total. If you have 20 cookies and put 4 on each plate, you are finding how many plates (groups) are needed: $20 \div 4 = 5$.

Commutative Property of Multiplication: The order of the numbers does not change the product. Visually, turning a $3 \times 4$ array (3 rows, 4 columns) on its side makes it a $4 \times 3$ array (4 rows, 3 columns), but both still contain 12 items. So, $a \times b = b \times a$.

The Relationship Between Multiplication and Division (Fact Families): These operations are opposites (inverses). If you know $4 \times 5 = 20$, you also know $20 \div 5 = 4$ and $20 \div 4 = 5$. They form a 'Fact Family' triangle with 20 at the top and 4 and 5 at the bottom corners.

Multiplying by 0 and 1: Any number multiplied by 1 stays the same ($n \times 1 = n$), like 1 group of 5 items. Any number multiplied by 0 equals 0 ($n \times 0 = 0$), like having 5 empty bags with nothing inside.

Skip Counting and Multiples: Multiples are the products of a number and any whole number. On a number line, skip counting by 3s ($3, 6, 9, 12...$) shows the multiples of 3, which are the answers to the 3 times table.