Can We Share? - Division as Equal Sharing

Division as Equal Sharing: This means splitting a large group of items into smaller, equal groups so that everyone gets the same amount. For example, if you share $12$ apples among $3$ children, each child gets $4$ apples. Visually, imagine $12$ circles being distributed one by one into $3$ different boxes until all circles are gone, resulting in $4$ circles per box.

Division as Equal Grouping: This involves finding how many groups of a specific size can be made from a total. If you have $20$ beads and you put $5$ beads in each necklace, you can make $4$ necklaces. You can visualize this by drawing $20$ dots and circling them in groups of $5$ to see how many circles you can draw.

The Terms of Division: There are three main parts in a division number sentence. The 'Dividend' is the total number you start with. The 'Divisor' is the number you are dividing by. The 'Quotient' is the answer you get. In the equation $18 \div 2 = 9$, $18$ is the Dividend, $2$ is the Divisor, and $9$ is the Quotient.

Division as Repeated Subtraction: Division is the process of taking away the same number again and again until you reach zero. To solve $12 \div 3$, you subtract $3$ from $12$ repeatedly: $12 - 3 = 9$, $9 - 3 = 6$, $6 - 3 = 3$, and $3 - 3 = 0$. Since you subtracted $3$ exactly $4$ times, the answer is $4$.

Relationship with Multiplication: Division is the opposite (inverse) of multiplication. If you know that $3 \times 5 = 15$, then you also know the division facts $15 \div 3 = 5$ and $15 \div 5 = 3$. You can visualize this using an 'Array' of $15$ stars arranged in $3$ rows and $5$ columns.

Properties of 1 and Itself: When any number is divided by $1$, the quotient is the number itself ($8 \div 1 = 8$). When a number is divided by itself, the quotient is always $1$ ($8 \div 8 = 1$). Imagine having $8$ candies and giving them all to $1$ person (they get $8$), or sharing $8$ candies among $8$ people (each gets $1$).

Division of Zero: When $0$ is divided by any number, the answer is always $0$ ($0 \div 5 = 0$). This is because if you have zero items to share, no matter how many groups you have, each group will receive zero items. Note that we cannot divide any number by $0$.