Division as sharing and as grouping

Two questions, one symbol

$12\div3$ answers two different questions. Sharing: twelve sweets shared between three children — how many each? Grouping: twelve sweets put into bags of three — how many bags? Both give $4$, but the $4$ means different things, and the word problem tells you which.

Division undoes multiplication

Because $3\times4=12$, we know $12\div3=4$ and $12\div4=3$. Every times-table fact you know is really three facts. This is the fastest way to divide at Stage 2: ask “three times what makes twelve?”

What is left over

$13\div3$ does not come out exactly: $3\times4=12$ and one is left. We say $4$ remainder $1$. The remainder is always smaller than the number you are dividing by — if it is not, you could have made another group.