Odd and Even Numbers
Odd, even and pairing up
Every whole number is either even or odd, and the difference is about pairing. An even number splits exactly into pairs with none left over: six is three pairs, ten is five pairs. An odd number always has one left over: seven is three pairs and one spare. This pairing picture is the real meaning of even and odd, deeper than a rule about last digits. It explains why the parity rules work, and it is where Year 4 starts: seeing a number as something that either pairs up cleanly or does not.
Adding two odd numbers
Adding odd and even numbers follows rules that the pairing picture explains. Two odd numbers each have a single dot left over after pairing; put them together and those two leftovers form a pair, so the total splits cleanly — odd plus odd is always even. The same reasoning shows even plus even is even (no leftovers at all) and even plus odd is odd (one leftover remains). Understanding why, from the leftovers, is far more useful than memorising the rules, because the picture makes each result obvious.
Telling odd from even
You do not need to pair up dots to tell odd from even — the last digit gives it away. A number is even if it ends in 0, 2, 4, 6 or 8, and odd if it ends in 1, 3, 5, 7 or 9. This works because tens, hundreds and thousands are all even, so only the ones digit decides whether anything is left over. Spotting the odd number in a group is then just a glance at the last digit. This quick test is the everyday way to judge parity, backed by the pairing idea underneath.
Odd and even when multiplying
Multiplying also follows a parity rule. A product is even if at least one factor is even, because an even factor contributes pairs that keep everything paired. Only when both factors are odd is the product odd. So four times seven is even (four is even), but three times five is odd (both odd). This rule lets you predict whether a product is odd or even without doing the multiplication — a useful check, and another consequence of how pairs behave.
The last digit decides
For any number, however large, parity is decided entirely by the last digit. 374 is even because it ends in 4; 285 is odd because it ends in 5; 1000 is even because it ends in 0. The digits in front make no difference, because every ten, hundred and thousand is itself even and pairs up on its own. This is why the last-digit test always works, and it means checking the parity of a huge number is no harder than checking a single digit.
The rules of parity
Pulling the unit together, odd and even follow a small set of fixed rules. Adding: even plus even and odd plus odd are even, while even plus odd is odd. Multiplying: a product is even unless both factors are odd. A table captures them all, and each rule traces back to the same pairing idea — whether leftovers cancel out or remain. With the meaning of parity understood and these rules in hand, a child can predict whether sums and products are odd or even, a simple but powerful property of whole numbers used throughout mathematics.