Odd and even numbers

Every number is either odd or even — there is no third kind. And there is a trick that tells you which one, instantly, no matter how big the number is.

A story to start: the buddy line

It was the morning of the school trip. Miss clapped her hands and said, "Everyone, line up in twos. Find your buddy and hold their hand."

Riya grabbed Arjun's hand. All around them, children shuffled into a long line, two by two, like a train. Talyzo drifted above the line, glowing softly, watching everyone find a partner. "Twenty-four of us today," said Miss. Every child had a buddy. Nobody stood alone.

The next day, one child was off sick. "Twenty-three today," said Miss. This time, when the line was done, Arjun was standing right at the end — with nobody's hand to hold. Then Talyzo floated down, went a warm shade of pink, and held his hand instead.

Riya was looking back down the line. "Wait," she said. "Yesterday there were twenty-four of us and everyone had a buddy. Today there are twenty-three and you're left over. Why?"

Arjun thought about it, the way he always did — one step at a time. "Let's count. Twenty-three: everyone pairs up and one is left standing alone. Twenty-four: everyone pairs up and nobody's left. Twenty-five — one left over. Twenty-six — none left over." Talyzo bounced once for every number.

"I think I see it," said Arjun. "When the number pairs up with nobody left over, that's an even number. When it leaves one child standing alone, that's an odd number." Riya's eyes lit up. "So twenty-four is even. Twenty-three is odd. Twenty-six is even." Talyzo flashed bright yellow.

Then Miss said the whole school would be at assembly — a hundred and forty-eight children. Riya groaned; that was far too many to line up and check. But Arjun was already grinning. "I already know. It's even. I only looked at the last number — the eight. Eight is even, so a hundred and forty-eight is even too." Talyzo bounced so high it nearly touched the ceiling.

Riya had spotted the whole trick in one morning. Here is exactly what she worked out.

What makes a number even

A number is even if you can split it into two equal groups with nothing left over. Think of sharing sweets between two children so both get the same. 2, 4, 6, 8 and 10 are all even.

Picture 6 sweets. Share them fairly and each child gets 3 — 3 and 3, with none left in your hand. Because it shared out evenly, 6 is an even number.

What makes a number odd

A number is odd if one is always left over when you pair it up. However you try to split it into two equal groups, there is one stubborn extra. 1, 3, 5, 7 and 9 are all odd.

Now picture 7 sweets. You can make 3 pairs — that is 6 sweets — but one sweet is left over on its own. Because there is always one left, 7 is an odd number.

The quick trick — look at the last digit only

Here is the part worth remembering. You never have to pair up the whole number. You only have to look at the digit at the very end.

It does not matter how big the number is. 348 is even because it ends in 8. 592 is even because it ends in 2. 731 is odd because it ends in 1. You did not have to think about the hundreds or the tens at all — just the last digit.

Where children get stuck

Many children think a bigger number must be harder to judge, so they try to work out the whole number. They do not need to. A three-digit number is decided by its last digit exactly the same way a small one is. One more thing catches children out: zero is even. A number that ends in 0, like 30 or 100, is always even.

Practise together

Try these five with your child. Cover the answers and reveal them one at a time.

Show 5 practice questions and answers

1. Is 24 odd or even? — even (it ends in 4)
2. Is 57 odd or even? — odd (it ends in 7)
3. Is 130 odd or even? — even (it ends in 0)
4. Write the next two even numbers after 16. — 18 and 20
5. Which of these is odd — 46, 82, 95, 60? — 95

What comes next

Odd and even numbers are one of the first ideas in number sense — the feel for what numbers are and how they sit together. When your child is ready for more, the free chapter puts this into a game, with a hint before every answer and a full explanation after.

Free account, no card required.

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