Odd and Even Numbers

What you will learn

• Say what makes a number even and what makes it odd, using pairs.
• Tell odd from even using the last digit, for numbers up to $100$ and beyond.
• Know whether an adding sum will be odd or even before you work it out.

Before you start: you should be able to count to $100$ and know the ones digit of a number. Comparing and Ordering Numbers gives a short first look at odd and even, and this lesson goes much deeper.

The idea

Imagine a dance class where everyone needs a partner. Eight children can all dance, because they make four pairs. Seven children cannot all dance. Three pairs form, and one child stands out.

That is the whole idea. Numbers that can be put into pairs with nothing left over are even. Numbers that always leave one on their own are odd.

Sharing into pairs

Put $8$ counters in pairs, and every counter has a partner.

Now try $7$.

Zero counts as even too. If you have no counters, nobody is left without a partner.

Telling them apart by the last digit

You do not need to draw pairs for every number. Look only at the ones digit.

• Last digit $0, 2, 4, 6$ or $8$: the number is even.
• Last digit $1, 3, 5, 7$ or $9$: the number is odd.

This works for any size of number. Think of $76$. Seventy is made of whole tens, and every ten splits into two fives, so the tens never leave anyone out. Only the ones digit can leave one over. The ones digit of $76$ is $6$, which is even, so $76$ is even.

Counting in 2s lands on evens

If you count in $2$s from $0$ you get $2, 4, 6, 8, \dots$ and you only ever say even numbers. You can see this in the shaded cells above. Start from $1$ instead and you say $1, 3, 5, 7, \dots$, which are all the odd ones. This links to Skip Counting in 2s, 5s and 10s.

What happens when you add

The pairs picture can tell you whether a sum will be odd or even before you do it.

• Even + even = even. Both sets make pairs with none left, so together they make pairs with none left. $4 + 6 = 10$.
• Odd + odd = even. Each set has one spare counter. The two spares make a new pair. $3 + 5 = 8$.
• Even + odd = odd. Only one set has a spare counter, and it has no partner. $4 + 5 = 9$.

The same idea works when you take away: even take away even is even, and odd take away odd is even, but an odd and an even together give an odd answer. And a double, such as $6 + 6$, is always even, because each counter has an exact copy to pair with.

Worked examples

Example 1: Is it odd or even?

Is $48$ odd or even? What about $95$?

1. Look at the ones digit only. For $48$ it is $8$.
2. $8$ is one of $0, 2, 4, 6, 8$, so $48$ is even.
3. For $95$ the ones digit is $5$. That is one of $1, 3, 5, 7, 9$, so $95$ is odd.

Answer: $48$ is even and $95$ is odd.

Example 2: Fair shares

Dev and Mina want to share $17$ marbles so they each get the same amount. Can they?

1. $17$ ends in $7$, so it is odd.
2. An odd number always has one left over when you make pairs, so it cannot be shared equally between two people.
3. They could each take $8$, and $1$ marble would be left.

Answer: No, $17$ is odd, so one marble is left over.

Example 3: Predicting the answer

Without working it out, will $9 + 7$ be odd or even? Then check.

1. $9$ is odd and $7$ is odd.
2. Odd plus odd is even, so the answer will be even.
3. Check: $9 + 7 = 16$, and $16$ ends in $6$. Even. The prediction was right.

Answer: Even. $9 + 7 = 16$.

Look at the last digit only, not the first. $12$ starts with a $1$, which is odd, but $12$ is even because its last digit is $2$. The first digit is a count of tens and tens never change odd to even.

Why it matters

Odd and even decide whether things can be shared fairly in two. They help when you pick teams, seat people in pairs or share a bag of sweets. Odd and even also help you check your sums fast: if you add two odd numbers and get an odd answer, something went wrong. And later on, even numbers turn out to be the numbers that divide exactly by $2$, which is the start of times tables and factors.