# How to teach the proof of odds and evens in KS1

We cannot rely on rhymes for teaching odds and evens, we must teach children the proof instead, says this teacher

I remember, with frustration, my first year of teaching odd and even numbers.

It was a Year 2 class.

“Just look at the pattern. Can’t you see it!” I remember myself saying with growing annoyance.

It was not the best approach, I have to admit.

## Teaching odds and evens

My LSA stepped in to suggest using a rhyme to help the pupils. It went something like: “0,2,4, 6 and 8 are even numbers at the gate; 1, 3, 5, 7 and 9 are all odd and out of time”.

Now, I obviously thanked her and was pleased when I saw the children reciting this rhyme and sorting these numbers into odd and even. I continued to use this during my time in Year 2 thinking, “Yes, I’ve cracked teaching that objective. Thanks, Mrs Lomax!”

But I hadn’t. I’d just found another cheat for the children instead of providing them with the understanding.

We do this too much in maths: expecting children to believe rather than prove something. As reasoning is a clear objective of our maths national curriculum, it should be the children noticing why a number is even and why a number is odd and developing their own proof. Not just, “Look at the pattern!”

So how would I teach this now?

## A reasoned approach

My starting point as always is concrete objectives. Using counters or cubes and 10 frames, I ask the children to create even numbers and ask if they notice anything about them, drawing out the fact that each even number can be divided equally into two parts.

Once this definition has been established, I ask: can they prove it with other numbers?

The next stage would be asking: so if that makes them even, what makes an odd number odd?

Get them to hypothesise, test and prove again using ten frames and counters. This will lead to the children noticing for themselves that odd numbers don’t divide by two equally. They now have a mathematical definition and understanding, rather than a rule to just follow.

You can emphasise the point using cubes – here they will have a very visual representation of when a number is even or odd.

Each time this is revisited the children should be reminded of the definition they found.

## Next steps

This is then a building block to move into prove other things on maths. For example, that addition of even numbers equals an even. An argument which is summarised by Daniel Tammet in Thinking In Numbers as follows:

Preposition: even numbers (of any quantity) added together make an even number
Clarification: since even numbers have half parts, their sum will also have a half part
Axiom: an even number is that which is divisible into two equal parts
Conclusion: therefore the sum of any quantity of even numbers is even

Since using this method, the children have a greater understanding of the concept – rather than a quick fix.

Although I still use Mrs Lomax’s chant (I just like it).

Kevin O’Brien is a Year 6 teacher and SLT member in St Helens

Want to keep up with the latest education news and opinion? Follow Tes on Twitter and Instagram, and like Tes on Facebook

It only takes a moment and you'll get access to more news, plus courses, jobs and teaching resources tailored to you

## Latest stories

### Tes FE Awards 2021: The shortlist revealed

Who will walk away with a Tes FE award this year? We reveal the shortlist of the best in the FE sector
Tes Reporter 23 Apr 2021

### GCSEs 2021: Most schools prioritise 'exam-style' papers

'There's no one-size-fits-all model, and no one thinks any of this is ideal,' say heads over GCSE and A-level grading
Catherine Lough 23 Apr 2021

### Pupils 'would benefit from thinking like Da Vinci'

Science and the arts should be taught together instead of in subject silos, say researchers
Tes Reporter 23 Apr 2021

### Today's school, education and teacher news: LIVE 22/4

The hub for specialist education news for those working in schools and everyone who is interested in them
Tes Reporter 22 Apr 2021

The DfE should "explain the rationale" behind its behaviour experts before spending a 'large sum of public money'
Amy Gibbons and John Roberts 22 Apr 2021

### Catch-up tsar: Don’t 'force' more hours on teachers

Sir Kevan Collins also says he would 'never advocate' increasing teaching time without raising pay
Amy Gibbons 22 Apr 2021

### GCSEs 2022: Ofqual undecided on 'full-fat exams' return

'Some easement' might be needed to take learning loss into account when exams return,' says Ofqual chief
Catherine Lough 22 Apr 2021

### Why theory must come before practical lessons in FE

If vocational education is to prepare students for a shifting world, 'know that' must come before 'know-how', says Sam Jones
Sam Jones 22 Apr 2021

### Revealed: The accuracy of pupils’ rapid Covid tests

New figures show how often secondary students' home lateral flow tests are backed up by lab based PCR tests
John Roberts 22 Apr 2021

### Sarwar accepts criticism over private school policy

Labour leader asked how stance on private schools squares with private education of his own children
Tes Reporter 22 Apr 2021