Roman numerals

National Curriculum: this is in the Year 4 programme of study, part of key stage 2 (Years 3 to 6). Schools have to teach the key stage 2 programme by the end of Year 6, and can introduce content earlier or later within it.

Children in Year 4 are 8 or 9, and turn 9 during the school year.

What it is

Roman numerals are written with seven symbols: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500 and M is 1,000. A child working to 100 needs the first five. The numeral is read along the row, adding as you go, so XXVII is 10, 10, 5, 1 and 1, which makes 27.

The exception is the part that has to be taught. Where a smaller symbol stands directly in front of a larger one, it is taken away instead of added: IV is 4, IX is 9, XL is 40, XC is 90. Those four are the only pairs of that kind in any numeral up to 100. A child who knows the four, and adds everywhere else, can read all of them.

What makes this unfamiliar is that position carries no value. In 42, the 4 means four tens because of the column it sits in. In XLII there are no columns: L is fifty wherever it appears, and all that changes is whether the symbol before it is added or taken away. The reading habit that works for 42 does not transfer, which is why children who are secure with ordinary numbers can still stall on these.

When children learn it

The first place the curriculum puts them is a clock face. Year 3 asks children to tell and write the time from an analogue clock, including clocks using Roman numerals from I to XII. Year 4 then asks them to read Roman numerals to 100 (I to C), and to know that the numeral system changed over time to include zero and place value, which is why the two sit in the same part of the programme. Year 5 extends the reading to 1,000 and to years written as numerals.

Both the Year 4 and Year 5 requirements say read. Writing a number as a Roman numeral is not asked for in either year, so if homework asks your child to write 24 as XXIV, that is a school going further than the programme of study rather than something they were expected to have covered.

What it looks like when it goes wrong

These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.

The smaller symbol added instead of taken away. IV read as 6, IX as 11, XL as 60. Every symbol has been added along the row. That is the correct method for the rest of the numeral, which is what makes this one stick: the child is not guessing, they are applying a rule that works nearly everywhere. It usually shows on IV and IX first, because those are the ones they meet on a clock.
One symbol read as another. L answered as 100, C as 50, or V and X swapped. The values are half-remembered rather than known. There is nothing in the shapes to work them back from, so this is one of the few things in primary maths that can only be met often enough to stick.
The parts written down side by side. Asked to write XLII in figures, they write 402, or 4012. They have read the numeral correctly as forty and two, then put the parts down in the order they said them instead of combining them by place. That belongs to place value rather than to Roman numerals: the same child writes three hundred and five as 3005. What these numerals do is hand the parts over separately, so a place value gap that ordinary numbers hide becomes visible.

How to help at home

Teach the four subtractive pairs as a short list and nothing else: IV is 4, IX is 9, XL is 40, XC is 90. Every other numeral to 100 is read by adding along the row, so those four are the whole of the difficulty.
Read a clock face together: what sits opposite XII, what number is at IX. Some clock faces print IIII rather than IV for four, which is a clockmaking convention and not a rule of the numerals, so say so before it confuses them.
Ask them to read a numeral rather than write one. Reading to 100 is what Year 4 asks for, and going from numeral to number is the easier direction.
Point them out where they already appear: chapter numbers, the year carved on a building, the date at the end of a film. Year 5 asks children to recognise years written this way.