10/10/2023
Oh my goodness! A Year 5 student I know has been given this question (in the first photo!) as maths homework recently, and it caused a lot of stress for the student and their parents!
It's a tricky question, as it involves not only understanding Roman Numerals, how they are written and read, numbers as written in words, rounding and evaluating which statement can be true and which can't, it's also in quite complicated English with extended sentences and phrases like "three and a half thousand" which relies on a student knowing that we use that phrase informally to mean 3,500. So we are already making it much, much harder for students who do not speak English as their first language, dyslexic students, students with working memory deficits etc to even understand what is required!
I completely agree that we should make maths relevant and involve problem solving but I DON'T believe we should be testing a child's knowledge of Roman Numerals in the 21st century!
For context, the second photo is the type of Roman Numeral question that often appears in Year 6 SATs papers. And after KS2 SATs, you'll never be tested on your knowledge of Roman Numerals ever again!
Remember - this was homework given to a Year 5 student!
In case you do want the answer... deep breath, here we go!
MMCM is 2900. M =1000, so MM is 2000. C =100, but because it is placed BEFORE the last M, it means that we take 100 away from the M, so 1000-100 = 900.
MMCMX is 2900 with an additional X (which equals 10). The X comes AFTER the last M, so we are adding 10 on, so MMCMX = 2910.
The final statement by Katie says that her number, when rounded to the NEAREST THOUSAND, is two thousand - 2000. Now, both 2900 and 2910 are much closer to 3000 than 2000, so Katie's statement is impossible.
And now you realise that the second load of information from Jessica is completely irrelevant. We've found the answer, we've explained it, we don't actually need to analyse anything Jessica says (sorry Jessica!)
At no point can we pinpoint exactly what number each girl is thinking of. Due to the rounding up rules, Katie must be thinking of any number from 2905 to 2914, but we can't work out exactly which one. Jessica's numbers are 3500, 3510 (MMMDX) and 4000 in her statements, and these are all possible, but we can only say that the number she is thinking of is any number from 3505 to 3514. Yet many students will be trying to think of the the exact number both Katie and Jessica are thinking of because of the way the question starts: "Katie and Jessica each think of a number." This can throw them off track right from the beginning.
I think that is a really challenging question! Whilst it's certainly not difficult in terms of maths - the maths bit is purely rounding to 10, 100 and 1000 - the way the question is written makes it a tough one.
Would I give this to a Year 5 maths student to work on independently? Unlikely. I might give this to a group to work together on, or work with a student on it.
What do you think? I'd love to know!
