In everyday language people often mix up "less than" and "smaller than" and in most situations it doesn't matter but when dealing with negative numbers this can lead to confusion.
I am a mathematics teacher in the UK and there are questions in national GCSE exams phrased like this:
Put these numbers in order from smallest to biggest: 3, -1, 7, -5, 13, 0.75
These questions are in exams designed for low ability students and testing their knowledge of place value and ordering numbers and the correct solution in the exam would be: -5, -1, 0.75, 3, 7, 13.
I think if the question says "smallest to biggest" the correct solution should be 0.75, -1, 3, -5, 7, 13. Even though it doesn't seem to bother most people, I think the precise mathematical language is important and "smallest to biggest" should be avoided but if it is used it should refer to the absolute value of the numbers.
So my question is: Which is bigger, -5 or -1?