Is -5 bigger than -1?
Solution 1:
Like all too many test questions, the quoted question is a question not about things but about words.
Roughly speaking the same question will have appeared on these exams since before the students were born. And in their homework and quizzes, students will have seen the question repeatedly.
Let's assume that the student has a moderately comfortable knowledge of the relative sizes of positive integers. It is likely that the student has in effect been trained to use the following algorithm to deal with questions like the one quoted.
Arrange the numbers without a $-$ (the "real" numbers, negatives are not really real) in the right order.
Put all the things with a $-$ to the left of them, in the wrong order. Why? Because your answer is then said to be right.
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Even if there has been a serious attempt by the teacher to discuss the "whys," at the test taking level, the whys play essentially no role.
The OP's suggestion that "size" might be more intuitively viewed as distance from $0$ is a very reasonable one. That is part of what gives the ordering question some bite. Students who follow their intuition can be punished for not following the rules.
Sadly, in our multiple choice world, questions are often designed to exploit vulnerabilities and ambiguities.
Solution 2:
The problem is that we have two notions of "bigger", coming from the two operations, addition and multiplication (or alternately, one comes from the fact that $\mathbb{R}$ is ordered, one comes from the fact that $\mathbb{R}$ is a vector space), and they coincide for positive numbers. In almost every situation except the negative numbers, either only one of the notions make sense or they both agree. Consequently, people don't feel the need to be careful in distinguishing the two notions.
Personally, when you say "smallest to biggest" I think the way you do, that we are looking at size in terms of absolute value (the multiplicative notion of bigger), but if you say "least to most" you would give the answer the test is looking for. In my mind, the latter is referring to quantity, while the former is referring to magnitude. As Geryy said, there is a context to where I would use these terms, and the context determines what I would consider the natural thing to be looking at. However, I don't think that everybody uses language the same way I do, and on a national exam where you can't ask for clarification, making assumptions like that is an easy way to get things wrong.
The one thing that would sway me towards their interpretation of the wording is this: have the students discussed absolute value in any great length, viewing it as the size of the number? Also, is there any chance that this question is a multiple choice question, and that only one of the "right" answers is an option?