One of the things I like about teaching is learning from my students.
We have started our work with rational numbers. Simplifying fractions and comparing the size of improper fractions and mixed numbers is one of the topics we study in class first. The concept of negative mixed numbers and the requirement that both the whole number and the fraction are both negative is difficult to remember for many students, particularly when we get to combining them through addition and subtraction.
While discussing negative mixed numbers with my classes on Friday, and reminding them that a negative sign in front of a number is really asking for the opposite of what follows it, one of my students said - "oh. so it would be like writing the mixed number in parentheses". What my student meant was that another way of writing -6 3/4 would be like this -(6 3/4); finding the opposite of a positive number.
Such a great insight. I know I had always thought of it like that but never articulated it to my class in that simple but powerful way. I think this will help me explain why both parts of the mixed number are negative much better than using a number line or the distributive property - (things I have tried in the past). I thanked my student profusely. It did not seem like my student fully understood my excitement.