Had a fantastic talk with the school earlier in the week. I am told that this is common behaviour, particularly with girls. Generally girls tend to 'behave' at school, whereas boys are a little more unpredictable.
I am informed that at school, DD is very well-behaved - not to the point of being an annoying "goody goody" sort, but the sort that participates in activities, asks sensible questions, completes tasks properly, follows instruction and is kind and helpful toward other children.
It was suggested that if she starts answering back/shouting, it is up to me to be the adult and set the standard for behaviour. In school they use the tactic of saying "I am going to ignore you whilst you are talking/acting like that. When you can speak nicely/calmly, then we will talk about [whatever it is]." Once you've explained this you can reiterate that this is not the type of behaviour you expect and that if it continues you will leave the room until they are calm. DO NOT SHOUT.
Secondly, having structure and routine can be really helpful. I'm going to try this. At school they have a daily tasks planner. So it'll say 9am - assembly, 10am - phonics, etc. There are words and pictures and the children put the pictures on daily. This gives them a feeling of control over the tasks, and it's easy to point them to the board and say "What should we be doing now?"
Tiredness is a problem for us too. DD has a very active brain. She is always asking questions about how things work, why things are what they are, trying to make sense of the world around her. That's great, but it's constant. She can't switch off. It doesn't seem to matter what time she goes to bed, or what the routine is before bed. She just keeps on and on. It was suggested to look at mindfulness techniques, so I'll be doing a bit of research on that later.
I'm not expecting miracles. I've been trying harder with how I react since I spoke with the school. As I said to the teacher, I'm not asking for an angelic little child, just the option of not arguing about stuff every day.