HouseofEliot:
OK first off - I think you and she have to sort out if this is just aimed at her - or if this is happening to others in the groups - so a form of 'rough teasing' that isn't specifically targeted at your DD.
If one day they take your DD's bag and the next they take someone's ruck sack - well it's not particularly kind - but that kind of thing can happen and laughing it off may be the best solution.
Knocking her lunch onto the floor - rather seems intentional. Again - was this rough housing gone wrong?
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I agree maybe an issue to raise with the form tutor - but I also think you and your DD need to have a heart to heart about this group of 'friends' and whether she really likes them.
I get that being on your own can seem really scary - but there are ways of keeping busy.
First off - has your DD considered joining any lunchtime clubs?
Second - has your DD considered going on to lunch with new classmates from her class just before lunch?
It can be awkward at first - and DD1 found it a bit odd to ask if she could join new people - but now she's continuously asked to join friends for lunch and doesn't feel left out. She's boxing clever and eating with one group one day and another group the next - and trying to build a wide circle of friends.
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I'ts a shame the library is not available except one day a week - but perhaps she can go to the 'learning hub/ IT suite' or because of the situation - perhaps her form tutor or Senior Management may see the need to arrange that she get a special pass to use the library more frequently.
She may also be able to volunteer to work at the library - thereby having something to do at lunchtimes.
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I'm sorry things have turned out like this for your DD. I hope it gets better.
PSBD