So worst behaviour ie hitting you, is the reward and consequence of x-box. I think worst behaviour should match the most deisred thing being the consequence.
Problem - hitting when angry
Your expectations - its ok to get angry, but when you get angry and feel like hitting, i expect you walk away, punch a pillow, go for a ride on your bike, go to your room and scream
Reward - If you walk away, punch a pillow, go for a ride on your bike etc instead of hitting me everytime. You get 2 hours of x-box, plus an extra half hour x-box time.
Consequence - if you do hit me when angry you dont get any x-box time
I think this one has to have zero tolerance, it is an all or nothing.
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Problem - breaking things
Your expectations - its ok to get angry, but when you get angry and feel like breaking things, i expect you walk away, punch a pillow, go for a ride on your bike, go to your room and scream
Reward - If you walk away, punch a pillow, go for a ride on your bike etc instead of breaking things. You get pocket money of £2 a day or whatever you think is a reasonable amount
Consequence - Your x amount of pocket money goes towards the cost of replacing whatever it is you damaged.
I think this one has to be zero tolerance, its an all or nothing
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Problem - name calling when angry
Your expectations - its ok to get angry, but when you get angry and feel like name calling, i expect you walk away, punch a pillow, go for a ride on your bike, go to your room and scream.
Reward - If you walk away, punch a pillow, go for a ride on your bike etc instead of name calling. You get sweets.
Consequence - if you name call when angry, you will told to stop and apologise, if you continue, no sweets.
This one you could add a sub clause, be a bit more flexible with, ie give him the opportunity to stop and apologise, before imposing the consequence.
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Stealing from your purse i would just hide my purse so he couldnt steal and deal with this one later, once you have problems under control, you can then change the above to address different problems.
Same as lying.
School refusal, i would be trying to sort out with the school first, as might be struggling.
Have to go out now for an appointment, will check back later, to see if my suggestions are any good for you.