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Great work adopting an RSPCA rescue kitten! The good news is that she is perfectly normal. Cats of all breeds can be very active and mischievous in their juvenile stage if their instinctive need for investigative, predatory and playful activity are not met.
The juvenile stage ends between about six and twelve months of age. During the juvenile stage cats become more independent and seek to learn through play, exercise and social contact. Providing these needs means that undesirable behaviour such as destructive exploration, scratching and overly exuberant activity are less likely to occur.
You’re on the right track, kittens should be provided with scratching posts but they also need toys for self-play and play with you. A nursery or play centre with perches, ledges, dangling toys and a variety of surfaces for scratching can be either purchased or made at home. Toys don’t have to cost the earth with cardboard boxes or paper bags providing hours of fun. Predation is a highly innate behaviour in cats so play sessions with you should provide some form of chasing and pouncing at targets. Battery operated toys, walnuts or ping-pong balls work well. Try toys that dangle from doors or scratching posts or toys on springs. Interactive play with yourself is usually one of the best outlets for kittens. Interactive toys such as wands, ropes and sticks with toys dangling from the end work very well.
Finally, toys are great but remember that they shouldn’t be so small or fragile that they can be chewed and swallowed. Be very diligent about keeping string, hair ties and thread away from cats and be mindful of Christmas decorations that may be appearing soon – they can be ingested and cause intestinal obstructions.