You could introduce your child to CircleMath, invented by Dr Stephen Taylor. It is a very simple process for using 2 bases at once, eg 9 & 10, 10 & 11, 9 & 11 is best because it has many more patterns and involves 'Greek 9s'. The method relies on estimation, which I suggest is the starting point for all calculations. This works in any base... and, until metrics and decimals and calculators took over, everyone once used multiple bases every day... pints/gallons, inches/feet, days/weeks, etc.
When I first met Dr Taylor in 1985 he was tutoring a half dozen 5-year olds in his lounge using a whiteboard. The children could do 'sums' like 37x58 in their heads... in under 10 seconds... and tell me, a complete stranger - how they did it. As I was at Teachers' College at the time, preparing to teach high school math, I realised I knew very little... So, Dr Taylor and I became friends, I have most of his books, and still teach CircleMath when I get a chance. I recently wrote a PowerPoint intro - for adults - if anyone would like to see it.
I frequently get amazed looks as people realise how intuitively obvious it is, but it has been overgrown by dull modern mono-base thinking... and there is always a real buzz about this 'new thing'. It's the buzz all teachers and parents love...
As an HoD Math I put this to the test at one of our regional math assoc meetings, and talked about 15 capable, qualified math leaders through the basics, building up to this one: 114622/514. Following the very simple rules they got the answer correct in about 20 seconds... then looked at me and each other in silence... then said 'how the hell does that work?' Tada! CircleMath :)
It had taken only 45 mins, and they all got it correct, but few really got it at all.
Sad to say, for years afterwards some of them joked about that session as the workings of a crazed mind... not at all open for people whose job it was to open students' minds.
Edit for clarification: there was a link but has lapsed since Dr Taylor died in the last couple of years. I'll contact his son who was also brilliant at this stuff.
Edit2 for clarification: Dr Taylor wrote a book Theory of Mind, in which he identified and promoted the human brain's 'intrinsic base', meaning if things are couched in the right way then they resonate with the brain's OS, as it were, thus obviating the need for us to try to engender or pander to the child's interest. Things put in the right way will be interesting to the child. It is a provocative book about what is intrinsic and extrinsic to mind, learning and understanding.