The amount of allowance of money you should give a 10 year old depends on your finances and how much you can afford.
On the low end $5.00 per week or $20.00 per month is a good allowance for a 10 year old but when I was 10 years old my parents gave me $10.00 per week which was $40.00 per month.
I spent a little of that and put the rest of it into savings to have some income as an adult when starting out.
Some people go by the age of the child and give them $1.00 per week for every year old the child is so that's what my parents did for me.
So an 8 year old would get $8.00 per week, 9 year old $9.00 per week and so on and so forth.