(not parent, but I used to do that thing as well and you might find this helpful)

It depends on their age and skill level. It goes without saying that younger kids need more guidance if they aren't extremely motivated.

This is worth looking into: https://artofproblemsolving.com, it's kind of the go-to website for the competitive math community. There are a lot of free high-quality resources on the wiki, and they sell courses and books.

A couple classic books: https://www.amazon.com/Art-Craft-Problem-Solving-3E/dp/11194... https://www.amazon.com/Problem-Solving-Strategies-Problem-Bo...

And obviously, competition problems! For example, this is the AMC: https://amc-reg.maa.org/default.aspx; competition websites usually have an archive of past editions freely available. Studying past problems is the meat and potatoes of actual competition training. Make sure they are age appropriate, because the difficulty level ramps up VERY fast.

If you are looking for a physical book, try Problem Solving Strategies (http://www.amazon.com/Problem-Solving-Strategies-Problem-Boo...) or Problem Solving Through Problems (http://www.amazon.com/Problem-Solving-Through-Problems-Larso...).