I think many kids (and parents) under-appreciate one very important way to learn Chinese: read aloud.

For our purposes, there are two types of Chinese reading: pleasure reading and focused reading.  They are for different purposes.

1.  Pleasure reading.  This is learning through large quantity of reading exposure, part of CLE and more of first language type of learning, at least in my mind.  The readers don’t have to know everything when doing pleasure reading.  Don’t smother their interest for pleasure reading by demanding that they read these aloud.  I believe dd#2 started reading comics in Chinese when she recognized half of the characters in the comics at 7 years of age.
2. Focused reading.  Focused reading is for “intentional and intensive studying” and the amount of materials covered is much less.  This mainly consists of passages in their Chinese textbooks.  One gets maximal benefit when one takes the time to learn to read these ALOUD to fluency.  Unless there is time constraint, I ask my DD to read textbook passages aloud to fluency first, in blocks over a few days, before doing any kind of writing assignment for the day.  Kids just want to get their writing assignment done and be finished with it, missing out on one important (if not the most important) part of learning: reading proficiency.  You would be surprised how many students can’t read their Chinese textbook passages competently.  It takes a lot of practice to do it right.  Since most children are learning more as second language learners, it is absolutely essential that they are doing high quality learning with the limited content presented.  Improving reading fluency through read-aloud greatly improves their general speaking proficiency also and is the most EFFICIENT way to do so.   Also, make sure that the child read ALOUD SLOWLY, with the right prosody.  That is CRITICALLY important.  The child’s Chinese proficiency will pick up by leaps and bounds if they take the time and effort to read aloud Chinese textbook and short reading passages to fluency.  You don’t even need supplemental materials!!  Reading aloud to fluency requires repetitive exposure to the same characters and sentence structures, such that the proficiency level for the same characters, expressions, and sentence structure go up IMMEDIATELY.  Do that for all the Chinese materials from school all the time and their Chinese proficiency will shoot up in no time.  I guarantee it!

This link provides some examples of dd#2 reading aloud over the years.