About 6 weeks ago we started using My First Chinese Reader. I have been very impressed at how my kids are picking up Mandarin using that program. It not only teaches how to say words and sentences, but it teaches your child how to read and write in Mandarin.
We are going slowly and thoroughly with side practice on pinyin and tones. We have been using sites like this one to practice hearing the different tones. We all work on it together and we have improved our discrimination of tones greatly from practice.
Here my boys are practicing making sentences with their Mandarin flash cards. I tell them a sentence and they have to choose the correct cards to make the sentence. The sentence made in the picture means “How are you?”