I was delighted when I found this app. It is called ChineseSkill and available for download on Android as well as the iOS devices including the iPhone and iPad. If you have both, they will synchronize so you can use one or the other while learning. You can use the iPad at home and continue with the iPhone on the go.
The app is completely free. I like its fun approach of helping you learn through a repetitive game like style. You can learn together with your child. I think the panda is kind of cute. Look at the panda poses in my screenshot after I completed the levels.
If you want to teach yourself Chinese, this app would be a good starting point. The best part is it is completely free. You unlock levels as you go along your learning Chinese journey.
In addition, they have a Facebook Page which you can check out. I like that they post cute posters about Chinese Characters. Go check out their Learning Chinese Images photostream. I love it. Here are a few examples of what you will see on their Facebook page.
The images below are reproduced with the permission of Chinese Skill.