I recommend pretty much anything from みんなのうた in the 1980s. Most of the songs are simple, and chances are your teacher will know them all.
For example;
YouTube - メトロポリタンミュージアム
YouTube - 真っ暗森の歌
YouTube - ラジャ・マハラジャ
etc etc
Possibly not at all familiar to your teacher, but a personal favorite of mine is るるるの歌.
Seriously, I love them and end up turning the tv up whenever any of them are on.
Regular version;
YouTube - るるるの歌
Birth version;
YouTube - るるるの歌 おとこオオカミ編
Future version (currently running);
YouTube - るるるの歌～未来編～