Short visit to Shanghai

I plan to study Chinese Language in Taiwan for 3 months, beginning May 21 and after completing the study in Aug 21, my wife and myself plan to visit friends in Shanghai for 5 days. Do we need a visa visiting China, we hold Canadian passports, If we do, we have a problem of applying for it in Vancouver on time, as we leave for Taiwan on May 20, and it is only valid for 3 months from the date of the application.