A great way to get students thinking about mistakes and misconceptions and hence deepen their understanding of topics is to have them mark the work of others. There are some great resources hosted on TES that will allow your students to do just that.
The resources I have come across are:
R Barnard’s Bob’s Ratio Homework
Craig Barton’s lovely little starter on Algebraic Misconceptions (this one is truly tried and tested – I used it as a starter for a lesson observation and followed it up with a class discussion on what advice students would give to students making the kind of errors here – it went down rather well with the observers!)
Kaszal’s Fractions Mistakes
and Damian Watson’s
Damian, Craig, Kaszal and R Barnard these are brilliant! Thank you.
On the subject of mistakes, the Classic Mistakes website has a gallery of posters of classic errors made in Mathematics. These could be a prompt for a useful discussion starter activity. Note that an audio file is also available for each poster.