My favourite open-ended problem always used to be – make 24 exactly using only and all of 3,3,8 and 8. I was taught this as part of my PGCE and I used to pull it out whenever my whiteboard wouldn’t switch on or when I finished my lesson too early. I realise it isn’t really open-ended but it was in a way because no class every solved it without several hints from me.
More recently I discovered Don Steward’s blog which is full of interesting problems. This week I’ve been using this – Four Operations and it’s gone down really well. I teach reluctant maths learners and they are particularly reluctant in the first few weeks. This is an activity that they can all do. I model it with an example to make sure it’s really clear. Then I let students work on it till we hear the first “Yes I got it”. Often that is the first maths success that learner has had for years and can be the start of my year-long maths isn’t torture campaign. I collate the different numbers students have tried on the board to help refocus the students and then we keep going till all three solutions are found. I prompt about the numbers dividing exactly if they are getting stuck but they have normally worked that condition out by themselves by that point. A satisfying and simple problem that is an easy win for students.