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.

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This is a nice problem to have in the tool set. Thanks for sharing. …and I agree with your take on Don Steward’s work! He is an awesome resource.

I forgot about 24! I used to use a version of that game all the time when I first started teaching. In the version I learned, we chose the 4 numbers at random. You had to use each number once and only once to make 24 using whatever operations you want. Which sometimes led to many different ways of getting to 24, and sometimes cries of “It’s impossible!” which led to good conversations too. Thanks for the reminder!

Ooh that’s a good way to do it. I think I’ve forgotten so many great ideas. Hopefully blogging will help me remember what I’ve done.

I’ve know about 24 and about problems like the four fours, but I’m always learning something new from the MTBoS! I haven’t ever explored the “four operations” problem. Thanks for not posting the answers! I’m off to do some tinkering…

In a bit of shameless self-promotion, I’ll mention that Challenge 05 over at CollaborativeMathematics.org has a similar feel to these problems, in the sense that the goal is to build an expression out of some given building blocks. If your students liked 24 and the four operations, they might like “pieces of eight” ! 🙂

Thanks for that link. Looks really interesting. I think the bigger question is why does US paper have three holes? How odd. 😉

Oops! I meant to refer you to Challenge 06, which is the one about building an expression. (Not that Challenge 05 isn’t cool too… it’s just less relevant to your blog post. 😉