mr barton maths

Open Middle Problems

Problems with a closed beginning, a closed end, but an open middle — encouraging deeper thinking, multiple strategies, and mathematical reasoning.

Browse Problems ↓

What are Open Middle Problems?

🔒 Closed beginning — every student starts with the same problem
🔓 Open middle — there are multiple ways to approach and solve it
🔒 Closed end — everyone is working towards the same answer
🏆 Optimise — find the biggest, smallest, closest, or most interesting solution
✅ Verify — check each other’s answers and strategies

How to Use Open Middle Problems

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Teachers

Try an example together first to establish the rules. Give students mini-whiteboards for messy thinking — they will need to try, erase, and retry. Use the 4-2 approach: 4 minutes silent work, then 2 minutes sharing strategies with a partner.

Tip: Stop the class regularly to share the current “best” answer, get everyone to check it, then challenge them to beat it.

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Students

Start by choosing some numbers and testing them out. Don’t worry about getting the best answer straight away — the goal is to explore, learn from what doesn’t work, and gradually improve your solution.

Tip: Each problem has an optimisation challenge. Once you find a valid answer, ask yourself: can I do better?

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Parents

Work on the problem together — each try your own numbers, then compare strategies. These problems are great for showing that maths isn’t just about getting one right answer, but about thinking strategically.

Tip: Ask “Why did you choose that number?” and “What would happen if you changed this one?” to spark great conversations.

Tips for Making Open Middle Problems Effective

Four strategies to get the most out of these problems in your classroom:

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Try an example together — choose some numbers as a class, test them out, and make sure everyone understands the rules and structure of the problem.
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Use mini-whiteboards — Open Middle problems get messy! Students will want to try numbers, rub them out, and try new ones. Much harder to do in an exercise book.
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Use the 4-2 approach — 4 minutes of silent, independent work to find a “best” answer, then 2 minutes of collaboration with a partner to share and learn from each other.
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Track the class’s best answers — stop regularly, ask who has the best answer, get everyone to check it, record it on the board, then challenge the class to beat it.
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I first heard about Open Middle Problems from Robert Kaplinsky on my podcast. The original collection, mapped to US Common Core Standards, is at openmiddle.com.

I’m adding new problems regularly — keep checking back for more! 🚀