**What's a Problem?**

A problem, in the mathematical sense, can be defined as "an inquiry starting from given conditions to investigate or demonstrate a fact, result, or law". The word originated in the late 14th century,'a difficult question proposed for solution', from Old French problĂ¨me, and directly from Latin problema, from Greek problema 'a task, that which is proposed, a question' (source: etymonline).

A problem from solvemymaths.com |

I like this quote from Jennifer Piggot, "A problem is something that you probably will not immediately see how to tackle or which once started will challenge your thinking. This means that at some point you are likely to get stuck and this is OK. In fact it is important that you get stuck so that we can talk about possible ways of getting unstuck" (source: nrich).

**My Favourite Problems**

During next week's Twitter chat I'd like to see examples of your favourite problems. These might be interesting questions that you use when teaching specific topics - for example do you have a great question on standard form? Straight line graphs? Sequences? Remember that we're focussing on problems as opposed to resources, activities or worksheets.

Here's one of my favourite problems:

Source: Chris Smith's Newsletter, Issue 51 |

Eventually I aim to pull together a set of good problems for each topic on the curriculum - I've made a start with this Pythagoras Problem Set.

Problems don't have to be highly complex. Any question that makes students stop and think is valuable. For example this week I was looking for a starter on coordinates for my Year 7 class. I could have gone for a standard plotting activity - I believe that ongoing procedural practice is very important - but instead I've gone for the question below:

From Squares and Coordinates (Don Steward) |

Finally, here's a problem that I've used a number of times when teaching surds - I love this one:

I really look forward to seeing your favourite problems in #mathscpdchat at 7pm on Tuesday - see you there.

**Problem Solving Resources**

- GCSE Problem Solving Materials - FMSP
- Support for Problem Solving - OCR
- GCSE Mathematics - 90 Problem Solving Questions - AQA (and PowerPoint collated by @EJMaths)
- Additional Mathematics Problem Solving Questions (& Teacher Guide) - AQA
- GCSE Problem Solving Questions (zip file) - Edexcel
- 55 Problems - MathsBox
- GCSE Foundation Problem Solving - Sheffield Maths
- Badger Maths Problem Solving Samples (Years 1 - 6) - via National Stem Centre
- Mathematical challenges for able pupils in Key Stages 1 and 2 - DfE
- Problem solving with EYFS, Key Stage 1 and Key Stage 2 children - DfE

**Problem Solving Links**

- Median Don Steward
- Solve My Maths
- Maths Problem Solving
- MathsChallenge.net
- Brilliant.org
- Nrich
- Openmiddle.com
- United Kingdom Mathematics Trust
- 1001 Math Problems
- Suffolk Maths - more problem solving links

**Further Reading**

- Taking Back The F-Word - solvemymaths.com
- What makes a rich task? - ATM
- What's in a task? Generating mathematically rich activity - QCDA
- Using Low Threshold High Ceiling Tasks in Ordinary Classrooms - nrich

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