What’s the question?

(This post is an update of my post from 2013 and now includes the more recent, excellent resource Goal Free Problems from Peter Mattock.)

Using diagrams as prompts like this is excellent for Retrieval Practice.

Seeing this well-received resource, GCSE Question Prompts on TES reminded me that I have successfully used this idea myself before. For example for GCSE revision I have given students a selection of various triangle diagrams and asked them what the question might have been. This proved to be a useful way of revising several topics – some of which students sometimes mix up! For several of these triangles there are many possibilities and students can be asked which lengths and / or angles they could work out.

Further excellent examples come from Mark Greenaway – GCSE Visual Prompts for both Higher and Foundation. Mark’s resources (Prompts 1) show the diagram first and then also include the complete question. Prompts 2 provides 25 starter prompts for students to produce their own questions and answers using the given information.

Higher – Visual Prompts

On a similar theme, not a diagram this time but an extract from a question: see Algebra Snippetts.

From Andy Lutwyche comes a very high-quality series of ‘The answer is …What was the question?’ resources. A variety of topics are covered and all answers are provided.

Peter Mattock has created Goal Free Problems, a site he set up, in his own words “to allow teachers to access and share goal free problems created by myself and others. Goal free problems have been proven to support pupils in improving their knowledge and understanding by removing the cognitive load of the goal and therefore not prompting means-end analysis of a problem.”

Here you will find hundreds of questions categorised by topic; there are also mixed questions available. A wonderful resource.

On the subject of diagrams, I really like Tom Sherrington’s post “Empowering students to own their learning solves maths problems“; a great idea to start with a diagram with no labels at all as a way into a problem. I tried this with Year 10 (very able students), presenting them with only Tom’s diagram and was very pleased indeed with the outcome. I didn’t even give them the question – just the diagram (a small copy each) and we started by deciding what the question might be. We quickly got onto areas as a possibility so then answered Tom’s original question ‘what fraction of the shape is shaded?’. The class happily discussed how to solve the problem and a student asked ‘can we write on the diagram?’ which of course was perfect – absolutely they could write on it. We solved the problem, revising some basics and had the discussion about what to do when you don’t know what to do! I will certainly use diagrams with no labels again.

This idea could be used for a starter on just about any topic – provide students with an image or perhaps just an expression and ask them to write a question to go with the image.

MEI have an excellent free collection of GCSE starters. Designed for the start of a GCSE lesson, the diagrams and questions are very clear and will display well on the IWB. There are several starters under the following headings: Mathematical Reasoning, Number, Algebra, Geometry and Measures and Statistics and Probability. Files with the answers and teachers notes are also provided. Many of the diagrams here could be used for students to write their own questions. It is not always possible to have the IWB up and running, particularly if you are coming from a different room and I do like to get students working straight away. Experimenting, I found that I could take a screenshot (I do like the Windows snipping tool) and fit eight to a page! I used a Word document with very small top and bottom margins and a two column layout.

Staying with MEI, Bernard Murphy has some great ideas here on using pictures in A Level trigonometry. Look at this diagram – all the trigonometric ratios!

How creative can you be? I wonder what they would make of something like this…

See also – Numbers – Visualizations

For a wonderful introduction to equations using diagrams – see Mobile Puzzles – Algebra

Perhaps a photo from the Bad Maths collection on flickr

cc licensed ( BY ND ) flickr photo shared by Danny Nicholson

Click here for the complete collection.

or a holiday snap!