**Year 7 Maths day: 6 lessons, 3 sessions, 160 pupils doing maths all day long.**

- Session 1: Codebreaking
- Session 2: Team Maths Challenge
- Session 3: Inquiry Maths

So, yesterday, I had an awesome day because I got to teach 3 double-lessons of inquiry maths to three different classes of pupils. At our school we have two parallel top sets, middle sets and bottom sets. Yesterday, the two parallel sets were combined to make two classes, each a mixture of pupils from each class. It was a great opportunity to teach some year 7 pupils that I do not get the chance to interact with on a daily basis.

Each group rotated around the 3 sessions, having a double lesson in each session.

The teachers running the sessions stayed with their activity, being the ‘experts’. I was the inquiry maths teacher, along with my Head of Department.

**How to choose the right prompt for the inquiry?**

Talking to Andrew Blair (creator of http://www.inquirymaths.com) confirmed what I already thought – the numberline inquiry was the best one to do with a class new to inquiry. However, as I have been doing inquiries with my top set all year, I had already done it with them, so we were forced to choose an alternative to use with the top set. I chose the parallel lines inquiry as I hadn’t done it before and it was incredibly open.

**Numberline inquiry**

The first class I had for this was the middle set year 7. As can often be the case with an inquiry (especially with a class new to inquiry), the start of the lesson felt a little lacking in pace – this is the first test for a new inquiry teacher as it can be tempting to start telling them what to do so that they are ‘doing something!’. I asked pupils for any comments or questions and they came up with the usual “the answer is always 2” and the not so obvious “why are the answers to the multiplications always even?” – fantastic!

As it was their first inquiry, I restricted them to choosing one of those two questions to inquire into as I felt those were the most mathematically valid. (NB I have, in the past, let pupils look into any question at all and this sometimes results in pupils doing something not very mathematical but has also resulted in pupils doing some great maths I wouldn’t have thought of – dilemma!)

**Highlights**** of the Numberline Inquiry**

One group decided to look into sequences and what happens if, rather than using the counting numbers, you go up in twos or threes, etc. Their findings are below:

For all pupils, they either practised something like multiplying negatives, decimals or long multiplication or thought about properties of sequences. Some groups Found that if they went up by 0.01 the difference was 0.002 and if they went up by 10 each time, the difference was 200. All fantastic stuff.

**Parallel Lines (or Straight Lines) Inquiry**

Pupils came up with questions and comments about the angles involved, the area of the ‘square’, whether or not it tessellated, the ratio of the lengths of the lines, how many lines there were and grid method multiplication. An interesting line of inquiry was to work out the bearings of the ‘paths’ that the lines traced out.

One group adapted the prompt by tilting a pair of lines and adding another transversal as below (described by Andrew Blair as a prompt to a guided rather than open inquiry, but the pupils came up with it themselves).

Although my top set were used to inquiry lessons, they found the straight lines inquiry much more challenging – perhaps because it is so open. I was disappointed that no-one thought about the equations of the lines and, if I were to do this inquiry again, I may consider running it around the time of a straight line graphs topic – although would this be me trying to engineer the outcome? Perhaps putting a co-ordinate grid behind it would have the same effect.

I struggle with the balance between allowing pupils the freedom and creativity to follow their own line of inquiry and guiding them towards mathematically valuable questions. Sometimes, they are unable to articulate exactly what it is they want to inquire into, so their questions seem uninteresting, but the maths that follows shows what they actually meant was something more sophisticated. On the other hand, it is depressing to watch a pupil come to a dead end whilst trying to answer a question which does not have an interesting answer.

I would argue that pupils ask better questions in the future if they are allowed the freedom learn from their mistakes. However, it is tough to justify the classroom time as I want them to be doing interesting maths as much as possible, so I have increasingly guided the class as to which questions to choose from. It’s a difficult one and I don’t have the answer.

What I do know, is that I thoroughly enjoyed the day and feedback from students suggest that they did too. I will end with a quote from a middle set year 7 girl: “Doing inquiry maths was the best maths lesson I ever had because it taught me how to think”.

Thanks for sharing this Mrs M! I guess part of being a mathematician is going down dead ends, picking yourself up again and trying another one. The student who said it taught her how to think was onto something! I guess if this was becoming a habit for a student I’d want to give more direction to help them get into the meatier maths but I wonder if we could coach them towards that rather than direct?