Should we move the decimal point?

So today I had a bit of a moment in my bottom set year 10 class.

It was our second lesson together, ever, and we were multiplying and dividing by powers of 10. Together, we constructed a place value grid on the board and worked out that if you divide by 100, the numbers move to the right, two columns. During the utterly thrilling session of Multiplying & Dividing by Powers of Ten Bingo, I noticed that some pupils were moving the numbers in the opposite direction to what we had decided on.


They were so used to moving the decimal point that, when we had discussed what direction they go in when you multiply or divide, they applied the direction to the decimal point instead.

At that moment I thought to myself “am I doing the right thing?”.

This class will always find maths a challenge. They will take their linear foundation GCSE at the end of year 10 in order to give them an early bash at it, followed by a re-sit in November of year 11 and then again in June of year 11. I have two years to help them get to grips with the subject and, here’s the crucial bit, I have the opportunity to help them attempt to get a C in Maths.

Should I teach them that the decimal point stays put and the numbers move? Or should I teach them to move the decimal point?

This throws up a massive question over the way I decide to teach these pupils for the next two years. I know that I could teach a ‘certain’ way in order to train them to answer exam questions, but this will be purely instrumental, tricks, rules, methods to follow.

My instinct was to teach relationally, especially as I have two years with them (for the past couple of years I have got yr11 bottom set when they arrived in yr11, so only had one year with them). However, when I realised they were so used to moving the decimal point, I wondered whether I wasn’t just making their life harder by insisting on drawing out the place value grid.

Or can I have a combination? Can I teach them about multiplication and division using a place value grid and then finish off with a “now you know how it works, here’s a quick trick to make your life easier”?

This decimal point dilemma has really got me thinking. What do I want? Pupils with a relational understanding, although this may take longer to achieve and therefore slow down the pace with which we cover content, or pupils who can follow methods and rules who may be able to answer exam questions through training and therefore be more likely to get a C and, thus, more likely to have choices in life. (I am torn, by the way, between ‘helping pupils to get a C in order to improve their opportunities in life’ and ‘not devaluing a C grade by training pupils to achieve it through following rules when they may not really understand it’. Some may say those pupils do not deserve to pass maths, but others may say it is those pupils who need our help more than anyone.)

It makes me uncomfortable and I’m not sure what I want. I know I want to do the best I can for them, so I’ll focus on building their confidence in maths and building trust and rapport with the class. I think I’ll have to work out what is right for them and what is right for us.

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Making a Maths Music Video

Thanks to #mathscpdchat I discovered this video and it came at just the right time as I was doing trigonometry with my year 10 class. They are an awesome group of pupils with such a mixture of different personalities. Their targets are Cs and Bs and most of them are on track, but they are a class for whom maths does not come naturally and, for many of them, it has never been their favourite subject.

All year I have been using maths songs to help them remember important formulae, such as the circle song, the area of a trapezium song, my cube number song (that I made up when I was 13, what a cool kid!) and one they got me to make up on the spot about stratified sampling to help them remember the definition (I’ve started taking requests!).

So, when they saw Gettin Triggy Wit It, their immediate response was “Miss, that was so good, can we make one?”. In that moment, I had to make a quick decision.

1. They could just be wanting to ‘waste time’ in making a video instead of doing more trigonometry…

2. They really loved that maths video and we already do maths songs, they want to make something ABOUT MATHS that cool that they can be proud of.

So I said, “Yes, yes we can!”

Next lesson, we split into three groups in order to come up with lyrics for three songs. The first, Y=MX+C to the tune of YMCA, is finished, I’m just waiting for the last 2 parental permission notes to come in before we go global (youtube). The second, about Pythagoras to the tune of Do Wah Diddy, is in the editing stage and the third, Transformations to the Cha Cha Slide has lyrics but filming may not happen as it was a little sketchy.

In total, we spend four lessons making the videos, plus about four hours of my own time editing (that’s one video’s worth of editing so far). Was it a valuable use of class time? You could argue it both ways. It is true that they did not spend those lessons practising mathematical skills or learning new content. For me, though, a big part of teaching Maths is about rapport, between pupil and teacher and between pupil and subject. (So much so, that I wrote my PGCE final masters level essay on Teacher-Pupil Relationships and their effect on learning). I knew that the process of making a maths music video would have a massively positive effect on their view of maths (for the right reasons? Not sure).

The amount of time I spent editing the first video was massively appreciated by them and, when I showed the video in class, it received a round of applause from them, plus a sea of excited, proud and pretty chuffed faces.

Amazing maths? No. Worthwhile lesson? In my opinion… totally.ImageYou can now find our maths music videos at or (the Vimeo link is the best quality).


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Year 7 Maths Day

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 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

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:numberline what they came up with
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.

straight lines prompt

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).

level 3 inquiry

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”.


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Year 7 Inquiry Maths Enthusiast

Year 7 Inquiry Maths Enthusiast

On Friday I did the ratio inquiry from the fantastic inquiry maths website:

One of my year 7s was so enthused by our inquiry lesson on Friday that he brought this in on Monday. He had spent some of his free time at the weekend writing up his inquiry and creating some more! Amazing. I love that he was so into what he was doing that he wanted to carry on, even in his own time.

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