Equation recall test

This was supposed to be a really quick job. For something I’m working on, I was looking at the equations students need to recall for the GCSE Physics exam (specifically AQA). And it annoyed me that they weren’t in a useful order, or a useful format for testing. So I’ve made a testing sheet, with pages for Energy, ‘mostly Electricity’ and Forces.

There are four columns, which are blank in the first three pages (for students) but completed in the answer sheet version. Because I’m good to you.

Download eqn testing sheets as PDF

Equation for…

I’ve given the word, not the symbol – thoughts? (Could/should that be another column?) I’ve removed a couple of what I see as duplications, and missed out momentum because I was thinking of this as for everybody. Plus it would have mean adding another row and I was sick of messing with formatting.

Which variables are involved?

For students to write in the variables in words, as a starting point. The idea would be that you can give partial credit for them getting part way there, because we should recognise the early stages of recall. You may off course have them skip this bit later on.

What are the symbols?

If they know the variables, can they write down what they will look like in the equation? This would be the other place for them to show they know what the ‘equation for…’ variable could feature in symbol form.


Formatted as best I can, in a hurry in Publisher. I’ve used the letters as listed on the formula sheet, p95 of the specification. Even when I disagree.

As ever, please let me know if/when you spot mistakes. Because it’s in Publisher I can’t upload the editable version here, but drop me a line in the comments if useful and I’ll send it your way.


Axes of Mathematical Doom

Just think… in a few weeks, you’ll have a new crop of brand-new Year 7 students. Shiny faces, uniforms without holes and a complete pencil case. For about a day.

So it’s nearly time to teach graphs.

You may have already seen the resources produced by the ASE on the Language of Maths in Science (LoMiS). If not, go download them for free and have a look. It’s worth it, really. For a quick taste, Richard Needham did a piece for the Royal Society of Chemistry a while back which is a great introduction to the aims of the project.

And here’s an approach I’ve come up with which you may find a useful beginning. It’s based on what I’ve done in lessons in the past with a final addition I’ve been discussing recently with delegates and colleagues at the SPN Oxford Summer School.

1 coordinates


1 Number Lines

Putting numbers in sequence on a line is something students start to do at a young age, long before secondary school. To be honest, if kids can’t put whole numbers in the right order then graphs are going to be a distant dream. I agree that decimals make this harder at times, but I’m working on something about that too. Next week, maybe.

So give students a list of values and ask them to put them on a number line in order. Add challenge by having them convert values between units first, or have different numbers of significant figures. Top half of image:

Number lines

2 Number Lines to Scale

They might do this automatically. If not, it shouldn’t be too hard to have them do so (image above). Once they have a scale sorted out for the line, placing laminated cards for your supplied values along it should be straightforward.

3 Number Line to Scale = Axis

If you now have your students put the two number lines (one from each set of values) at right angles, they should be able to see that they’ve defined each point.

4 Mathematical Axes Of Doom

Two wooden dowels from B&Q (other DIY stores are available), with insulation tape wrapped round at regular intervals. I deliberately chose different intervals. Next time, I’d probably use wooden dowels with rectangular cross-section, simply so they don’t roll. You could use metresticks but I wanted to avoid any numbers. The tape is all you need, really.

2 axes

Put them at right angles and you have a set of axes, with the intervals clearly marked. Add the coordinate cards – because students have used the idea of a coordinate system for a lot longer than they’ve used graphs to tell a story – in the right places. They’re easy to adjust, so there’s less stress. (Low stakes, yes?) And if they look from above, any pattern is clear and anomalies can be considered. They can even see the best-fit line.

3 plotted

Extension ideas; use larger or smaller cards to get over the idea of precision in the readings. There is a link here to the idea of error bars, something we don’t usually cover but may find useful.

Thoughts, ideas, suggestions? Please let me know in the usual ways.

NB: you get funny looks if you carry the sticks on to a train.

Numbers Game

Now, before you groan, we’re not just going to ‘do’ maths. We’re going to use maths to solve a problem. Or at least define a possible problem. So don’t give up just yet, okay? And no, this isn’t about data tracking, important as that is.

Let’s imagine that a school has a half dozen members of SMT. Let’s presume they all have a keen interest in teaching and learning, keeping up with CPD in their subject and so on. They’re in a position of power/responsibility, and they want students to learn more and their grades to improve. All fair assumptions so far? (Stop sniggering at the back.)

Between government initiatives and their own ideas, let’s assume that each half term every member of this notional SMT has to try something new in their classrooms. I don’t just mean a different kind of starter, but trialling or testing something that might have a wider impact.

It might be the latest DfE-endorsed SPAG marking policy. It might be a new behaviour tracking system. It might be something they’ve picked up at ResearchEd or NorthernRocks. Whatever it is, it gets tried out and the member of staff reports back to their fellow senior colleagues. Let’s say only one in six of these changes – all intended to make a difference – are rolled out more generally. SMT meetings correctly minute that ideas a b and c have been rejected due to lack of impact, that d and e from the local authority can be done in a way that doesn’t affect classroom staff, and only idea f will be actioned by so and so.

Each member of SMT tries one idea at a time with their classes. If this takes an extra ten minutes per class over a fortnight timetable, that’s a rough average of an extra half-hour per half term per class. On a fifty percent timetable, that’s maybe five or six classes. This is perhaps 30 minutes extra per week, but the teacher can see the difference and believes, honestly, that the time is worth it. They are sincere. They might even be right.

You can see where this is going, can’t you?

Six members of SMT. Over a year, each supervises one new intervention (in their management time, because this will end up being part of their TLR performance management). Oversight gets added to the school calendar, it’s listed in agendas and discussed in emails and INSET.

For a classroom teacher with a full timetable, each of these six initiatives adds an hour per week to their workload – but it’s cumulative. By the end of the year this would work out as six hours extra every week. It’s arrived gradually, and in many schools the cost is concealed by reduced timetables due to study leave and the post-exam lull. But in September…

Time is a limited resource. If we work hard – and I really think we do – then adding more jobs can only work in three ways:

  1. Do less of something else
  2. Do other things less well
  3. Take more work home

This last option – effectively invisible overtime – is often what happens.

An Alternative

Each term, based on my approximations above, there will be twelve proposed initiatives. It shouldn’t be too hard to work out what the impact would be for a few ‘generic’ staff members :

  • Mr Lower-School (mainly KS3, some KS4 teaching)
  • Ms Olderkids (Mainly KS4/5 teaching)
  • Mr P. Art-time
  • Mrs SM Tee with 30% timetable
  • etc

Now, it’s likely that these will show who is affected most. For example a colleague with mostly sixth form classes won’t necessarily appreciate the effect of mock exams. If each of 120 scripts (that’s the rough total of yr10 and yr11 papers I had to do) takes 10 minutes, that’s 20 hours – and that was the second set of mocks this year. On the other hand, I don’t teach much KS3 so a colleague who has lots of yr7 and yr8 classes will suffer much more from something changing our reporting system for them.

I hate to use reality TV as a model for schools, but there is perhaps something to be learned. Every new initiative is supposed to be examined for impact on workload anyway. So how about we make this assessment – which is done by SMT anyway – open to colleagues, with voting and comments from the people who will have to put them into practice?

Now, sometimes it’s not a question of whether we change something or not – it has to be done. But surely this will give more information about how and when we put a new demand into place? Listing existing interventions, and the time each of them takes, would also be interesting. Obviously marking loads, coursework deadlines etc vary between subjects. But at least we can then have the discussion about what will be removed to make time for the new approach. What are SMT prepared to sacrifice so that we can fit this latest demand into the zero-sum game of our time?

I’d be really interested in ideas and comments from colleagues who have been part of this process. Maybe I’m being unrealistic – maybe my numbers are miles off. But until I’m part of SMT (roughly a week after flying pigs are sighted over my school) it’s as close as I’ll get without your help.

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Maths Skills For Science Lessons

After taking part in a recent online CPD trial with the Yorkshire and Humber Science Learning Centre, I’ve been trying to find ways to help my students use their maths skills in a science context. (And no, this wasn’t prompted by the recent SCORE report.) As we discussed during the course (and yes, I want to blog about it in more detail) the issue isn’t always that they don’t have the skills – it’s that they don’t use them. Sometimes it’s about language differences (positive correlation vs directly proportional, for example) and sometimes it’s just some kind of mental block. I’m trying a few different things:

  • providing science formula sheets to Maths to use for practice in lessons
  • producing data sets that they can use in Maths lessons
  • display work highlighting similarities and differences between science and maths vocabulary

But the focus for the blog post is something different. I’ve produced (but not yet finished trialling) a booklet for students to use and refer to in Science lessons. It covers a few areas identified by students and colleagues as causing problems. Each page includes an explanation, worked examples, hints and tips, possible applications and practice exercises. I’m making it available here in this untested state for comments, suggestions and improvements; click on the image for the pdf.

To Come (Hopefully)

  1. Corrected version if (when?) you find problems with it, with included pages for write-on answers/notes
  2. Markscheme/answer booklet
  3. Accompanying A4 display pages with extracts
  4. Additional pages if sufficient (polite) demand

I’d really love some feedback on this, everyone – please comment with improvements and suggestions.