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Simultaneous Equations

March 10, 2019 3 comments

It’s been a while since i last wrote anything here. Which says more about how busy I’ve been than my desire to write, but I hope to start writing more regularly.

This week I was teaching simultaneous equations and a student asked a question that made me think about things so I thought i would share.

I was teaching elimination method and I had done some examples with the coefficients of y having different signs and I put one on the board with the same signs and asked the class to think how we may go about solving. One of the students in the class put uo his hand after a while and said he thought he had solved it.

5x + 4y = 13

2x + 2y = 6

I asked hime to talk us through his thinking and he said “first I multipled the bottom equation by -2”

5x + 4y = 13

-4x – 4y = -12

“then I added the equations as before”

x = 1

“Then I subbed in and solved.”

2 + 2y = 6

2y = 4

y = 2

“so the point of intersection is (1,2)”.

This wasn’t what I was expecting. I was expecting him to have spotted we could subtract instead, but this method was clearly just as correct. It wasn’t something I had considered as a method before this, but I actually really liked it as a method and it led to a good discussion with the class after another student interjected with her solution which was what I expected, to multiply by 2 and subtract.

It was a great start point to a discussion where the students were looking at the two methods, and understanding why they both worked, the link between addition of a negative and subtracting a positive and many more.

I was wondering, does anyone teach this as a method? Have you had similar discussions in your lessons? What do you think of it?

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Another Year Over

July 22, 2018 Leave a comment

So this is summer, and what have you done, another year over and a six week holiday just begun. – What Lennon may have written had he been a teacher.

I know what you are thinking, “why are you up so early? It is sunday and it is summer!” And you are right to wonder. Usually its my body clock that makes it so, but this year my 6 year old daughter has taken on that responsibility. Argh.

This year has been a good one for me. Tough in places, but enjoyable over all. I work at a school where I like my colleagues, like the vast majority of the students, feel that the department I work in is strong and that the senior leadership know what they are doing and are making decisions that are pushing the school in the right direction. When I moved to my current school, which was in the process of academy conversion following a 4 Ofsted grading, part of the draw was the chance to be part of affecting a positive change and improving the chances of the students. In the 2 years I’ve been here I’ve seen massive improvements and can see the trajectory we are on.

There’s been some tough times, but there has been some good ones too and I look forward to next year and our next steps in the journey.

This year I’ve spent a lot of time improving subject knowledge amongst the department. I feel this is something that needs to continue. It was made necessary this year as we had a number of non specialists and trainees in the department and most of the experienced maths teachers had never taught the new content that is now on the GCSE. This is something that needs to conrinue next year. We have no non specialists next year, but do have NQTS, trainees and staff who still wont have taught the new content. These sessions allow not only for building content knowledge but also for discussing subject specific pedagogy and possible misconceptions.

I’ve also thought a lot about transition from KS2 to KS3, this has been driven in part by a need to improve this area and in part by a fascinating workshop we hosted led by the Bradford Research School. I hope to write more about the workshop and the fascinating findings I’ve had while looking at KS2 sats data, nationally and locally, and the KS2 curriculum. Suffice to say, if you are a secondary teacher who hasn’t looked, your year 7s probably know a considerable amount more than you think they do on arrival.

The KS2 sats provide some great data and there really is no need to retest students on entry. Except maybe the ones who have no data. I’ve always been averse to KS2 SATS but the data they produce is so rich I feel I’m coming round to them. Although I’m not sure I agree with the way they are currently reported and I certainly stand against the idea of school league tables.

I’ve not written as much as I would have liked on here this year, and I hope to change that going forward. I didn’t decide to blog less, it just sort of happened, so hopefully I can turn that around.

Now it’s summer, I’m looking to relax, have fun and to teach my daughter how to enjoy a lie in….

Eid and Exams

June 15, 2018 2 comments

Today is the day that all the students in year 11 at my school, and I believe a majority across the school, sat their final GCSE paper. It was a physics paper. Today also happens to be Eid al-fitr. Eid is a holy day in the Islamic faith and marks the end of the holy month of Ramadan.

Eid al-Fitr is an important day in the Islamic faith. Muslims start it out by attending the mosque for prayers, before sitting down to share a meal with their families, which will be the first time they have done this during daylight in a month.

I teach in a school where, I believe, around 30% of the student body practice Islam. This year has been particularly hard for year 11, as many have been observing the fast of Ramadan during their exam period and have had to miss important parts of their Eid rituals and celebrations in order to sit their final exams. Eid al-Fitr, and Eid al-adha – the most important Islamic holiday, follow the Islamic calendar and as such move year on year. Next year, Eid al-Fitr falls on June the 4th, the same day as one of the English Language GCSE exams, which ALL y11 students will sit, along with Business and music exams. This date will also feature A Level papers for English Language, English Lang and lit, art, RS and Chemistry.

Personally, I would advocate for all holidays of all the major religions to be made bank holidays as the UK becomes an increasingly wonderful multi-cultural and diverse place, but I understand we are a long way from that dream becoming a reality. However, I am certain that a more achievable goal is becoming a society that manages to schedule GCSE and A-Level exams around such an important event.

Many students this year have been disadvantaged this year because they have had an exam on a day that is massively important to them, their families and their religion. GCSE exams that fell today cover science, taken by the vast majority of students, and Citizenship, an exam I would argue was extremely important. A level exams that fell today were PE, Economics, English literature, Mathematics, Further Mathematics and Chinese.

In the 2011 census Islam was the second biggest religion in the UK behind Christianity, and also the fasted growing religion. There are many local authority areas in the UK where more than 25% of the population follow the Islamic faith. These included Bradford, which is where I work, Blackburn, Luton and Birmingham. Some areas are over thirty, which includes Tower Hamlets, which has around 35% of its population following Islam.

GCSE and A Levels are important examinations; they massively affect the future of those that sit them. The stresses on students at this time is massively high and I feel that it is hideously unfair to make this more difficult on one subset of students purely based on their religion. To have a few fallow days during the exam period would mean what? Lengthening the session by a few days?! Surely it’s time we stopped punishing students for what they believe in.

Angle problem

December 5, 2017 2 comments

Today has been quite a geometric based day for me. I spent a couple of hours solving non-RAT trigonometry problems with year 10 and then a while with year 11 looking at various algebra angle problems. Then I went on Twitter and saw this from Ed Southall (@solvemymaths):

A couple of nice parallel lines questions that I might grow at y11 tomorrow.

Both are fairly straight forward to solve. I looked at the first one, imagines a third parallel line through the join if x and saw x must be the sum of 40 and 60 hence 100.

The second I saw an alternate angle to the 50 in the top triangle and used angle sum of a triangle is 180 to spot that x is a right angle. I glanced down at the responses and saw the vast majority had the same answers as me. That would probably have been the end of it but then I noticed this response:

The same thought process for the first one, but a significantly different approach to the second.

It made me wonder what approach others would take, and which approach my students would take. I wondered if the first problem had led this respondent into this solutions the second, and if so why it hasn’t had the same effect as me.

I don’t know if either approach is better, I just thought the differences were interesting. I’d love to hear your thoughts on it and how you would approach it.

Reverse percentages and compound interest

November 15, 2017 3 comments

The other day a discussion arose in my year 10 class that I found rather interesting. There was a question on interest which incorporated compound interest and reverse percentages. One student was telling the other how to find the answer to the reverse part, “you need to divide it, because it was that amount times by the multiplier to get this amount and divide is the inverse of times.” All good so far, then they discussed how to complete it if it was a reverse of more than one year, “so in that case it’s the new amount dived by the multiplier to the power of how many years.” I was pleased at the discussion so I didn’t really interject.

Then one of them aid, “if I’m looking for two years ago, can’t I just times it by the multiplier to the power -2? Wouldn’t that work.” I thought this was an excellent thought process. The other student disagreed though, sating “no, it has to be divide.” So I thought at this point I’d better interject a little.

“Does it give you the same answer?” I asked. They both thought about it and tried it and discussed it and said yes. So I asked “does it ALWAYS give the same number?” they tried a number of scenarios using different amounts, different interest rates and different numbers of years. Eventually they had convinced themselves. “Yes, yes it is always the same.”

“So is it a valid method then?” I probed. Some more discussion, then one ventured “yes. It must be.”

“Why does it work?”, I then asked. And left them discussing it.

When I came back to the pair I asked if they could explain why it works and one of them said, “we think that it’s because multiplying by a negative power is the same as dividing by the positive version.”

Dodgy Microsoft Graphics 

October 10, 2017 1 comment

So my new laptop arrived today and I quickly set about using it. It’s a Windows 10 laptop and as such has all the usual Microsoft stuff preloaded in it. I was going to set chrome as the default browser when it suggested I try Microsoft edge as it’s apparently faster and made for Windows 10. When I opened it it showed me this graphic:

Immediately I called shinanegans. The 5% difference between the green and the blue looked far too big. Initially I thought it was just down to the scale starting from 25000 and the size, but looking deeper there are also 4 extra sets if 5 notches on the blue which further add a to the illusion.

All in all a terrible diagram. Poor form Microsoft. Poor form.

Infuriatingly impossible exam questions

February 9, 2017 4 comments

Today I was working on some Vectors exam questions with my Y13 mechanics class and I came across this question:

A student had answered it and had gotten part d wrong. What he had done was this:

I have recreated is incorrect working.

Obviously he had found out when the ship was at the lighthouse, instead of 10km away. I explained this to him and started to explain how he should have tackled this when a sudden realisation angered me.

Now for those if you that didn’t work through the question, here is the actual answer:


Can you see what had me infuriated?

This is an impossible answer! If the lighthouse is on the trajectory of the ship and it will hit said lighthouse at t=3 then that would stop the ship! At the very least it would slow it down!!!! In reality it would have to avoid the lighthouse and change trajectory. Meaning the second answer, T=5, would not happen under any circumstances!

My initial thought was: “are they expecting students to spot this and discount the second answer? That’s a bit harsh.”

So I checked the markscheme:


Nope, they are looking for both answers. Argh! I can understand using a real life context in mechanics, I really can. But why not check for this sort of thing!

What do you guys think? Is this infuriating or am I just getting get up over nothing? I’d love to hear your views in the comments or via social media.

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