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The Bumping Method

Almost a couple of weeks ago now (I can’t find the original tweet) John McCormack (@JohnJMcCormack) tweeted to me this “bumping” method for subtraction.

I haven’t seen this method promoted before. It makes use of the fact that the difference between 9 and 4 say is the same as the difference between 15 and 10:

Subtracting a number ending in zeros is clearly easier than subtracting a general number from another and this is the inspiration for the bumping method. This is something that I (and probably a lot of people who have a good number sense) do when performing mental calculations, but I wouldn’t have thought to do it as written method. The only difficulty is remembering of the carry.

Here’s another example:

John has a website where he has posted some black and white examples

I’d be really interested to hear what you think of this method – I quite like it, but I’m not sure I’d want to teach it as the general method for subtraction.

Would you teach this method and why? Do you have any examples where you think this will be helpful or where it won’t work?

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Stuart’s Puzzle

A couple of weeks ago Stuart Price (@sxpmaths) posted this question on Twitter

I hadn’t really thought about it before but it is a bit strange that we ask similar questions about the mean in Year 7 but (I at least) have never asked an A-Level student this kind of question before.

I think it’s a really nice little question, one that is harder than you expect and gives students plenty of time to practise their algebra. My workings are below; as you can see I made a few little errors that I had to correct as I went and of course I used Wolfram Alpha instead of solving the quadratic manually!

I will definitely be using this next year when I teach S1.

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Another Fantastic Day -#mathsconf4

After having to set my alarm for 04:30 in the morning to make the train I needed to get into London and enduring an annoying rail replacement bus I’m glad to say that #mathsconf4 was fantastic; as the previous ones have been!

Before I describe in a bit more detail I want to mention the only negative aspect – no breakfast pastries. If you know me you will know that I get strangely excited about that kind of thing, so this was very sad. The cute little pot of jam that was given to me by (@tessmaths) did make me very happy though.

I’ll try to briefly describe the best bits of the sessions I went to, and leave the detail to the people who them!

Speed Dating

The day started with speed-dating to swap activities. In the past I haven’t been great at this, and always wish I had recorded what I had spoken to people about more. So this time I was more planned (I shared my Further Pure 1 geogebra conics task which I have described here) and wrote down the great things I was told about:

Dawn Denyer (@mrsdenyer)  shared her worksheet for low attaining groups which has the answers for each question somewhere in a grid for them to find and know they have likely done it correct. I’m going to try this with some of my classes.

Deb Friis (@runningstitch) talked about the idea of using the “boxing up” technique to get students to write number stories, structured like they would write a story in English. I have seen this technique before from @HelenHindle1 of Growthmindsetmaths.com, but I really liked seeing how it could be used in conjunction with a problem solving lesson to structure pupils thinking without guiding them on what to do.

Japleen Kaur (@japleen_kaur1) talked about using the date as a starter similar to the Commonly known Four Fours problem. I think this is a great starter if you are moving rooms and need something simple students can do whilst the computer loads etc as it reinforces key skills. If as Japleen does it is done regularly it could become a good habit to ensure maths is happening straight way. I liked how even her Sixth form class found this useful.

For the last person I spoke to someone I wasn’t already following on Twitter; Jen Chan (@JenJenDes) showed me a learning grid for area and perimeter. I keep meaning to try these after I had been shown one in my school by an English teacher, so it was good to see an example of a maths one!

Mark McCourt

Mark delivered the keynote this time round, and it was nice to have a change from the last two, especially as Mark is always an entertaining speaker. He was speaking on the subject of “How can we improve Mathematics Education for all”. His starting point was the fairly depressing assertion which is – we can’t. He discussed Japan, which is seen as a high achieving nation but still reflects on their maths education system and wants to find ways to improve it.  He showed this quote from Japan:

“[If in Japan], the aim of mathematics education is to make pupils hate mathematics, then in this point we may have succeeded”

He also used another quote that I like to refer to from a paper by Jeremy Hodgen (@JeremyHodgen), who is now at the University of Nottingham and co-authors:

“For every aspect of mathematics education linked to high performance in one country, a contradiction can often be found elsewhere'”

This quote led nicely into Mark’s main point – the importance of culture. All the High performing Shanghai countries have a very different culture to ours and this has a massive impact – what works in one place may not necessarily work elsewhere. I was really interested to hear about the paper where the high performance of western born children of East Asian descent was investigated. Tim Stirrup ( @TimStirrup) kindly supplied a link to the paper and I will definitely be reading this during the next week or so.

Mark ended by saying that something that teachers can do to improve maths education is for them to be “intelligent, independent and not just tow the line”. I whole heartedly agree with this.

Now onto the workshops!

From Euclid to You

Emma Bell (@El_Timbre) delivered an excellent session looking at some books in her impressive collection of old maths books. She has uploaded a padlet containing her source materials here.

The mention of Euclid’s elements led to an interesting discussion about Euclid’s five postulates and which ones are used when answering a variety of geometry problems from across the key stages. Maybe we should bring more history into our lessons? I know I don’t mention the postulates in a regular lesson on shape!

Emma also shared a great problem concerning birds from Leonardo of Pisa’s (Fibonacci) book “LiberAbaci” from 1202. I think I may write a separate post about this as it is a good introduction to under-determined systems…

There was a lovely quote from a 1958 book where Bodmas was described as a “travesty of mathematics”. I liked this whole page of division questions phrased in different ways

And I thought the way this question concerning the days between different months of the year was particularly nice:

I recommend that you take a look at Emma’s padlet where the presentation can be downloaded with some of the source materials. Emma has also shared an essay she wrote during her PGCE on proof – I’ll try to have a read of this at some point. Thinking I should also share a 6 lesson plan I wrote on circle theorems during my ITT – I’ve not looked at it since!!

The Best of the U.S.

This session was delivered by Craig Jeavons (@craigos87) who talkedabout some things from the States. Maths educators from the U.S. are very active on Twitter and maintain a directory of members of the MtBOS community here. Craig explained that he liked using stuff from the States as they are culturally similar to us and their Common Core State Standards (pretty controversial over there) are actually quite similar to our new curriculum.

I’ve used the websites estimation180.com and grapthingstories.com before. I find graphingstories really good when working on real life graphs, with all ability ranges – some of them are actually pretty tricky. The fact that the website is american also provides a good excuse to look at imperial measurements. I’ve only recently come across the website openmiddle.com, and am curently putting some of their questions into my school’s new Year 7 mastery curriculum. As the name suggests, each question has the same start and end point but there are multiple ways to get to the solution (i.e. an open middle). The website is really useful as it categorises the questions by their Grade (remember that a US grade 6 is the same as an English Year 7), and goes up to the end of high school. I really like this question:

Craig then talked about Robert Kaplinsky’s Depth of Knowledge (DOK) charts, for example the one below which I hadn’t seen before

I’d heard of the DOK as an alternative to Bloom’s Taxonomy (I’ve always been pretty derisory of Blooms to be honest!) before but I hadn’t seen it applied to maths topics before – very interesting and lots of questions OpenMiddle questions in the grid too. I think it would be nice to have something similar for all topics really.

I’m also grateful for Craig pointing out the curriculum maps on emergentmath.com. These link to the Common Core Standards and contain some links to great activities, such as this one “Square Roots go Rational” from NCTM. I’ve bookmarked these for a proper explore during the summer holiday.

Tweet Up

After a great cooked lunch (thanks LaSalle, the lamb stew was really good!) it was time for the tweet up. I played a very minor part in helping run this, all organised by the wonderful Julia Smith (@tessmaths) and with Dawn Denyer (@mrsdenyer) providing us all with some great T-shirts.

From Left to Right: Dawn DenyerNicke JonesJulia SmithEmma BellMartin NoonDanielle BartramJo Morgan and me.

We had lots going on, including Jo’s lowest integer game, the QR Cubed Cube, a photo booth, some lovely  O-Level questions. Make sure you come along to the Tweet Up at the next conference everyone had fun – here’s Beth (@MissBLilley) with her folded cube:

What I Learned from Teaching new GCSE content to Year 10 and 11 Students

This session was delivered by Sarah Flynn, a head of department who is also a maths advocate for AQA and as such helps schools in delivering AQA content. I was hoping that there would be more discussion on ways to teach some of the new content, but it was definitely good to look at some questions on topics (mainly graphs and Venn diagrams) that are going to be in the new syllabus and see exam questions from the Linked Pair Pilot programme. We discussed the following question:

The question asks you to estimate the distance travelled by the snowboarder and state the units of the answer. I was surprised to learn from Sarah that the mark scheme said that the graph should be approximated by 5 shapes – seems like overkill to me! I need to go away and look at the mark schemes for these kind of questions before teaching to get an idea of the error bounds and what is expected. During this session @MissNorledge showed me this trick for finding the exact trigonometric ratios for 0,30,45,60 and 90 degrees.

I hadn’t seen this before, and generally aren’t keen on tricks – I’d obviously prefer for students to just learn them or be able to derive them, but I do think this is pretty neat!

For me the take home message from Sarah’s session is to not underestimate the students. They may be able to do some of the questions that we feel are more challenging even if they don’t manage the more “basic” questions.

The past papers from the Linked Pair Pilot are worth checking out, there are some quite nice questions, such as this one from 2014:
These questions do generally seem less challenging than the questions in the new specimen papers though!

The Art of Leading a Mathematics Department

I was really looking forward to this session by Amir Arezoo (@workedgechaos) and it definitely didn’t disappoint! I decided to go this one as leading a mathematics department is something I aspire to, and I thought it was worth getting some tips early 🙂 I was annoyed though that this session was blocked against Martin Noon’s (@letsgetmathing) session about marking – luckily he tweeted out a link.

Anyway, back to Amir’s session (which I like to think was enhanced by the use of my clicker haha). I loved how he used his wife’s description of him to start the session – “daddy, mathematician, geek and moody” – thought it was really useful that he had split the talk into the following 11 key questions to ask yourself as you take over a department

1. Is your department serving the needs of its students?
3. Do your staff currently have the capability to meet these needs?
4. How do you determine what is best for your students and staff?
5. What does your curriculum look like?
6. How do you engage your students?
7. Do you and your staff reflect on practice?
8. How do you know that you’re moving in the right direction?
9. Who do you look to for guidance?
10. Why did you become a leader?
11. How do you grow the essentials?

Using a set of questions to frame the talk seemed to really help me to reflect on my views as the session progressed and after.

Amir emphasised that he didn’t believe that recounting what worked for him was useful as what works in one department wouldn’t work in another. This led to a nice tie in with Mark McCourt’s point that context is important – the context of the department within the school / within the community is important. How the community views the importance of mathematics is going to affect how your pupils view mathematics and what your student’s needs are. I was very interested in his mention of a “common calculation policy” and looking at my notes has reminded me to ask him more about this! His retort that “Bodmas is a waste of Oxygen” led to a bit of a discussion between a few of us about why we don’t like Bodmas on Twitter which was good.

Amir shared his experiences of things which didn’t work for him, such as trying to change everything in a department in one go.

When talking about point 5 he referenced the great picture from William Emeny of Great Maths Teaching Ideas shown below

The high resolution image is available here. I love this network so much that I have it on display in my classroom. As Amir says, it is important that any curriculum addresses the topics that have the highest weight in this network. He talked about having an open door policy – I really like this idea, and I try to ask for feedback from any other teacher that walks into my lesson.

There really is too much good stuff from this session to write about here – Amir please can you blog about it yourself?

To sum up the main points of the session I will use the same quote that Amir used “Character succeeds where personality only promises” – the human side of leadership is important!!

Other Stuff

Meeting more people who i have spoken to on Twitter in real life was great, and I had some fantastic discussions in the pub afterwards; both with people I have met before and those I met for the first time at mathsconf4. There are too many people to mention here…

I’m also sure I have forgotten many great things from the day too.

It was another fantastic event organised by LaSalle and I can’t wait for the next one.

Categories

A Little on Japanese Multiplication

The Japanese method of multiplication seems to be everywhere at the moment – Julia (@tessmaths) I noticed had advocated it ( I think prompted by a tweet by @missradders) on Twitter overtone weekend and one of my oldest friends posted a video of it on my Facebook page yesterday asking how it works and if it will always work.

This method is apparently taught to Japanese primary school pupils (note to self: ask the Japanese exchange pupils when they next come!) as an easy method for multiplying large numbers (larger than the times tables anyway).

It works due to the way that numbers are written down in base 10. For example, 325 is 3 lots of a hundred plus 20 lots of ten plus 5 lots of one. This along with the distributive property of multiplication allows us to split numbers up when multiplying. If I was working out 24 times 12 mentally I would split it up into two multiplications – 20 times 12 and 4 times 12 – then add the results. Mathematically, this can be written as:

$$24 \times 12 = (20 + 4) \times 12 = 240 + 48 = 288$$

The Japanese method takes this a step further and says that both numbers can be split up in this way and so that

 24 \times 12 = (20 + 4) \times (10+2) = 20 \times 10 + 20 \times 2 + 4 \times 10 + 4 \times 2 = 200 + 40 + 40 + 8 = 288 

To multiply using the Japanese method you represent 24 as two parallel lines, a large gap and then another parallel line and represent 12 as 1 parallel line with a gap then 2 further parallel lines. The lines for 24 and 12 cross each other. Then to calculate the product you count the intersections on the right for the units column, the tens is calculated by combining the two sets of intersections in the middle and then the number in the hundreds column from counting the intersections on the left.

I think that makes a lot more sense in a picture, so here is another example:

Some are harder than others:

In the example above the number of intersections in  the middle is 16 and so 10 of them have to be carried to the left, increasing the number of hundreds from 6 to 7.

For larger numbers this method becomes incredibly cumbersome – what withdrawing all the lines, counting intersections and dealing with the carries. See the example below for two 3 digit numbers:

I much prefer the lattice/Chinese/Napiers Bones method myself, but that is for another day.

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Thoughts on Edexcel Mechanics 2

Firstly, after a discussion on Twitter the other week I’ve decided to delay publishing my workings of the Edexcel exam papers until I know that they are already out there on the Internet. My personal feeling is that the exam papers (not solutions) should be made publicly available (I.e. Not in any secure sections of websites) by the exam boards no more than a week after they have been sat. I can’t see how there is any commercial value in them not doing this, and these days a past paper can’t be used as a Mock (not least because they are released by the exam boards before mocks are likely to take place for A Levels) without students having the potential to have seen them. Having said that, these posts will become password protected before the next academic year – any teachers who want a password just email me.

Anyway, back to the topic of this post – the Edexcel Mechanics 2 exam; my students were pretty worried about this paper. In light of this I think that the paper was pretty nice – not quite as hard as in previous years, but still some things to challenge the students, especially those who don’t like non-standard questions.

The paper started nicely, with Question 1 being a fairly straightforward  application of F=ma in conjunction with work done.

I really liked Question 2! The first part is a standard centres of mass of a lamina, but the second part is trickier and isn’t a “standard” question so to speak. As long as you apply the knowledge of what it means for the lamina with the extra weight hanging vertically through a particular line then, with the help of a good diagram, finding the extra mass is a nice problem to solve.

Question 3  is a simple exercise in applying the definition of impulse and then finding out the increase in kinetic energy following the impulse.

Stuart ( @sxpmaths) commented on Twitter that Question 4 is a classic example of the type of question where all intermediate steps are removed (I talk about these kind of questions here). As long as the students are ok at drawing the diagram then the question isn’t any harder than if the diagram had been given. The difficulty is increased though as the question doesn’t guide you through the necessary steps.
For Question 5, you’ll see that I made some silly calculation errors in working out the solution to part b – my excuse: it was late!!

Question 6 was a (in my opinion) a standard kinematics with variable acceleration question – nothing non standard about this.   The projectiles question was non-standard in the sense that you don’t often see questions with the angle of the particle at a particular (non-initial) point in the motion. Nice numbers hadn’t been used either so you ended up with horrible decimal answers – hopefully students stored the full values in their calculator for subsequent parts. I actually think this should be a requirement, and if they don’t then at most 1/2 marks for subsequent parts – a bit harsh I know.

The final question  was a really nice projectiles and conservation of linear momentum question finding an inequality for the coefficient of restitution and then investigating further questions.

Overall I think that like most Edexcel papers this year, this paper wasn’t really nice for the students but it could definitely have been a lot harder!

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The great Prism Debate

Whilst I was out tutoring last night I missed a post from Jo (@mathsjem ) about Prisms… There was a debate about whether a cylinder was a prism.

I had always understood a requirment of a solid being a prism was that the base of a prism was polygonal – i.e. made up of straight lines. This means that a cylinder cannot be a prism. However, the formulae sheets from GCSE papers seem to disagree, as this picture from the Edexcel papers shows:

Here we have a “prism” that clearly has curved edges forming the cross section.

I know quite often the volume of a cylinder is taught by referring to it as a prism with a circular cross section, but I haven’t seen any reliable definitions of prism that include cross sections with curved boundary. Instead, all definitions I have seen specifically require that the face is polygonal, for instance this definition from Wolfram’s Mathworld. Here they reference an old book on solid geometry as a source of this definition – Solid Mensuration with Proofs by Kern & Bland – @El_Timbre do you have a copy of this by any chance?

Keith (@MrKMorrison ) suggested that the word prism comes from the greek ‘prisma’ which literally means ‘something sawed’, suggesting the same face throughout, and so a cylinder should be a prism. I think the root of the word is largely immaterial, once an accepted definition is present. For instance multiply is a word in general usage and with a precise mathematical meaning, the root of multiply is the old French (I believe) for increase, but mathematically we wouldn’t use the word multiply to mean this.

In the grand scheme of things I guess it isn’t really a big deal to call a cylinder a prism – a cylinder certainly “behaves” like a prism, and maybe for lower attaining students calling a cylinder a special prism perhaps helps. For students going on to study maths though I think being loose with definitions can lead to problems, especially once they get to university.

I alluded to prime numbers in a tweet this morning as being what I think is the most dangerous example of miss-teaching of definitions / miss understanding of a definition. I’ve had so many students (including undergraduates) say to me that 1 is prime because it only has 1 and itself as factors. This is despite the definition of a prime number explicitly excluding 1. I’ve always found this quite odd……

Update: Mike Lawler (@mikeandallie) provides me a link to this nice definition from the Art of Problem Solving

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The Ethos of a Good A Level Classroom

I’m not sure why (someone probably asked me at school) but yesterday I started thinking about what I think leads to a good ethos in an A Level class and what I strive to achieve with my classes.

My guiding principle with A Level groups is equality – I don’t want to be seen as a teacher who is above them. Real mathematics is a collaborative attack on problems where you are looking for an elegant, neat solution; this is hard to achieve amongst a group of people who don’t feel equal. I don’t want them to see me as a teacher above them who they can only ask questions of – I want them to suggest approaches and paths to the solution of problems too. I think one of the easiest ways to encourage this is to let them call me by my first name. I know some teachers wouldn’t like this, and it is of course important to keep a professional distance from your students, but, I really think little things like this encourage them to be comfortable to give me their thoughts and suggest ways to tackle a question that they are doing as a class.

Another thing that I think is important for an A Level group to understand is the necessity to be stuck. In a Further Maths group especially some of the students have probably never struggled with maths before and it can be a shock when they begin to. For this reason I try to emphasise in the first few weeks that this is ok and a normal part of doing mathematics. Problems which either can’t be solved, or can be solved in multiple approaches, one of which takes significantly longer than another approach are valuable to reinforce that being stuck is ok! I also use exercises that I haven’t looked at until I get into the room as examples for this reason – I believe it’s good for them to see that I don’t always do the correct thing first time when solving a problem.

Collaborative working is something that I try to foster with certain activities – certainly for me, maths at A Level was a very solitary activity. This isn’t really reflective of the world of mathematics and whilst it is important for students to have plenty of  practice at solving questions on their own, talking about and discussing mathematics is incredibly valuable.

This post is a work in progress and I’m going to add to it as I think of other things…..

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The GCSE Frenzy

I don’t think anyone in the UK can have missed the media frenzy over the first Edexcel maths GCSE paper of this year. For example see here and here.

Having done the paper I don’t think it was particularly unfair or hard. There were plenty of standard, well trodden questions aimed at the C/B range. The questions targeting students looking for an A or A* are designed to stretch the most able and should be hard. I think there was a clear change in how se of these questions were written and I suspect this is a reflection of questions to come with the new GCSE.

One of the questions that has gone viral is the “Hannah’s Sweets” question

Apart from the pseudo-context (I don’t see how you could know this probability without knowing how many sweets we’re in the bag to begin with) I quite like this question. It brings together probability and algebra, using algebra as it was designed – a tool for solving problems. In fact, as long as a student writes out what they know from the question it is in fact fairly easy. At A Level I emphasise writing out what you know from a question if you don’t know where to start, but in the past I haven’t really done this to the same extent with my GCSE classes.

This question, however, is unlike any of the probability questions on recent year’s past papers and this is, I think, where the problem lies. I try not to teach to the test, but the fact that some of my students struggled with this question shows (depressingly) that to some extent I do. A lot of my revision lessons, probably like most teachers, have focussed on past paper questions as a way to prepare students – for this question this approach has failed.

From what I remember in one of the new specimen assessment materials there is a tough looking probability question involving a spinner similar to this… To prepare our students for these new exams I think I am going to need to change how I do exam preparation at GCSE. I don’t think this is necessarily a bad thing, maths is a problem solving tool, students shouldn’t just be expecting to see the same style questions year in, year out. I suspect that past papers for the new GCSE won’t be able to be used to coach pupils into the question style, at least not for the high attaining questions.

This is a good thing in my opinion, but my main concern though is the time necessary to build this deep understanding, especially for the first couple of cohorts for the new papers who won’t have had the required preparation at Key Stage 3. For The new Year 7 we are going down the mastery route and this should allow us the time to build this deep conceptual grasp of topics and how they inter-relate which will be good.

Going back to this year’s Paper 1 another question that a lot of my students were talking about was the “conical grain store” question. I loved this question, nice numbers to work with and it essentially boils down to a pair of simultaneous equations to solve using substitution. Substitution is a method that in hindsight, I strangely down do enough of at GCSE, but would use almost exclusively with an A Level group. The question concerning the perimeter of a shape made up of 4 congruent triangles and 4 congruent rectangles was also nice – just Pythagoras in disguise. I’d wager a bet though that a large portion of students didn’t even attempt these questions due to the unfamiliar context.

All in all I think it was a completely fair paper, and I’m looking forward to seeing tomorrow mornings paper. I wonder if there will be another Twitter frenzy….

Update: Ed at Solvenymaths (@solvemymaths) has written a fantastic post with some thoughts on how to address the gap between current student’s problem solving skills and what will be required for the new style GCSE questions.

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Thoughts on Edexcel Mechanics 1

Yesterday morning students at my school sat M1, FP2 and the OCR FMSQ papers. This is the first of three posts looking at these papers and I’ll start with the Mechanics paper.

I’ll admit I’m feeling pretty tired at the moment and so I made a few mistakes that I had to correct as I went through the paper – have fun spotting them. Overall I think it was a standard M1 paper which included the obligatory question using a 3-4-5 triangle.

Question 1 was a very straight forward conservation of momentum question – as long as you don’t get confused with the direction the particles are moving in there are easy marks to get here.

I thought that the projectiles question on this paper (Question 2) was really nice; no projection at an angle, just straightforward motion under gravity. Nice numbers too so that the arithmetic was relatively easy. The last part of this question was straightforward, though I can see some people working out the time to get from 14.7m to 19.6m and then the time back down instead of using symmetry.

My students commented on how Question 3 was nice as you got 7 marks for just resolving in two directions. A very simple question really as long as you are confident with solving simultaneous equations.

The first question that I made an elementary mistake on was Question 4. This year ion concerned a lift inside of which was a crate. If you recognise when to consider the motion of the system and the crate separately it is pretty easy. However, when I district did it and considered the motion of the lift-crate system I included the normal reaction of the crate in my force balance – very silly of me.

Question 5 was a typical moments question with a bar suspended from the ceiling and with particles suspended from it.  Taking moments about two points allows you to easily find the tension in the ropes for the first part. The second part is marginally trickier as you need to have an understanding of how the rod would move if the particle was changed.

Question 6 part a seems hardly worth asking as a distinct question, but I guess it is only worth one mark. I have also realised I did part c in a much more complicated way than necessary 🙁

I found question 7 strange as I realised that I had worked out most of part b as I drew the graph. So maybe it is only the shape of the graph and the relative gradients of the acceleration and deceleration that they are looking for in the mark scheme of the first part        . Finding V for the final part of the question is straight forward given the stepping stones you are led through in part b.

Overall I liked the final question. However, I remember that when I did my A Levels finding the resultant force exerted by a string on the pulley was something that I struggled with. Indeed this is the part of the paper that most of my students said they struggled with. They also all said they were surprised that the first part of this question was worth 11 marks.  I agree I think, it could easily have been worth less marks so it’s quite a nice question to end the paper on I think

I’d be interested to know what you or your students thought of the paper….

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Tesco Maths

Yesterday I was pleased to notice that the packaging for the new recipe flavoured milks includes some nice maths puzzles on three of the four varieties (only the chocolate fudge flavour doesn’t contain a number Puzzle)

I think these are pretty nice for their target audience – which I guess is a lot younger than me!!

Go on, spend a minute and give them a go 😉