I’ve put together a list for my students of what came up on paper 1 and what hasn’t appeared so far. Health warning: mine are target 6 students, so there are some topics missed out, and I have done this having left the paper at school, so I may have forgotten something! However, as always, if you find it useful, use and adapt as you wish. Questions all taken from edexcel past papers, and using new spec questions as much as possible.
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This warm up powerpoint is aimed at students targeting a grade 6. It’s a mixture of reminders and questions – it’s possibly got too much in, but as I was writing it I just kept thinking of something else I hoped they remembered! Feel free to use or adapt as you wish!
My sixth mathsconf, so it’s about time I blogged about the fab day organised by @Emathsuk and his team at @lasalle.
As often as possible I try to start mathsconf with the Friday night meet up. It’s a great time to catch up with maths teachers we’ve met along the way and through Twitter, as well as meet new folks. Despite a mix up with Julia, @Tesmaths, trying to meet in the foyer of the hotel, then realising we were in different ones, I made it up to All Bar One with Jo, @jolocke1. We’d both started new schools in September, so lots to chat about. At the bar I was chatting with @rach_2210 who was in Sheffield on her first mathsconf, and through our “where about do you teach” introductions, discovered we lived in the same town a couple of miles apart, and Rachel teaches at the school my 10 year old has put down as his preferred choice! Small world! It was lovely to catch up with Jo, @mathsjem, and hear of her experience so far as head of maths.
So onto the mathsconf. After introductions from Mark and Andrew Taylor of AQA, who talked about post 16, it was over to Matt Parker, @standupmaths, who as you can imagine, was an instant hit. Not only was there lots of laughing out loud, but some neat maths too:
Choose a random 2 digit number, cube it and Matt will tell you the original number. It’s all to do with expanding a trinomial and the affect on the 10a and b when cubing. Going to have to explore this one a little more – but isn’t that the point – creating a hook to explore some maths.
Then Matt introduced us to his favourite spreadsheet. Just a spreadsheet with cells coloured in red, green or blue, but when you zoom out it’s a picture of Matt! Here’s mine, created from Matt’s pixel spreadsheet downloader on his excellent website think-maths.co.uk. Amongst other things there are downloads for building 3d fractals, including a festive fractal Christmas tree, and if you visit megamenger.com, you’ll find details on building the world’s largest menger sponge from business cards, along with all downloads and instructions.
Matt finished off with a round up of websites and events. I’m particularly hoping we’ll be able to take some year 11s to the mathsinspiration.com event in Birmingham in November. Fingers crossed!
During speed dating I met Jack from Nottingham Uni Samworth Academy who showed me the spreadsheet they had made to support strategies for rewarding positive behaviour and effort. It was just the thing to implement with a couple of my groups, as I was looking for ideas of how to record all the positiveness in the classroom. Pete, @MrMattock showed us BBC Skillswise, the adults learning site, and the resources it had for older children who needed further support on the basics. Clear resources without the gumpf! I was also able to have a catch up with Bruno, @MrReddy, and was happy to share that one of my first responsibilities in my new department is to get TTRockstars properly up and running!
This was my contribution – at the end of school on Friday, a year 8 lad was excitedly telling his form tutor all about the probability tree he created and what each of the parts meant. He was in the nurture group, and the hook to get him engaged in probability trees was making it! All from my colleague Emily next door.
Onto the sessions, and first it was Sarah, @Schamings28, with Developing Resilient and Confident Mathematicians. Perfect, as 3 out of my 4 teaching groups are nurture groups, and resilience and confidence are in short measure. Sarah gave an inspiring workshop, clearly addressing the issues and giving excellent practical advice for taking back into the classroom straight away. She gave some excellent phrases to use to support confidence and resilience, as well as ideas for resources that get pupils practising resilience in low entry challenges which can then be used as a starting point to praise the process of resilience. I would highly recommend Sarah’s workshop if she were to do another one.
Next was an overview of Richard Skemp’s work: Relational Understanding and Instrumental Understanding from Gordon, @gordon-brough. I thought the effects of instrumental and relational teaching and learning was very pertinent. I have downloaded a copy of the paper so I can read through it again.
Jonny’s, @studymaths session on Primes, Patterns and Purposeful Practice was a whirlwind of ideas to engage students in their maths learning.
From “tricks” for squaring n+0.5 two digit numbers, based on expanding brackets like earlier, to factor skyscrapers, HCF/LCM pyramids, the Ulan Sprial, Goldbach’s conjecture, happy numbers, Kaprekar’s routine, Sierpinksi triangle and Chaos Game to name a few, Johnny provided us with many ideas, with quite a few being being enable from his excellent mathsbot.com site. It’s always great when you get an “aha, that’s perfect for when I teach …. next week” moment in a session, as well as a collective “wow” that came with the Chaos Game. Jonny’s session slides can be found here.
Finally I went to see Amir, @workedgechaos, and was treated to a review of how he would and does implement turning research and “current thinking” into practice with his staff. Amir has been a head of department and is now an assistant vice principal. It is very true that there is so much out there at the moment that it can easily become overwhelming. Amir took his big 3 – Bloom’s Mastery, Englemann’s Direct Instruction and Cognitive Load Theory and looked at the common themes. He then boiled it down to Question, Model, Check, Praise and Retrieve. It is, of course, a bit more detailed than that! You can find Amir’s slides and handout here. Amir shared with us an overview of a year’s scheme and how this was delivered each week. For spacing and retrieval, I loved how a topic was spread over several weeks (but not taught over several weeks):
Week 1: Topic A
Week 2: Mini test on topic A
Week 3: DIRT on topic A
Week 7: Review lesson on content A
But it’s not only the speakers and workshops which give great ideas. I happened to bump into Naveen and Dani, @Naveenfrizvi and @danicquinn, and got to ask a couple of questions I was intrigued about. Firstly rolling the timetables and implementing it with a group, and secondly from Dani’s podcast with Craig Barton @Mrbartonmaths, where she said they differentiated by time, so lower groups went slower. I just couldn’t fathom how these groups could have the same expectations if they went slower. The answer is obvious really – they have more time; more lessons!
I know I can’t do justice to some excellent workshops in such a short summary, but if it means that it interests someone to attend the next mathsconf14 in Kettering, March 10, then that’s great. A huge thank you to Mark and his team for another fantastic day of maths teaching CPD, and all the speakers who gave up their time to prepare and deliver such wonderful sessions.
Next for me is to give back and deliver a workshop myself, but for that I need to know I have something to offer that will be of interest to others and that’s worthwhile for teachers to give up their time for.
Oh, and I almost forgot, I need to do a bit of shameless plugging of our #TMBrownhills on Saturday 18th November, featuring @teachertoolkit Ross McGill, author of Teaching Backwards @oteacher Mark Burns and many local teachers presenting on classroom practice.
In September 2015 I inherited a foundation year 11 class. The class had previously had low achievement levels and included a few pupils (at least 50% if I remember correctly) with SEN. We struggled during the first half term, particularly with getting maths notes and examples written in books. I was printing out an awful lot of write on worksheets and gluing them into books. I then read @mathsjem’s post on resourceaholic.com about her foundation group in which she wrote about the folders she used to organise their work and study packs for each lesson. See her updates on this here and here. I thought this would be an ideal way of working with my year 11 group, particularly in supporting their note taking, so many thanks to Jo for introducing me to this plan.
The ring binders were such a fab idea, and it just so happened that at the very point I was thinking about this, a friends workplace were closing down and skipping a load of lever arch ringbinders, which she kindly collected for me. Perfect!
Two years on, and it appeared so successful after the first year, that I repeated it last year with a similar year 11 group.
I’ve added a page with the folder sheets I have used over the last couple of years. I’ll admit I’m quite anxious about putting them all on as I know I’ve used resources that others have kindly shared. I’ve gone through and deleted resources that are from subscription or prominent sites. I’ve linked to TES resources I’ve used from there, but I’m still worried I’ve missed something that someone else took their time to create, so please accept apologies in advance and let me know if I need to credit you.
The first benefit of the folders is the organisation of the students work. We had 5 sections: Classwork, Homework, Assessments, Practice Papers and BBQs (more on those later!). It’s great to sling the assessments and past papers into after the follow up work.
For the classwork, I prepared a page, usually double sided, for each lesson, with the learning question already written on. I also decided to number the sheets with unit and lesson number on!
The real bonus of these sheets is that notes can be laid out for better referral back to them, and all the questions are already on there, so no glueing in! They tended to get a pattern of boxes for facts and speech bubbles to annotate examples.
Although it took time to make these sheets, these were the resource for the lesson. I didn’t make a powerpoint to go with them, as I used the visualiser I was lucky to have in my classroom. It wasn’t just a “copy these notes down”; as I was filling them in the same time as the students, it was all about the questioning too.
The BBQs are my starters I use. They stand for bread and butter questions; I first used Just Math’s bread and butter questions here, but then I wanted to use certain questions for my group, so developed my own. At the start of the year, I chose a selection of questions and then for four lessons in a row they would do the same set of questions (different numbers!). However, once we started doing papers, whether in class or for homework, I would choose mostly fluency questions which most of the class had got wrong, so the first session has more guided questions and then the next 3 would allow for further practice on these areas. Next job is to upload these!
I would totally recommend using folders for GCSE work. I would imagine if I were to do these with a higher foundation group, or a higher group, then I would leave more blank spaces for the students to make their notes, rather than the prescriptive layout I’ve been using with the groups I’ve had.
Eeek, I’d been all prepared and printed out resources I had thought to share for speed dating at #mathsconf6, only to leave them on the printer at home. So next best thing I could think of was to get hubbie to take a couple of pics, email them to me and post about them on here.
What I was thinking of sharing was a resources from another maths teacher that I had found extremely useful, and had shared with my department, for tackling problem solving, and the difficulties students have sometimes in getting started on a problem.
Back in July I read this post from @mrlyonsmaths on his blog mrlyonsmaths.wordpress.com about problem solving and the lack of resilience in even starting at solving a problem. Mr Lyons suggestion was inspiring and I’ve used his resource as a basis for problem solving with my groups this year.
It’s a fab way of getting students started on a problem as to begin with they are rewriting the key points of the question. Highlighting is good when you recognise where you’re going to go next, but for the less confident pupils, thus actually gets them started on writing something, and then some maths just seems to lead on from there.
These are just three examples of questions I’ve used the format for, for different year groups and abilities of students.
So a big thank you and shout out to @mrlyonsmaths for giving some of my students an entry way into problem solving.
In an attempt to get myself blogging more regularly, I decided to join the #MTBoS blogging initiative, so here is my first entry, a day in the life. I thought I’d choose Tuesday of this week, as it was a full day of teaching, followed by parents evening, but as it happens, there was to be a twist in the tale.
7.15: Today my husband was able to take the boys to the childminder, so I can head straight to school, arriving at 7.50. Before school time was devoted to marking my year 10 assessments. There were only 10 of them, so I knew I had time, and was even able to set up the tracking spreadsheet, as well as getting all my resources in order for the day ahead.
8.35: Department briefing, which I came out of with quite a to do list! School starts at 8.50 and I was straight to assembly with my year 9 form. This weeks theme is setting high expectations.
9.10: The teaching starts with yr 12 maths resit group. Just had 7 pass their November resit, so the class had shrunk a little, and with mocks going on, there were even less! Started as I always do with a corbettmaths 5aday, then it was working through a past paper as they have their mock at the end of the week. Saw an email that the head had to cancel all her praise appointments with pupils….
10.10: Guidance with my form. We were looking at Businesses today. A split lesson, so half an hour of Guidance, then half hour break, before the second half hour of Guidance. Had good discussions around a Dragons Den clip, and which offer was the best. Saw an email that there was a full staff briefing at 3.20pm.
11.40: My beautiful top set year 7. A group full of high ability pupils, who love learning. Spent some improvement time on their home learning and previous class work, then it was into learning how to plot a graph from its equation.
12.40: Year 11 GCSE foundation group. These are a hard bunch of kids. Most haven’t got much motivation and very little belief in themselves. They were calculating circumference of a circle, and could do it, but were struggling to settle down and focus just on their work.
13.40: A half hour break for lunch, in which I printed out my data sheets for parents evening, then onto the last lesson. Another year 7 group, set 2 (out of 3). Again, started with some improve my work in their home learning, then was finishing their first algebra topic on formula – writing and substituting into. A lively bunch, who are on the whole quite keen, but chatty too.
15.10: The teaching day finished and time to head for a staff meeting. You may have guessed by now that the head had received the OFSTED phone call in the morning, and they would be arriving the next morning. Our school is currently requires improvement and everyone had been working really hard to improve. We knew they’d be coming soon, so not unexpected, but not great timing with most teachers about to head into the hall for 2 1/2 hours to meet with year 8 parents. I make a phone call to my husband to see if there’s any chance he can take the boys to the childminders again in the morning so I can head straight into school.
16.00: Parents evening starts and it’s busy to begin with. Have lots of positive things to say to most parents. It gets a bit quieter towards the end, and although my last 20 minutes weren’t booked, I stay until the end as I really wanted to see those 2 parents who hadn’t turned up earlier, and am just hoping they were late.
18.30: They didn’t turn up, so I head back to my classroom to start preparing for the next day. Most of my lessons are planned, but I had some assessments for yr 11s to file in their folders, which now really need to be in there before tomorrow’s lesson. Those other little tidying jobs on my list couldn’t wait now either.
19.30 I finally leave school, seeing several classroom lights still on as I head for home. It’s not that we want to be different for OFSTED, but know everything must be at the best of what we do, something that would be impossible to do all the time, although it always what we strive for.
21.00: I’ve been home half an hour. Boys were in bed, and my husband has made tea. I’ve had a sit down, refuelled, and it’s back to work. I knew I had my feedback lesson to prepare for year 10s, but with our visitors now coming, I also had to change my planned year 7 lesson from a basic skills fortnightly lesson to a normal curriculum lesson, my seating plans to update and print out in case they were needed, the Teacher Toolkit 5 minute lesson plans to fill in – this wasn’t too hard as I plan in my head using these – and a couple of tweaks to my yr 11 and yr 8 lessons.
00.30: I fall into bed knowing the alarm is going off in little over 5 hours. I wouldn’t normally stay up that late working, but I want to do my best for my school over the next two days. We work extremely hard to do our best for our pupils and I want OFSTED to see that.
It’s been a pretty full on term so far, as it always seems to be, so it was lovely to have a break yesterday evening and do some maths for ourselves! We were fortunate enough to welcome Trevor Starbuck to the first Birmingham and Solihull Further Maths Support Programme network meeting hosted at John Willmott School. The intention of these network meetings is to bring together teachers from across the city who have an interest in meeting with other teachers to explore issues relating to the teaching and learning of mathematics and further mathematics at A Level.
Trevor had spent part of the afternoon talking with some of the higher achieving Year 11s, and then turned his attention after school to a small but very enthusiastic group of willing maths teachers. Not having had the privilege of teaching A Level, and still holding a passion for all the mechanics modules I chose at Uni oh so many years ago, I was really looking forward to this session.
The classroom we were meeting in had been transformed into a den of mechanics experiments. Trevor’s enthusiasm for the subject was radiating from him as he introduced the two experiments we were to undertake. These involved, amongst other things, half pipes, marbles, clamp stands, metre rulers and timers.
Firstly, there was timing a marble rolling some given distances. The metre long pipe, marked into 20cm segments, was kept as shallow as possible for the marble to roll. It was then timed 3 times each for rolling each distance from 20cm to 1m and the mean value taken. Results plugged into Autograph and the following graph was produced:
The second experiment involved the the rolling of a marble across a tilted table. Our job was to track its path as accurately as we could, to gather data on its path, distance and time. We first set the pipe and clamp stand so the marble could travel a decent path up and across the tilted table. Next was to identify the end point of the path, which crated the x-axis. This path was timed (at least 5 times, and a mean value taken) and the axis was then split into 8 equal parts. Rolling the marble as consistently as possible, we tracked when it passed each division (again, 5 times for each, taking the median of the points we had plotted on the division lines).
We ended up, as you would expect, with a lovely parabola. The final two measurements to take were the height of the middle division – the point where the marble started its downward journey, and, using a bit of trigonometry, the degree of inclination of the table.
These experiments were reminiscent of those undertook by Galileo in the late 16th Century. Ofcourse, he didn’t have electronic timers, so we were quite relieved when Trevor didn’t insist on use using a water hour glass timer, similar to what Galileo would have used. As well as rolling balls across inclined planes and measuring their distance, Galileo also used the Tower of Pisa to give him a vertical height from which to drop objects. He was able to demonstrate that a body dropped from height starts at zero velocity and increases his speed over time (rather than the constant velocity, that was larger the more the body weighed, assumed by those before him). This also involved his discovery that the velocity of a falling body is independent to its weight and the mathematical expression that, the speed of an object increases as the square of the time, hence our quadratic graph from the results of the first experiment.
Fast forward 100 years and armed with Newton’s Second Law of Motion, we are now able to form some calcualtions from our data.
And so we have it; practical experiments and calculation enabling us to derive a (very approximate) value of gravity. There is of course discussion time here for all the aspects not taken into consideration, the main one being air resistence, but our time had come to an end.
The Birmingham and Solihull FMSP network hope to meet at least termly. It was a really enjoyable, practical session; a chance for us teachers to focus on mathematics, from those of us who would like to brush up on our A Level to those who have been teaching it for many moons! Each meeting will have a specific focus such as this, but there will always be time for discussion of other matters according to teachers’ interests and concerns. I do encourage any local teachers who are interested in A Level maths (you don’t have to be teaching it) to get involved with the network. For more information, please contact: