15 October 2017

5 Maths Gems #78

Welcome to my 78th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Access Maths
I first blogged about @AccessMaths' resources in Gems 47. Last week he started sharing a new set of resources for GCSE teachers. One thing that caught my eye was his 100 'Crossover Style' questions revision mat. I have to set cover for my Year 11s on Friday and they'll be getting this activity, printed on A3.
There are loads of new resources on Grant's 9 - 1 GCSE page, many of which I have now added to my resource libraries. Do check them out.

2. Puzz Grid
Dave Taylor (@taylorda01) tweeted about an addictive website called Puzz Grid where you can easily set up your own grids or play other people's grids. It's a timed game where you have to select groups of four squares that are linked together. Dave shared one of his own creations here.
This website works just as well for maths as it does for other subjects. It's really fun - have a go and you'll see what I mean.

Parallel Line Mazes (again!)
In my angles in parallel lines presentation at #mathsconf13, I shared one of my all-time favourite resources, which was created by Daniel Schneider (@MathyMcMatherso). I first blogged about this back in Gems 26 and I have used it in lessons many times since then.

I had forgotten that there were similar and equally awesome activities in the geometry section of Daniels's blog until he mentioned it after #mathsconf13. So I decided to feature this resource again - the second time it's been in a gems post - because I love it.

4. Add 'Em Up
I spotted an activity that I've not seen before in this tweet by Jae Ess (@jaegetsreal)

The idea is that each group of four students is given a card. Each student solves one of the four problems. Once they've all solved their problems they add up their answers and the sum should equal the number in the middle. If it doesn't then the group has to look at the four solutions and figure out which one is wrong. Sara Van Der Werf (@saravdwerf) blogged about it here.

5. TickTock Maths 
Richard Tock (@TickTockMaths) wrote a post about #mathsconf13 in which he said that he was going to start sharing his resources for free. It's worth having a look at Richard's resources and blog posts because there's some great stuff there. I enjoyed his recent post 'Interesting Questions' where he wrote about task design.
I had a quick browse through Richard's resources and liked the uncluttered layout of his slides, and his clear explanations.
He uses nice activities in lessons - check out his factorising linear expressions slides for some examples.
In case you missed it, I recently wrote a post about saving the FMSP, and I blogged about BCME 9.

Colin Foster (@colinfoster77) shared a great article that he wrote for the MA journal Mathematics in School. It's about different methods for finding the nth term of a sequence. If you're teaching quadratic sequences this year, give it a read. This is the kind of subject knowledge development that teachers need more of!

If you teach mixed attainment or you're an FE teacher teaching GCSE resit then note that two conference dates have been announced and added to my conferences page. The next Mixed Attainment Maths Conference is in London on 27th January. The GCSE Maths Resit Conference is on 17th March in Sheffield.

I'm speaking about resources at the Power of Six Conference in London this Thursday. Do say hello if you're there (though I have to leave at 11am to get back to school for a 1pm lesson, so sorry if I have to rush off!). 

Finally, my maths teacher friends and I had a great time at the Festival of the Spoken Nerd show in Redhill on Thursday. It's not too late to get tickets for the tour - I highly recommend it!

11 October 2017

Save the FMSP!

A level teachers love The Further Maths Support Programme, and it's clear to see why. It has actively supported us for many years, having a direct impact in our classrooms. Just look at the uptake of maths and further maths A level in England - an incredible success story that can be partly attributed to the effectiveness of the work of the FMSP.
Taken from MEI's Annual Review 2016 - 17

The FMSP makes A level maths and further maths accessible to students who otherwise would not have the opportunity to take it. Imagine a society in which our most talented mathematicians stop studying maths aged 16 because they live in the wrong area or go to the wrong school. It's clear to anyone with even a shred of social conscience that the work of the FMSP is incredibly important.

What's changing?
In response to the Smith review, the Department for Education announced a new Level 3 Maths Support Programme (L3MSP), with £16 million of funding from April 2018. Although we were led to believe that this was exciting 'new money', my understanding is that it will replace the previous level three support. Hence the Core Maths Support Programme and the much loved Underground Mathematics have already gone, and the FMSP (in its current form) will go too.

In MEI's recent newsletter it said that the FMSP will continue to provide A level maths and further maths support for schools and colleges until the new L3MSP is in place.

So the FMSP, which has been running since 2005, will be superseded by the L3MSP next April.

The new L3MSP will support Core Maths and A level mathematics and further mathematics, but will focus on the DfE's twelve 'Opportunity Areas' (these were selected from areas identified by the Social Mobility Commission as having particularly poor social mobility). So I think this means that those of us who work in schools outside of those Opportunity Areas will see our level three support withdrawn, or at least reduced.

This suggests that most of us will no longer have access to the FMSP's affordable high quality training courses on how to deliver A level topics. This comes at a time when we are teaching a brand new A level curriculum (which, particularly for the further maths specification, requires a great deal of subject knowledge development) and we have dwindling numbers of specialist maths teachers. This also comes at a time when A level uptake may have dropped significantly due to the impact of the new GCSE. We won't know official numbers for a while, but at my school we were surprised that our A level maths uptake fell by 32% this year - I certainly hope that this is not representative of the national picture. Either way, given the current situation, the timing of these changes couldn't be worse.

What can we do?
We're too late to save Underground Maths and the Core Maths Support Programme, but perhaps we're not too late to save the FMSP. We need to make our voices heard! We need to make sure that the Department for Education knows where we stand on this.

If level three support will end in all but the Opportunity Areas from April 2018 then the Department for Education need to be transparent in their communication about this. Maths teachers need to know that this is happening.

I'm hoping that we can do something about this. If I have to organise an actual protest outside the DfE then I will! Just watch me.

I'm just a teacher - I blog independently without income or affiliation - but I think this is worth fighting for.


4 October 2017


Tickets went on sale for BCME today. This is exciting news! BCME (the British Congress of Mathematics Education) brings together the members of the Joint Mathematical Council of the United Kingdom (JMC) for one big mega-maths-conference. It takes place in Warwick over four days in the Easter holidays... and it will be huge! The number of speakers is staggering.

These events have been running since 1991. BCME 8 took place in Nottingham in 2014. Given that I'm still a relative newbie to the maths conference scene, this will be my first ever BCME. And I am very much looking forward to it.

I go to a lot of conferences these days, but BCME is very different to the conferences I usually attend. For the last three years I've gone to a La Salle conference every term - I absolutely adore these events. I can't recommend them enough. BCME is a totally different kind of event. I see it as an extra bonus conference to attend next year, on top of my usual La Salle conferences.

Unbelievably, there are over 350 sessions to choose from at BCME! I can't even begin to imagine how hard it will be to choose! This does mean that there will be plenty to appeal to everyone though, from EYFS through to university. I'm looking forward to seeing lots of speakers who I haven't seen before.

If you attend all four days of BCME then you can go to ten different sessions, plus there's loads of other stuff going on including a number of plenary speakers and social events. Hannah Fry (I love her!) is speaking after dinner on the Thursday night. On the Friday there is a special event to celebrate the life of Malcolm Swan.

Of course you don't have to attend all four days - there are various different ticket options. If, like me, you're worried about the cost of this event, then you'll be pleased to hear that bursaries may be available from the LMS and UKMT.

Below I've listed some examples of sessions, just to give you a flavour of what's going on. All 350+ sessions look amazing! Do check out the session booklet to see the whole lot.

A6 - Variation: beyond the definitions - Anne Watson
This session will be a workshop of mathematics tasks and discussion to open up a range of meanings and roles for 'variation' in mathematics teaching. Some of the jargon around this word is taken as prescriptive, when it is merely descriptive - there is more to describe. 

A10 - Mathematics from East to West - Andra Ghencea 
The aim of the session is to look at the differences and similarities between the approach in the teaching and learning of mathematics in Eastern versus Western Europe. The opportunity to explore both worlds in depth, through personal education and work in the educational sector, has given me a clear image of what leads to mastery in the subject.

B10 - The Black Heroes of Mathematics - Nira Chamberlain 
The 2017 released film, Hidden Figures, is based on the true story of a group of black female mathematicians that served as the brains behind calculating the momentous launch of the NASA astronaut John Glenn into orbit. However, these mathematicians of colour are not the only 'Hidden Figures'. In this this talk, The Black Heroes of Mathematics, we will discuss other inspirational men and women who overcame obstacles to prove that 'mathematics is truly for everybody'! 

B11 - Making Resits Work - Emma Bell and Anna Bellamy 
Compulsory mathematics GCSE resits are a thorn in the side for students and practitioners alike. In this session - run jointly by two teachers, for teachers - research and practice come together to examine how we can best help those students. Anna Bellamy's research focusses on Student Voice and the effects the forced resits have on those students while Emma Bell specialises in motivation, ensuring that students have belief and confidence in their mathematical abilities. How can we make mathematics resits work for all of our students?

 B17 - Teaching multiplication with deep conceptual understanding - Katie Crozier
This workshop will explore how deep conceptual understanding and visualisation of multiplication can be developed through exposing structure and making connections. Part of the workshop will explore the use of the Numberlink Board, developed through action research in the Y4 classroom, to teach multiplication facts with understanding. 

D17 - Pop-Up Maths - David Sharp 
In this creative and active session, you'll make pop-up 3D shapes, including cubes, tetrahedrons and dodecahedrons. You'll also make flexagons, including tri-tetra-flexagons and tri-hexi-flexagons. We'll look at how these can be used in the classroom.

G14 - Ideas that transformed my teaching - Jo Morgan
In 2014, Jo joined the mathematics teaching community on Twitter. Within months it had transformed her teaching. Immersed in resources, debate and advice, Jo felt empowered to try new ideas in the classroom. Inspired by best practice, she started to refine her teaching routines and approaches. In this session Jo will share some of the most effective changes she's made over recent years.  

G4 - Many Mischievous Mathematical Misconceptions - Craig Barton 
Using data from the tens of millions of answers to questions on my Diagnostic Questions website, together with the actual written explanations given by students, I will unearth some of the most surprising, interesting and deadly mathematical misconceptions that our students hold. How do these misconceptions vary by age group? What are the most important misconceptions to resolve early in order to prevent problems further down the line? And is attempting to resolve misconceptions more trouble than it is worth? Expect a bit of controversy, as well as a fresh round of everyone's favourite quiz: Guess the Misconception. 

Doesn't it look awesome? Bookings are open now.

27 September 2017

5 Maths Gems #77

Welcome to my 77th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Interactive Manipulatives
Jonathan Hall (@StudyMaths) is the creator of the excellent website mathsbot.com. I blogged about the features of MathsBot last year. Jonathan has recently added lots of new content to MathsBot, including a set of virtual manipulatives which are well worth exploring. They are very helpful for demonstrating things on the board before students have a go with actual manipulatives, such as algebra tiles and Dienes Blocks.

2. Revision Maze
A quadratics worksheet from CrashMaths caught my eye on Twitter so I explored some of their other resources. I discovered this lovely GCSE revision maze for the higher tier. You can download it from their website with solutions. I have added this to my collection of GCSE 9 - 1 revision resources.

3. AQA A Level Resources
AQA has launched its A level maths e-library. I put a lot of work into this project so I really hope it's useful. It's a great place to search for resources when teaching the new A level. AQA has also published a new set of topic tests for A level.
Links to these topic tests and other new A level resources can be found on my New A Level Support page.

4. Stickers
Have you seen these amazing stickers from Maths Gear? Take a minute to read through them. I love maths jokes! 
If you're ever buying a present for a maths teacher, I recommend two brilliant websites for mathsy gifts: mathsgear.co.uk and presentindicative.com.
5. Rolling Numbers
Naveen Rizvi (@naveenfrizvi) shared a blog post about introducing rolling numbers at her new school. It's worth reading about how she motivated reluctant students. Rolling numbers is a fantastic way of improving students' fluency in times tables. You can download the lyrics from Bruno Reddy's blog.

Here's Naveen in action. Impressive!

Also check out this video of @tkendalluk rolling numbers at Michaela Community School. This was shared by Jo Facer on Twitter.

I've taken on two new jobs at school and have had lots going on every weekend in September, so I've really struggled with workload this month. Hopefully things will start to calm down a bit now.

I was very pleased to be co-opted as Chair of the MA's Publicity and Media Committee and am looking forward to getting stuck into the role during October. It's a really exciting position and I am honoured to have been appointed.

A few months ago I blogged about the importance of joining the MA. Recent rumours that our profession might lose the FMSP - one of our most highly valued organisations - means it is now more important than ever to join the MA. We need to come together as a profession to make our voices heard. Please join if you haven't already.

I'm looking forward to seeing lots of maths teachers at #mathsconf13 in Sheffield this Saturday, and at the pre-conference drinks on Friday night. I will be presenting on angles in parallel lines, as part of the project I described here. There are only a few spaces left in my workshop so if you want to come along and haven't chosen your workshops yet, please do.

In case you missed them, here are my recent posts:

I also updated my new A level resources page and my Topics in Depth page, and I've added a few new Pret homeworks (thanks to continuing generous contributions!).

In October I will be presenting on resources at the Power of Six Conference in London. Do check this one out - tickets are now only £50 and there are some excellent speakers lined up to present.

Finally, don't forget to book tickets for the Festival of the Spoken Nerd Tour! I'll be at the Redhill performance on 12th October. Can't wait!

20 September 2017

Challenges and Competitions

I thought it might be helpful to pull together a list of national maths challenges and competitions. Please let me know what I've missed!

Key Stage 2
The Primary Maths Challenge
This lovely maths challenge from the Mathematical Association is aimed at pupils in Years 5 and 6 in England and Wales, P6 and P7 in Scotland, and Years 6 and 7 in Northern Ireland. 63,000 children took part in 2016. In November, children sit a 45 minute individual maths paper at their school and are awarded a certificate for achievement or participation. High scoring pupils are invited to take part in a bonus round the following February. Example papers (for both the November challenge and the February bonus round) can be downloaded here. It costs £11 for a pack of 10 papers.
Examples of questions from the Primary Maths Challenge

The National Young Mathematicians' Awards
This team maths competition, now in its eighth year, is run in conjunction with NRICH and is designed to inspire and challenge talented mathematicians from across the UK. Schools can enter a team of four children from Year 6 or below. The first round is a regional knock out undertaken at an Explore Learning centre in early November. Winners go through to the Semi-Final at the end of November, and the Grand Final takes place at the University of Cambridge in December.

Primary Team Challenge
The UKMT provides a set of free resources for schools to run their own team maths challenges. These may be helpful for: 
  • a primary school running their own maths event for Key Stage 2 pupils
  • a secondary school running a maths event for children from feeder primaries
  • a maths hub, multi academy trust, local authority or other organisation running a regional maths event for primary children

Key Stage 3
Junior Mathematical Challenge
The Junior Mathematical Challenge is a multiple-choice competition for students up to Year 8 in England and Wales, Year S2 in Scotland or Year 9 in Northern Ireland. It is run by the UKMT in April each year. Over 300,000 students participated in 2017.

The cost is £13 per pack of 10 papers. Like the other individual challenges listed here, students complete their paper at school in test conditions on the designated date. To recognise the highest performers, the top scoring 40% of participants are awarded bronze, silver and gold certificates in the ratio 3:2:1. Around 1,200 of the very highest performers are invited to take part in the Junior Mathematical Olympiad and around 5,000 to take part in the Junior Kangaroo.

It's worth checking out the UKMT Problems on Diagnostic Questions and the UKMT Problems on DrFrostMaths for interactive practice.
Example question from the 2017 JMC
Team Challenge
The Team Maths Challenge is a UKMT competition which gives pupils the opportunity to tackle a variety of engaging mathematical activities while developing teamwork and communication skills. It is open to students in Year 8 and 9, and equivalent year groups in Scotland and Northern Ireland. Each school is invited to enter a team of four pupils to a Regional Final. Regional Finals run at over 65 centres across the United Kingdom from February to April. Entry costs £35. The winning team at each Regional Final will receive an invitation to the National Final which takes place in June.

National Cipher Challenge
The National Cipher Challenge runs from October to January. It is a free competition offered by the University of Southampton. It has been running since 2002, and regularly attracts entries from teams at over 700 UK schools and colleges. Students of any age can take part, so schools often promote this competition to teams from all year groups. Entrants are set a series of eight codebreaking challenges online, with points awarded for speed and accuracy.

The Alan Turing Cryptography Competition
Now in its sixth year, the Alan Turing Cryptography Competition is aimed at secondary school children at Key Stages 3 and 4. This free competition is organised by the University of Manchester and runs from January to April. Like the National Cipher Challenge, entrants are set codebreaking challenges online. In May there is an Alan Turing Cryptography Day in Manchester which includes a prize ceremony.

Key Stage 4
Intermediate Maths Challenge
The Intermediate Mathematical Challenge is a UKMT multiple-choice challenge for students up to Year 11 in England and Wales, Year S4 in Scotland or Year 12 in Northern Ireland. It takes place at schools in February and costs £13 per pack of 10 papers. High scorers are invited to compete in the Intermediate Mathematical Olympiad or Kangaroo.

Year 10 Maths Feast
The Maths Feast is a team competition run by the FMSP for Year 10 students. It promotes problem solving and communication skills and takes place in the spring term. Around 70 events take place each year across the country attracting entries from over 750 schools. Materials from previous competitions are available which schools can use as enrichment activities to develop problem solving skills.
Example question from the FMSP's Maths Feast
Key Stage 5
Senior Maths Challenge
The Senior Mathematical Challenge is a multiple-choice challenge for students up to Year 13 in England and Wales, Year S6 in Scotland, Year 14 in Northern Ireland. Organised by the UKMT and run in schools in November, it is £13 for a pack of 10 entries and top performers are invited to take part in the British Mathematical Olympiad Round 1 or the Senior Kangaroo.

Example question from the Senior Maths Challenge 
Senior Team Challenge
The Senior Team Mathematics Challenge is organised by the FMSP in partnership with the UKMT. This annual competition takes place in November and attracts entries from over 1,000 schools throughout the UK. Winners of the regional heats are invited to the national final in London in February.

I have only included UK-wide challenges here, but there are a large number of regional competitions too. For example, Rock Wrangles are wonderful events in which Year 6 and Year 7 students compete on Times Tables Rockstars. In 2017 Rock Wrangles took place in five cities in the summer term.

The Scottish Mathematical Council has been running an annual Mathematical Challenge since 1976 which is split into Primary, Junior, Middle, and Senior Divisions.

I hope this list is helpful! Please do let me know of any national annual competitions that I've missed. If you're interested in international maths competitions, check out the list on Wikipedia.

If you're looking for other enrichment ideas, have a look at my posts on in-school speakers, maths clubs and maths trips.

13 September 2017

The New GCSE Debate

On Saturday I participated in an Institute of Ideas panel discussion on the new maths GCSE. Here is the description of the session from the researchED programme:

At the start of the session each panel member was asked to speak for five minutes. Here is the transcript of what I said:
"There is so much to say on whether the new GCSE is fit for purpose. We can approach this discussion from the perspective of a number of different types of student, and I sincerely hope that we will cover all of those perspectives over the course of the debate today. But the one aspect that I want to focus on initially is whether the new GCSE is going to give us a stronger future generation of mathematicians. This includes the engineers, the physicists, the computer scientists, the statisticians, the maths teachers... - all the professions that are apparently so important to the 'success' of our country. Are we on track to create higher quality candidates for these professions?

Improving the 'top end' was one of Gove's key drivers. In his 2013 statement to Parliament, Gove said "[The new maths GCSE] will provide greater challenge for the most able students by thoroughly testing their understanding of the mathematical knowledge needed for higher level study and careers in mathematics, the sciences and computing".

So did it work?
I'm afraid that I'm not convinced that the new GCSE has had - or will have - a significant impact on the mathematical fluency and conceptual understanding of students coming through to A level maths. One week into teaching my new Year 12 classes, it seems to me that the gap is exactly as it's always been. It may even have worsened at some schools, because they are no longer able to offer AQA's Certificate of Further Maths in Year 11 (nationally, figures for this qualification have fallen by 34%).
Even though our new Year 12s have had more maths lessons over the last two years than previous cohorts, we still have students who got a grade 7 - equivalent to an A - who can't do the basics. The grade boundaries were such that these students may well have got all the algebra wrong in their GCSE. 
I have blogged previously about using an entrance test to assess algebra skills at the start of Year 12 - this wouldn't be necessary if the GCSE was doing its job correctly. I know of a student who got zero out of fifteen on his entrance assessment - which consisted of pretty basic algebra questions - even though he got a Grade 6 at GCSE. This begs the question, what does a Grade 6 in maths really mean? 
I'm not convinced that standards have improved. I'd argue that mistakes were made in designing the content of the new GCSE specification. 
Over the last two years, maths has gained extra teaching time in most schools. This has often come at a cost to other subjects. Many schools have gone from three maths lessons a week to four, or even more. But the extra time in the classroom has not been spent improving fluency in algebra and tackling fundamental misconceptions - which would have been the best way to spend the extra time. Instead we have had to spend the extra time teaching all the new, random, bitty topics that were added to GCSE - quadratic sequences, functions, iteration, frequency trees and so on. The breadth of the GCSE is vast - there are 97 topics listed in the government's specification. Why exactly were all the new topics added? 
It isn't a head start on A level at all - if our students spend a few lessons rushing through functions in Year 11, we will still have to teach them functions from scratch in Year 13. Due to time constraints, most students will only gain a superficial understanding of the A level topics that were added to GCSE.
What would have been better - what would have actually made a difference to our A level mathematicians - would have been fewer topics on GCSE. I am pleased that Higher GCSE got harder, it used to be too easy for many students, but in my opinion it got harder in the wrong way. I would have liked to have seen the questions on the important stuff - algebra, number, trigonometry - made harder. I'd have liked it if it was impossible to get a high GCSE grade without true algebraic fluency and understanding.
This increased level of difficulty - but on fewer topics - would have better equipped our students for the challenges of A level. Depth was the answer. And depth is the answer in many high performing jurisdictions. But our government went for breadth.

It all comes down to curriculum. It will be a few years until we are able to start measuring the impact of GCSE reform in any meaningful way - perhaps even longer, as we wait for the changes at Key Stages 1 and 2 to filter through to Key Stage 4. But at the moment, whilst the specification remains so broad, it's hard for me to see there being any significant impact on our future generation of mathematicians". 

There were some really interesting points raised during the debate, and I was frustrated that I couldn't address every point in as much detail as I'd have liked (particularly points relating to the suitability of the Foundation specification and the experience of students who struggle with maths). Apologies if you were at the session and raised something that we didn't have time to properly explore - it would be great if we (ie the maths teaching community) could continue the conversation on Twitter or at a future conference. It's really important that teachers make their voice heard in discussions about qualifications and curriculum.

Many thanks to the Institute of Ideas Education Forum for organising the debate, and to Tom Bennett and all those involved in researchED for hosting an excellent conference.

10 September 2017

Cover Work

No one likes being put on cover. We have precious few free periods and we're always ridiculously busy, so last minute cover is an absolute day-ruiner. I lost count of the number of times I had to do cover for other subjects last year. It prompted me to think about what makes a decent cover lesson.

Unlike long term supply, a cover lesson for an unplanned absence is normally delivered by a randomly chosen teacher from another subject who happens to have some non-contact time. These lessons are planned in a hurry, either by an unwell teacher who has logged in from home, or by a busy Head of Department. I think we have to accept that a student may not learn anything new when their teacher is off sick. As long as it's rare, that's not the end of the world. There are plenty of useful things that a student can do independently when their teacher is absent - in fact, it can be a really good opportunity to do some focused practice. To me, the worst kind of cover lessons are those where:
  • The lesson requires expert knowledge on the part of the teacher delivering it. No one should be expected to stand up and teach a full lesson on something that they know nothing about. Cover lessons should be written with non specialists in mind. 
  • The lesson is hard work for the cover teacher. From a staff welfare perspective, we must be nice to our colleagues and not give them anything complicated to deliver or challenging to oversee. Activities should minimise opportunities for disruptive behaviour. No one wants a cover lesson from hell.
  • There isn't enough work for students to do, or the instructions are unclear, or the required technology doesn't work, or there aren't enough resources to go round. Four students huddled around a single textbook isn't ideal. 

Ideally we should always set an assessment in a cover lesson. That works perfectly. The cover teacher simply has to invigilate, and may even be able to get on with their marking or lesson planning. Instructions are clear and the risk of behaviour problems is minimised. However, sometimes the timing isn't right for an assessment.

From a maths perspective, the next best option is a whole lesson's worth of independent work - starting with a reminder of a method (in a textbook, on a worksheet or in a video), then a good set of practice questions and some extension problems. Ideally this lesson will be a continuation of the topic covered in the previous lesson. If your school has textbooks then this is easily done, but for schools without textbooks, I think that Corbett Maths is a very useful source of material.

Below is an example of a standard set of instructions for this kind of cover lesson - this can easily be copied and adapted for any topic.

Cover Lesson: Solving Quadratic Equations by Factorising
  1. Students write down the date and title in their exercise book.
  2. Show this seven minute video: https://corbettmaths.com/2013/05/03/solving-quadratics-by-factorising
  3. Display this slide on the board for the remainder of the lesson: https://drive.google.com/file/d/0B9L2lYGRiK2bRkhHM19WeGVPT1E/view?usp=sharing 
  4. Hand out these worksheets: https://corbettmaths.files.wordpress.com/2013/02/solving-quadratics-by-factorising-1-pdf.pdf. Students must work independently in their exercise book. They must write down the questions and show all workings.
  5. If a student finishes the entire sheet, hand them these extension problems: http://donsteward.blogspot.co.uk/2011/09/two-root.html
  6. Five to ten minutes before the end of the lesson, display or read out the answers and ask students to mark their own work: https://corbettmaths.com/2016/10/15/solving-quadratics-by-factorising-1

This lesson is easy for a non-specialist to deliver. The video ensures that all students are reminded of the method and therefore able to get started. Students then work independently throughout the lesson, getting lots of worthwhile practice done. Perhaps the cover teacher will allow them to quietly ask their partner for help if they get stuck. Meanwhile, depending on the class, the cover teacher (assuming they're not a maths teacher) may even be able to get on with their work.

Mathsbox provides helpful cover lesson resources (with subscription), but I don't know of any other resources available that are specifically designed for cover. Corbett Maths videos and textbook exercises seem to work very well though. I'd love to hear if you've come up with another approach to cover lessons that makes them easy to plan, easy to run and worthwhile for students. Please share!

2 September 2017

5 Maths Gems #76

Welcome to my 76th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. 'For Interest'
Dr Frost has made a set of 'Just For Your Interest' posters for A level mathematicians. These provide great subject knowledge development for maths teachers too.

I met Jamie Frost for drinks over summer - he has loads of exciting plans for his website so it's worth following him on Twitter (@DrFrostMaths) for updates. Lately he has been publishing PowerPoints for the new A level so do check them out if you're teaching Year 12 this year.
Drinks with Jamie Frost (@DrFrostMaths)
and Megan Guinan (@MeganGuinan1)
2. thaMographe
I was very pleased to receive a free thaMographe in the post! This is a wonderful invention that combines an entire maths set into a single piece of equipment.
I admit that I'm not great with accuracy at the best of times - constructions are my least favourite part of maths. I hate to see students struggling to use a pair of compasses and I very much hope that the thaMographe will one day be widely used by school children. It is certainly easy to use and accurate enough for school level mathematics - as demonstrated by my quick perpendicular bisector:

Ed Southall has written a thorough review of the thaMographe here.

You can order a thaMographe from www.thamtham.fr - shipping is free! Hopefully it will be available to buy in the UK soon.

3. Subtraction Methods
I love this graphic showing alternative methods for subtraction. It was shared by James Tanton (@jamestanton) who tweeted "Math is for each of us to own and do in whatever good way suits us best".
4. Graspable Maths
In Gems 75 I shared an algebra maze from MEI that was very popular. Through a comment left on that blog post, I discovered graspablemath.com, which is an exciting new interface for working with algebra. It's lovely to use - if you're on a computer and have some time to spare, have a play with the online algebra maze.
5. A Level Problem Book
Stuart Price (@sxpmaths) has been hard at work pulling together a large set of problems for A level maths. He has collated questions on a topic-by-topic basis, in four sections: Techniques; Problem Solving; Puzzles & Challenges, and Exam Review. The idea is that students can use these sets of questions for independent study throughout the course.

It's work in progress, but if you want Stuart to email you a link to his work so far (it's great!) please contact him via Twitter.

Here are my recent posts, in case you missed them:

I also launched my new 'Topics in Depth' page.

I was very grateful to a kind Summaths attendee for lending me copies of these 'Developing Thinking...' books which will help me in my research for my Topics in Depth project. These books come highly recommended.
If you're going to researchED next Saturday then do come along to the debate about maths GCSE - I'm on the panel of speakers.

Have you booked your ticket for #mathsconf13 on 30th September in Sheffield? I hope to see you there.

TES Maths Panel
On Tuesday I spent the day at TES with the lovely members of the Maths Panel which is led by Craig Barton. The TES Maths Panel reviews all free maths resources that are uploaded to TES. We do them in batches every now and then - it's a great way to discover hidden gems. We also do project work, for example we created a page of recommended resources for every single GCSE topic. TES are considering setting up panels for other subjects, and are changing the way that the review interface works, so we spent the day discussing this and other things related to maths education. It was a really good day and I was very pleased to finally meet Chris Smith (@aap03102), writer of the awesome maths newsletter that I blogged about in my 'Newsletter Gems' posts here and here.
With one of my favourite Scottish mathematicians - Chris Smith

Pizza with the panel

I had Inset yesterday and I start teaching on Monday - exciting!

Don't forget that my resource libraries might help with your lesson planning.

I'll leave you with this thought from Underwood Dudley, taken from his excellent piece "What Is Mathematics For?". I think this is quite inspirational at the start of a new school year.

"...when I am before a bar of judgement, heavenly or otherwise, and asked to justify my life, I will draw myself up proudly and say, “I was one of the stewards of mathematics, and it came to no harm in my care.”"

28 August 2017

Summaths 2017

My Summaths event took place yesterday in the glorious sunshine at Bletchley Park. In this post I just want to share a few highlights and say a few thank yous. This was the fourth maths teacher event that I've organised (my previous events being Christmaths 2015, Maths Meet Glyn and Christmaths 2016). I think that our online maths teaching community is wonderful so I really enjoy getting everyone together in person.

I fell in love with Bletchley Park when I visited it last summer. I knew that it would be a great venue for a maths teacher event.

75 teachers arrived bright and early on Sunday morning and spent the day exploring the beautiful Bletchley Park. Thomas Briggs ran a series of workshops on codebreaking which were very well received by all. In another room, there were maths activities and excellent Enigma demonstrations.

After a lovely lunch and glass of Pimms on the lawn by the lake, we wandered round to the National Museum of Computing. This place is awesome. They have loads of cool stuff for mathematicians, including collections of slide rules and calculators. I loved playing Mario Kart on an old N64, and one of the highlights of my day was a virtual reality dinosaur.
We returned to Bletchley Park for a super hard quiz which was won by Angus, Em, Jan, Brian, Em, Chris and Rob who only dropped one mark! Very impressive. The quiz is here if you'd like to have a go (with answers, and previous quizzes). Thank you to Ed Southall (@solvemymaths) for contributing the cryptarithm and anagrams.

Each attendee got a goody bag which contained freebies from @TTRockStars, @JaneAppleton24, @AQAMaths, @OCR_Maths, @thinkmaths, @FlipTheSystemUK, @Cipher_Master and @BuzzardPublish. Thank you very much to each of these generous contributors.

A large group of us went to the pub for dinner afterwards, and had a really nice evening.

Huge thanks to Thomas Briggs (@TeaKayB) from Bletchley Park and Jacqui Garrad (@JacquiGarrad) from The National Museum of Computing for helping me to organise the event. Thank you to everyone who enthusiastically participated, and special thanks to those who helped me fill and distribute goody bags. Finally, a huge thank you to my lovely colleague Lizzie Stokes (@MissStokesMaths) for giving me a lift to Bletchley and back.

It was a hot and tiring day, but I loved every minute. All of my photos are in a Facebook album here, and check out the hashtag #summaths to see more photos and tweets from the day.

I'm back to school on Friday, feeling inspired and raring to go.

15 August 2017

Planning for September: Year 12

I'm looking forward to teaching the new linear A level to two Year 12 classes this year. I've been preparing some materials for these classes and thought it might be helpful to share them here, in case they are of use to anyone.

1. Scheme of work and resources
When preparing schemes of work, schools have had to look very carefully at timings to make sure they can fit all of the A level content into the two year time frame (I blogged about this here). At my school we took the estimated hours from Edexcel's scheme of work as a starting point and cut everything by around a third - it just about works, though our teaching will be rather rushed.

My school's new A level scheme of work looks very similar to our GCSE scheme of work, with a front page showing an approximate timeline and then a more detailed page for each topic showing the specification and resources. We won't have any student textbooks so links to resources are vital. I've blogged about A level resources before and many of these are still useful for the new A level. There are a few gaps for new topics but we'll have to cross that bridge when we come to it.
Although the content of the maths specification hasn't changed dramatically, there are a few minor tweaks that we need to look out for. For example the AS specification now includes fractional inequalities like those shown below (these were previously on FP2 for Edexcel). It's a subtle change and straightforward to teach, but could easily be missed.
From Pearson Textbook Pure AS (spot the typo!)

Many schools are planning to teach the pure content first and leave the applied content until later in the year. When we come to the applied content, it will be useful to refer to Edexcel's Teaching Guide for Mechanics and Teaching Guide for Statistics.

2. First lesson
I've created a PowerPoint for my first lesson with Year 12 which you're very welcome to borrow and adapt. It includes course information, some introductory algebra activities (from Don Steward, Susan Whitehouse and Underground Maths), and the entry assessment I blogged about here.
First lesson activity from Susan Whitehouse
3. Student blog
At my previous school I was a Key Stage 5 Coordinator and really enjoyed running a simple blog for Sixth Form students. I hope to do this again this year. I've set one up at glynmaths.blogspot.co.uk and will use it to share information and exercises with students. As they won't have textbooks, it's important that I make sure they have access to plenty of independent study material throughout the course.

4. Student handbook and checklist
Our Sixth Form students are required to keep a course handbook or specification in their folder for every subject. This year I have updated our handbook for the new A level, including the topic checklist at the back. If you'd like to borrow and adapt this, there's a Word version here.
Delivering the new A level will be hard work for all involved, particularly for those teaching Further Maths. Initially we will have all the same challenges that we had for the new GCSE - a lack of past papers, relatively few resources, no grade boundaries and uncertainty around timings. But nevertheless, I think we're all really looking forward to getting stuck into teaching it next month.
Teaching support from Tarquin A level

4 August 2017

5 Maths Gems #75

Welcome to my 75th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. New Displays
I recently updated my displays page with some lovely new resources. This might be useful for teachers preparing their classrooms or corridors for September. One of my favourites is the new Maths Word of the Week display from @missradders.
2. Algebra Maze
Last month I joined the MA and received an exciting parcel full of publications. This included an edition of Mathematics in School in which I spotted this algebraic expressions maze from MEI.
The MEI wrote eleven consecutive articles for Mathematics in School and are soon to start up again. You can access all eleven of these MEI Insights here - thanks to @MEImaths for sharing these.

3. New A level Resources
I now have a page of resources for new A level topics. It's much like my new GCSE support page, but I'm still hunting for resources.

Thankfully a few new A level resources have been published recently:

4. Sector Area
In my post 'Polygraph Rocks' I wrote about the wonderful Desmos classroom activities. There's now a huge collection of activities on Desmos - they're definitely worth exploring. These lessons are really easy to run and work well if you have access to a decent IT room or if your students have tablets or laptops in the classroom. I spotted 'Sector Area' on Twitter recently and really like the way it's designed. It's a proportional reasoning activity in which students explore the relationship between circle area, sector area, and sector angle.
5. xaktly
I found the website xaktly.com by Dr Jeff Cruzan (@DrCruzan) which is like an online textbook for maths, physics, chemistry and biology. The maths section contains very clear explanations and some helpful graphics on misconceptions, definitions and methods.
The page on the metric system is a good example - Dr Cruzan's method for unit conversions is interesting and worth a look.

There's lots of A level content, including a page on optimisation with very useful example problems. 

In case you missed them, here are my latest posts:

I also published a list of maths education conferences for 2017/18 and my case study was featured on mtpt.org.uk.

My Summaths event is in three weeks and now I've seen the programme of workshops I'm even more excited. I'm also really pleased that I've had some generous donations of freebies to hand out on the day. There are still a few tickets left and booking closes on 14th August.

Do check out Craig Barton's latest podcasts and Adam Creen's list showing where to buy the cheapest calculators this summer.

In case you missed it, I'll leave you with this wonderful news about the success of the UK team at this year's International Maths Olympiad in Rio. The UK finished in ninth place, out of 111 participating countries, and top of all European nations for the first time ever.
The UK is hosting the International Maths Olympiad in 2019. Incidentally, Dr Geoff Smith's 'Advice to Young Mathematicians' is worth reading.