25 October 2016

5 Websites You Should Know... #2

I'm writing a new series of posts about five maths teaching websites that you may not be familiar with. My previous post was about the brilliant Corbettmaths.com.

The second website that I'm featuring is relatively new. I first wrote about MrCarterMaths.com in Gems 55 back in April 2016. Since then its content has grown considerably, though the website has retained its lovely sleek design.

The best thing about this website is how easy it is to use, which makes it perfect for busy teachers who don't have time to login and search through complicated websites to download resources. It has two simple menus: Differentiated Topics and Worksheets.

Differentiated Topics
The writer of this website is Darren Carter, a maths teacher from Sheffield. He has created bronze, silver and gold questions for a large number of topics.

Each page of questions follows the same simple format. Here's an example for changing the subject:

and here are a couple more examples: factorising quadratics and surds with brackets.
The questions are designed for fluency practice. There's no adverts and no clutter so these are suitable to display in the classroom using a projector. The menu system is so straightforward, the questions can be accessed instantly during a lesson when required. There are two simple buttons: one to generate new questions and one to reveal answers.

I tend not to use bronze, silver and gold questions in my lessons but I still find this website incredibly useful. I was recently planning a lesson on quadratic inequalities for Year 11 and wanted to give them five factorising questions as a starter, so I visited MrCarterMaths.com and did a quick screenshot of five questions and answers. This website is a great time saver in many ways.

Darren is adding new topics all the time, and even takes requests for topics through Twitter! What a star. It's great that he has started adding new GCSE topics - check out iteration, functions and quadratic sequences... and keep an eye out for more topics over the coming months.

The second section of MrCarterMaths.com features worksheets. These are useful if you don't have a projector or if you prefer students to have questions printed out. You select a difficulty level and a topic then print off a worksheet straight away. Again, these are straightforward, sensible worksheets for fluency practice.

The beauty of this website is its ease of use. It has quickly become very popular amongst teachers on Twitter, and word is now spreading further afield. The range of topics covered continues to increase all the time - follow @MrCarterMaths for updates. Huge thanks to Darren Carter for putting so much effort into building a lovely website that is such a time saver for teachers.

23 October 2016

5 Websites You Should Know... #1

I recently presented at a MathsMeet organised by Paul Collins. My presentation was entitled '5 Maths Teaching Websites You Need to Know'. My aim was to share five excellent sources of maths teaching resources that attendees may not have been familiar with. I plan to write a series of posts sharing the contents of that presentation.
The first website I'm featuring is Corbettmaths.com. You're probably familiar with this website, but have you explored it lately? Do you know everything it has to offer...?

The writer of Corbettmaths is John Corbett, a maths teacher based in Somerset who shares an astonishing volume of resources. His website has been around for quite a while - it was established in 2011, and over the years has accumulated thousands of free resources which are now used by teachers all over the world.
I thought I knew this website pretty well but when I was exploring it in preparation for this presentation, I found some stuff that I'd not seen before. For example, the Class Quizzes section has caught my attention. This is a new section of the website that is still being developed, but there are enough resources here to get started.
The idea is that these quizzes are given to GCSE classes to help them memorise key facts, formulae and processes. Students write 1 - 10 in their books and the teacher reads out the questions. I really like this idea and plan to start using this with my Year 11s from January. I think my students may also find these useful for self-quizzing at home during the final countdown to their GCSE exams.

John writes great maths puzzles and shares them in the Conundrums section of his website. These problems are challenging yet accessible.
John's 5-a-day resources are widely used. Each sheet features five quick questions from a mixture of topics. This allows students to revisit previously taught topics on a regular basis ('interleaving').

The range of resources here is impressive - there's a whole year's worth of 5-a-days for new GCSE at five different difficulty levels: numeracy, foundation, foundation plus, higher and higher plus. There's also a set of 5-a-days for A level (Edexcel Core 1) and later this year a collection of primary 5-a-days will be added to the website.
Some teachers use these resources as daily lesson starters, others have a corridor display where students can pick up their 5-a-days. John has blogged about the various approaches here.

Videos and Worksheets
John's videos and practice questions are a big part of the website. I find these particularly useful if I have a student who has missed a lesson or struggled with a homework - I email them a link to a Corbettmaths video (I like it that these can be accessed without the need for a login). Each video comes with a booklet of exam style questions and a textbook exercise. John has a blog post about how to use his videos and practice questions here.
John has started adding new GCSE topics to his collection, for example he already has videos and questions for quadratic inequalities, Venn diagrams, quadratic sequences, functions and pressure. Teachers who are nervous about teaching these topics for the first time might find John's videos useful in lesson planning.

Revision Cards
Higher and Foundation GCSE revision cards are now available to buy from Corbettmaths.com. They cost £8.99 per pack (discounts are available for bulk orders). This is a good use of pupil premium budget. These have been very well received by teachers on Twitter. They have the unique feature of a QR code on the back which takes students directly to a video for each topic.

If you didn't already know all the features of Corbettmaths.com then do explore. Hats off to John Corbett, a hard working teacher making our lives easier and helping students over the world.

Look out for the next post in my '5 Websites You Should Know' series, coming soon!

15 October 2016

The Folder Experiment

I'm trying something new with my Year 11s this year.

I ended up in a bit of a mess with this class last year. Their exercise books overflowed with worksheets, in fact it got so bad that at one point I was emailed by a parent complaining about the amount of loose paper her son was carrying around. Some of my students tried hard to keep things tidy, but my worksheet habit overwhelmed them and even the tidiest books buckled under the pressure.

I know I'm not the only teacher with this problem. Here are some of the causes:
1. I don't have access to textbooks. I use printed resources (often Don Steward and MathsPad) in every lesson... I love resources, in case you hadn't noticed.
2. I do try to display as much as I can on the board instead of printing it out (to save printing budget), but most of my activities don't work as well if not printed out.
3. I used to teach girls - most would fold and stick their worksheets beautifully (see picture below). I now teach boys... most aren't so bothered about keeping things neat.
4. I'm not particularly good at reminding students to stick sheets in during the lesson.

I don't think that messy books are the worst thing in the world, but I felt that there was room for improvement.
Good sticking!

My solution is to give a ring binder to each student. I've always had my A level students use ring binders but I've never done it at Key Stage 4 before.
So far, it's awesome. It's working really well. I will explain here what I'm doing, and report back later in the year on whether it's still working well.

For each lesson I prepare one double sided A4 sheet which includes a starter, space for notes, the main classwork exercise and an extension activity. If they need more space for notes or classwork, they have a stack of paper at the back of their folder.

The worksheets are now a well established routine. They give my lessons a really clear structure - this fits well with my teaching style. With a dedicated space for notes and examples, I'm seeing an improvement in their note taking (which was almost non-existent last year).

Revisiting Year 10 topics
My Year 11s have nine hours of maths a fortnight (last year Year 11 only had six, so this is a big improvement). Because I have young children I only work 4 days a week, meaning that one of their nine lessons is taught by another teacher. In her lessons my students are given a one hour Edexcel topic test to work through (these can be downloaded from the Emporium) - these are kept in a separate section in their folder. So once a fortnight my students are spending an hour doing exam style questions on previously taught topics. This is good preparation for their upcoming mocks and allows me to get on with teaching new content.

Multiple choice quizzes
I wrote here about the multiple choice open book quizzes that my Year 11s do every week. I love these! There's a section in their folder to keep their marked quizzes. When they get a quiz back they record their score on a tracking sheet so they can easily see topics that need more work.

There's also a section in their folders for marked homeworks. This means that when my Head of Faculty does a book scrutiny she'll easily see the feedback I've given. In previous years my marked work often ended up lost in a stack of loose sheets, so it looked like I never did any marking.

I set one assessed homework per fortnight that I mark and give feedback on. This gives me a good sense of how each student is getting on and, along with the quizzes, ensures they get regular feedback. Every other week I set a self-marking homework. My workload is far too heavy to mark homework every week for every class.
My Year 11s have an 'information' section in their folder which includes a topic checklist, topic timeline, progress data and exam information.

So far I'm loving the switch to ring binders. It's working really well. My students' maths notes and classwork are well structured and organised. This will be beneficial when they revise for their GCSEs. Although a few folders are getting a little bit messy (eg file dividers falling out), the majority are in really good shape. I do worry that the folders might overflow by May - perhaps lever arch files would have worked better given the volume of work we get through.

This was a fairly pricey experiment for me (I'm reluctant to spend any of my own family's money on equipment for school but this cost me £40 for foldersfile dividers and paper). One minor setback is that I teach this class in three different classrooms and most choose to leave their folders with me, which means I have to carry folders between rooms at the end of the day. Life would be easier (in many respects) if I were based in one classroom.

Overall my folder experiment is going really well. I will report back at the end of the year on whether I'll do it again next year!

9 October 2016

New GCSE: Capture-Recapture

If your school plans to use Edexcel for GCSE from 2017 then you may have spotted the capture-recapture method in the Higher Tier specification:
Source: Edexcel GCSE (9 - 1) Mathematics Teaching Guidance

Here's the sampling content in more detail:

Source: Edexcel Content Exemplification FAQs

It's worth noting that both Edexcel and AQA list stratified sampling as a topic that has been removed from GCSE. However, this comes with a caveat - both sampling and proportional reasoning do feature in the 9 - 1 GCSE, so it would be reasonable for exams to include a stratified sampling question even if students haven't been explicitly taught this topic (as long as the question doesn't use the word 'stratified' without explaining its meaning). So my advice - whatever board you're using - is to look at a few stratified sampling questions with your GCSE class, whether in a statistics lesson or a ratio and proportion lesson.

Stratified sampling is a great opportunity to use proportional reasoning, as is the capture-recapture method. If you've taught Edexcel's GCSE Statistics then you'll already be familiar with capture-recapture, but I'll explain it here in case you've not seen it before.

A simple example
Try this question... it will only take you a second.
I captured 50 fish from a lake. I marked a big cross on the back of each fish with a permanent marker*... 
I put the marked fish back in the lake and they happily swam away to join their friends. 
The next day I captured 20 fish from the same lake. 10 of them had a cross on their back. 
Can you estimate the total population of fish in the lake?
*no fish were hurt, promise.

I'm sure you spotted that the proportion of marked fish in the second sample was 0.5, and we can assume the same proportion of marked fish in the whole population. Given that I marked 50 fish, we can estimate that there are 100 fish in the lake.

A formula
If the numbers are less straightforward so the estimation can't be done mentally, it's easy to set up a formula to work out the population. This is certainly not a formula that students will need to memorise - it can be deduced using proportional reasoning.
You can see that the formula on the left simply shows that proportion of marked fish in the population is equal to the proportion of marked fish in the sample. The formula on the right has been rearranged to make N the subject.

Here's an example from the Biology section of BBC Bitesize. It would be better if they had shown the proportional reasoning and rearrangement process rather than just give a final formula.
Source: BBC Bitesize

The example goes on to list some assumptions - these are certainly worth discussing with your students.
  • There is no death, immigration or emigration (ie the population is closed)
  • The sampling methods used are identical
  • The marking has not affected the survival rate of the animals 

We also assume that animals do not lose their marks, that marking does not affect the likelihood of recapture, and that sufficient time is left between marking and recapture for all marked individuals to be randomly dispersed throughout the population.

An exam question
So what might this topic look like in a GCSE exam? Here's a question from Edexcel's 2014 Higher GCSE Statistics paper.
A scientist wants to estimate the number of fish in a disused canal. He catches a sample of 30 fish from the canal. He marks each fish with a dye and then puts them back in the canal. The next day the scientist catches 20 fish from the canal. He finds that 4 of them are marked with the dye. 
(a) Estimate the total number of fish in the canal. (2)
(b) Write down any assumptions you made. (2)

For part b, candidates have to mention two ideas, including something about the population being unchanged, or the idea of randonmess, or that markings remain unchanged.

Teaching ideas
I think this will be quite a nice topic to teach. Here are a few useful links:

I expect we'll see some more student resources appear on TES over the coming year.

Finally, here's a nice video to show in your lesson - Johnny Ball estimates the number of black cabs in London.

4 October 2016

5 Maths Gems #64

I haven't written a gems post in a long time! I've been too busy at work. So I've got a big list of resources and ideas from Twitter, enough to fill three or four posts. Let's make a start...

1. New GCSE Resources
Teaching new GCSE? Edexcel have come to our rescue by launching a set of resources for new GCSE topics. There's loads of useful stuff here including worked examples, exercises with answers, and extension material. Sixteen topics are covered include functions, iteration, Venn diagrams and geometric progressions.
Extract from 'N15 Bounds (Foundation and Higher)'

2. Fractions Task
Thanks to @MaxTheMaths for sharing this lovely fractions task. This is taken from Buzzard Publishing's Arithmekit Bundle (@BuzzardPublish). Check out CanDoMaths.org for more resources like this.
3. MathsFrame
It's been a long time since I last taught Year 7. Now I've got a low attaining Year 7 class I'm going to start adding lots of new resources to my resource libraries (for example I've recently added place value and addition). With my Year 7 class in mind, resources from mathsframe.co.uk (@Mathsframe) have caught my eye. There's over 200 free resources here - they're aimed at primary schools but secondary teachers may find them useful too.
Extract from Year 6 fractions assessment

4. Inspect the Spec
Craig Barton has been writing a great set of 'Inspect the Spec' posts on TES. If you're teaching new GCSE, you'll find these posts helpful. They contain information about what's in the GCSE specification (what's changed and what's the same) along with recommendations of TES resources. 

5. Number Line
Megan Guinan (@MeganGuinan1) first tweeted about this tool ages ago, but it's taken me a while to find a use for it. I recently used the zoomable number line from mathsisfun.com to help explain decimal place value to my Year 7s. Now I realise it will be useful for quite a few topics. My Year 7s were 'wowed' by it and asked me to keep zooming in (forever!). Then they realised it could also zoom out to show really big numbers. It's always great to see kids getting excited by numbers!

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

I've now sold half the tickets for #christmaths16. There's still 60 tickets left but bear in mind that the first 60 tickets sold in only 9 days so I recommend that you book now so you don't miss out! Visit christmaths.co.uk for more information.

I'll leave you with this lovely picture from an old maths textbook. Thanks to @john_overholt for sharing this.
The XXth Century Arithmetic published in 1903

1 October 2016


I had a great time at #mathsconf8. Thanks to Mark McCourt and La Salle Education for organising another fantastic event for maths teachers.

Friday night
We had a big turnout at the pre-conference drinks on Friday. It was lovely to catch up with people I've not seen in a while. Workload was a common discussion point - sometimes it's helpful to let off steam about the challenges of the job as well as sharing the highlights.

The best part of the evening was our Pringles Enigma machine activity! When we visited Bletchley Park over summer we were treated to a display of a real Enigma machine by Tom (@TeaKayB). At the time Tom mentioned that it's possible to make an Enigma machine out of a Pringles tube so we invited him along to #mathsconf8 drinks to show us how! Here's what I came up with, assisted by @JoLocke1 (it works! We were able to decrypt a message). 
Kim (@MsKmp) didn't have a Pringles tube but managed to make her Enigma machine out of a wine bottle! If you're interested in having a go at this activity, all the instructions and materials are here.

At the pre-conference drinks I also chatted to Craig Barton. I was interested to hear that he has relaunched his website mrbartonmaths.com. For a resourceaholic like me, this is exciting news! I'm looking forward to exploring all the resources that Craig has pulled together. For every topic he has provided specifications, videos, worksheets, diagnostic questions, lessons, rich tasks, interactive resources and probing questions. Amazing.

The conference was brilliant. I thoroughly enjoyed my day and went home feeling inspired.

The day kicked off with Mark McCourt talking us through the 1089 activity. I've heard of this activity before but not looked at it in detail. I really enjoyed doing the maths (even in base seven!) and can see that this would make a brilliant lesson for students. I hope to use it at school at some point this year.

I also enjoyed the speed dating session where I picked up a couple of excellent resources.

The first session I attended was Kris Boulton's talk on Engelmann. I saw the first part of this talk at researchED Maths and Science in June which I wrote about here.  Kris continued to talk about Engemann's ideas, including examples of how Kris has applied these ideas to his teaching. I find all of this really interesting, and it does make me question whether I use the most effective method of instruction.

It was interesting to see a snapshot of Kris' planning process for a sequence of lessons.
Thanks to @MathsWebb for this photo

I enjoyed watching videos of Kris' teaching in action, and was pleased that he spoke about the way he handled a student's negative behaviour (I don't think enough teachers speak about the challenges we face with regard to behaviour management, so this was refreshing to hear). The most striking thing Kris did in his video was remain silent when solving a pair of simultaneous equations on the board. I always talk through what I'm doing step by step, and I wonder if my talking distracts students from following what I'm writing. I need to think about this.

At the break I bought a calculator! It's likely my A level students will be using these next year so I'm going to start using it now to ensure I'm well practised by next September.

The second session I attended was about mastery and was delivered by Mark McCourt, a thoroughly entertaining and knowledgeable speaker. If you're interested in what Mark has to say about mastery, read his recent blog post #MasteryFail and look out for his next post too.

At lunch it was great to see so many teachers enjoying the maths activities at the Tweet Up.

After lunch I attended a session on subject knowledge by Ed Southall. I learnt lots from this session - my favourite thing was the word discorectangle (also known as a stadium). I learnt about the etymology of the word integer (not touching / standing alone).  I also learnt the difference between an oval and an ellipse (an ellipse has two lines of symmetry) and lots of other lovely snippets of maths knowledge. I love learning new things about my subject. You can download Ed's slides here.

All three sessions I attended were excellent.

I presented in the final slot of the day. My session was about new higher GCSE topics. I promised that I'd share my slides so you can use them to deliver training at school.
  • Here is the version I presented at the conference.
  • Here is the 'uncut' version which has lots of additional information. If you're presenting to your department I recommend using this one (split over two or three sessions).
  • Here are the GCSE questions that I used as a starter activity.

Links can be found in the slides themselves or in the notes section. I hope these slides are helpful, please let me know if I can clarify anything.
Thanks to @letsgetmathing for this photo

I really enjoyed catching up with Twitter friends and meeting lots of new people. Thanks to Mark McCourt for promoting my #christmaths16 event which you can buy tickets for here.

If you've not been to one of La Salle's maths conferences before, do come along to Bristol on 11th March or London on 24th June. Tickets will be available through mathsconf.com.

Finally, thanks to superstar Rob Smith for running the tuck shop and doing an amazing job of raising money for charity throughout the day. Every conference should have a tuck shop!

28 September 2016

Going Well...

I'm struggling with workload at the moment but I'm taking a quick break from the marking and UCAS references to share three things that are going really well this year.

1. Low Stakes Quizzes 
I started doing regular multiple choice quizzes with my Year 10s last year and instantly loved it (I wrote about it here). I've never done anything before that's given me so much insight into my students' understanding and the effectiveness of my teaching. My Year 10s ended up being taken by a PGCE student for a significant part of the year so the quizzes stopped, but I have reintroduced them this year with the same class (now Year 11) and again I'm reminded of how awesome these quizzes are.

My weekly quizzes take 20 minutes to run in the lesson (we do it every Friday), plus about 20 minutes to mark after the lesson. The quizzes don't take long to make when I'm planning my lessons - lately I've just been using the snipping tool to take questions from Diagnostic Questions (shhh, don't tell Craig!). You can view my quizzes here.

I give each student a grade (A, B or Not Yet) and anyone who scores 100% gets a sticker (they love that!). The quizzes are open book so there's no stress for students - in fact they love them (I get a cheer when I say it's time for the quiz!) and they are always excited to see their score in the next lesson. For me 'it's like I'm looking at the freaking Matrix' (in the words of Nathan Kraft in this post about vertical whiteboards!). Seriously, this is one of the best things I've ever done.

2. Folders
My Year 11s now use ring binders instead of exercise books. It's brilliant. I need to write a separate post about how this works because there's lots to say. Loads of people told me it wouldn't work, mainly because the folders would quickly become disorganised (which may still happen - we're only three weeks in), but I've designed a good set of resources that minimise the risk of messy folders. I'm pretty confident that it will continue to work well. Watch out for a post about this!

3. Times Table Rock Stars
I'm not sure I'm allowed to put photos of my students on my blog, but if I could then you'd see the happy faces of my Year 7s absolutely loving Times Tables Rock Stars (whilst wearing wigs and sunglasses!). All Year 7 teachers at Glyn now have one lesson in an IT Room every fortnight to run a Times Tables Rock Stars lesson. I do the paper version with my class too, plus I've just launched an after school 'Rock Gods' club for keen Year 7s. A number of teachers have also set up other classes (Year 8 to Year 10) and it seems to be going well all round. My students happily sit there for a full hour enthusiastically practising times tables, and I get to listen to rock music so it's win-win...!

So that's three things are going particularly well for me this year. Are you trying anything new that seems to be working? Please tweet me or comment below.

24 September 2016


I'm very excited to share the details of this year's Christmaths event, which takes place in London on Thursday 22nd December 2016.

#christmaths15 was a great success (read about it here). We had an afternoon of CPD with brilliant speakers followed by food, drinks, puzzles and a quiz.

I know that many maths teachers are looking forward to the opening of the new maths gallery at the Science Museum, so I decided to organise a different type of Christmas event this year. Here's the plan:

3pm - 5pm
: Group visit to Mathematics: The Winton Gallery. Explore this exciting new gallery in the company of fellow maths teachers.

5pm - 7pm: We will have exclusive use of the Media Space Cafe at the Science Museum where you will be treated to a glass of fizz and a mince pie. The Big Fat Christmaths Quiz will return! Tickets for this reception are only £12. There are 130 spaces available and I expect these to go quickly so book now!

From 7pm: If anyone fancies a bit of festive socialising, we'll be going round the corner to The Hereford Arms afterwards. This isn't ticketed so you can just decide on the day if you'd like to come along.

For full details of the event and to buy tickets visit christmaths.co.uk. Please invite your friends and colleagues along too! All welcome.

17 September 2016

The Deadly Sins of Maths

A Twitter conversation with Ben Ward got me thinking about a display idea...

There are some misconceptions and mistakes that come up time and time again. Last week I set a lovely Don Steward quadratics homework for my Year 11s and was dismayed to see a number of them do this:
(x + 2)2 =  x2 + 4
When I returned the homeworks I talked to the whole class about this common mistake. I told them that it makes me cry every time I see it so they must never ever do it again! When I asked them why it was wrong, they were able to explain what had happened and tell me the correct way to do it (phew!).

When I next spot common misconceptions in my students' work, I'm going to tell the perpetrators that they've committed one of the deadly sins of maths, and point them in the direction of a classroom display. Making a big deal about these mistakes (in a half-jokey way that will stick in their heads) is a good way to lower the risk of students repeating the same mistake in an exam!
You can download my posters here (there are 20 posters to pick from - you may not agree with all my choices). I've also made a US-friendly version (using the word math instead of maths) which you can download here.

Some of these posters will make students stop and think - it might not be obvious to them what the mistake is.

In our teaching we should try to preempt common misconceptions - this is where clever questioning and well-written resources come into play. But sometimes we can't see mistakes coming - this is why effective marking and feedback are essential.
These days marking doesn't have to be handwritten - websites like Hegarty Maths can do it for you.

If you're looking for resources for highlighting and tackling common misconceptions, here are a few starting points:

I have a misconceptions page here that links to various websites and resources relating to common misconceptions.

If you use the 'deadly sins' idea, I'd love to hear how it goes!

Two days after creating this display, it was up on @jase_jwanner's classroom wall.  He has also suggested creating a students' display called 'Maths Heaven', where they write down the correct versions eg (-5)2=25.