12 January 2019

Five for Five

My friend Ceri recently told me about something she does in her maths lessons. It works really well for pupils who lack confidence in maths. I asked her permission to share it here. It's simple but effective. She calls it 'Five for Five'. I'm sure there are teachers all over the world doing something similar. Here's Ceri's version:

Start by producing a set of five mixed topic questions for the week. It's important that these are tailor-made for your class. You could download something generic, but it doesn't take much longer to write the questions yourself once a week. The advantage of writing the questions yourself is that you can choose five topics that are relevant to your class, for example something they struggled with on a recent assessment, or something they learnt for the first time a few weeks ago. Writing the questions yourself also means you can can get the difficulty level right.

Here's an example of a typical set of questions:


Ceri follows the schedule described below (of course this can be adapted if you don't see the class five times a week).

Monday
Ceri gives her class the five questions at the start of the lesson. They have a go on their own, but Ceri knows (because she wrote the questions) that they will struggle. Ceri then spends a good amount of time - half the lesson if necessary - going through the questions. Her pupils annotate their questions with detailed notes.

Tuesday
Ceri gives her class the same five questions with different numbers. Pupils complete the questions on their own but are allowed to look at their work from previous day. Ceri spends a shorter amount of time going through the questions afterwards.

Wednesday
Ceri gives her class the same five questions but again with different numbers. Again, they can refer to their notes and answers from the previous lesson. This is now a fairly quick starter activity. Often they can do it in five minutes ('five for five in five') but there is no time limit. There's something else for pupils to get on with until everyone is ready.

Thursday
Same again. By now they should be getting them all right.

Friday
Same five questions, different numbers, but this time they start the lesson by completing the questions on their own in test conditions without looking at their notes. Even without their notes, it's very likely they will now get them all right. 


Success is very motivating for pupils who struggle in maths. Going from zero marks on Monday to full marks on Friday is very powerful for transforming a pupil's attitude and confidence.

Let me know if you try it.

Thanks to Ceri for letting me share this!






1 January 2019

5 Maths Gems #101

Happy New Year! Welcome to my 101st gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Euclid's Elements 
Nicholas Rougeux (@rougeux) has made something incredible. He has recreated Byrne's 1847 edition of Euclid's Elements including interactive diagrams, cross references, and a new poster of all the original illustrations.
You can read an in-depth blog post on how it was made here. It's absolutely wonderful.
2. Retrieval Facts
Jonathan Hall (@StudyMaths) added a retrieval facts section to mathsbot.com. It's primarily designed for printing but can be projected onto the board too. I can see this being a helpful revision tool for Year 11.
If you think that regular quizzing is a good way for students to learn facts and formulae, then look out for an exciting new book which will be available for students to buy in 2019. Listen to the end of my recent podcast with Craig Barton if you want to know more about this.

3. Surds Bricks
Thanks to @pwdrysdale for sharing this surds activity. Each brick is the sum of the two beneath it.
4. A Level
Whilst preparing some CPD on Large Data Set for A level I discovered this cute video explaining how oktas work. If you teach Edexcel A level then you might find this helpful. The Examiner Report suggests that most students taking their A level exam in June 2018 were clueless on oktas.


While we're on the subject of A level, do check out this letter from a cat food company. @mathematicsprof wrote to them about how they could minimise material if each can’s height equals its diameter. They wrote back to explain that it's way more complicated than maths problems suggest. Next time I teach optimisation I will be showing my students this letter!
A level teachers might also like this Integration a Day Advent Calendar. Designed by Tom Bennison (@DrBennison) for Christmas, this would work well at any time of year - an integration question every lesson is a very good idea!
5 . Puzzling App
Henk Reuling (@HenkReuling) has created a free puzzle app which involves adding and multiplying integers. It's great fun for teachers, and it might be useful for students learning to work with negatives too.
It's really fun so do have a go.

Update
In case you missed them, I wrote two posts over the Christmas holidays:


Check out @literallyjustq's latest thread about calculator functions which includes a calculator 'cheat' for finding the nth term of a quadratic sequence. 

Thank you to Jamie Frost (@DrFrostMaths) for hosting drinks for maths teachers at his house again last week - I had a great evening.

I'll leave you with @Blogdemaths' lovely 'How to Draw a Regular Pentagon, IKEA Version' (inspired by the work of @ideainstruction).

All the best for 2019.







27 December 2018

Factorising by Inspection

In 2018 I decided to write more short posts about approaches or methods that teachers might not have seen before. When I share these posts, I am well aware that there will be many people who already know the thing I'm blogging about, but I figured that it's still worth sharing even if it's only new to a handful of people.

My first post in this series was about using vectors for enlargements. Today's post is about a way to save time when factorising a non-monic quadratic expression (ie a quadratic where the coefficient of x2 is greater than 1) by inspection.

Back in September I had a post published on La Salle's blog about methods for factorising non-monics. I showed that by looking at old textbooks we can see how methods have changed over time.

I explained that I prefer to factorise by inspection, but most teachers these days factorise by grouping (ie 'splitting the middle term'). In response to that post I had lots of teachers either (a) try to convince me that grouping is better than inspection (b) try to convince me that another method is better than inspection. Often teachers argue that their method is great because their students really liked it in the lesson, but I'm more interested in the extent to which methods 'stick' in the long term. When I used to teach factorising by grouping my students were always happy with it at the time, but a few months later they would struggle to remember the full procedure.

Factorising by inspection is intuitive and logical, so there's no procedure to memorise. I appreciate that most teachers still prefer the grouping method, and I do not intend to try to convince anyone to change their mind. But for those of you who like factorising by inspection, here's a tip from Susan Russo (@Dsrussosusan):

Let's say you have to factorise 6x2 + 17x + 12.

Factorising by inspection is super-quick once you get the hang of it, but here both 6 and 12 have multiple factors so this one might take a bit longer than others.

If you list all the possibilities and check each one, there are twelve cases to check.
(6x + 1)(x + 12)
(6x + 12)(x + 1)
(6x + 2)(x + 6)
(6x + 6)(x + 2)
(6x + 3)(x + 4)
(6x + 4)(x + 3)
(2x + 1)(3x + 12)
(2x + 12)(3x + 1)
(2x + 2)(3x + 6)
(2x + 6)(3x + 2)
(2x + 3)(3x + 4)
(2x + 4)(3x + 3)

Yawn!

An expert would probably work out the correct combination fairly quickly without writing down all the options. For a novice it's a pain that there are twelve options to think about here. At first it seems like it might take a while to select the correct combination.

Susan pointed out something which should be totally obvious but hadn't occurred to me before. We can teach our students to refine their guesses in order to make this method more efficient. Here's the key: each bracketed expression shouldn't contain any common factors. For example if you have a 2x then you can't put an even number in with it.

Let's look at that list again and immediately disregard any option where there's a common factor in one or both brackets.
(6x + 1)(x + 12)
(6x + 12)(x + 1)
(6x + 2)(x + 6)
(6x + 6)(x + 2)
(6x + 3)(x + 4)
(6x + 4)(x + 3)
(2x + 1)(3x + 12)
(2x + 12)(3x + 1)
(2x + 2)(3x + 6)
(2x + 6)(3x + 2)
(2x + 3)(3x + 4)
(2x + 4)(3x + 3)

It turns out there are actually only two cases to check by inspection. Students fluent in expanding brackets should be able to do it in seconds. You can immediately see that the first option will give a large coefficient of x, so we check (2x + 3)(3x + 4) and find that it works.

For some reason I've never shared this time-saving tip with my students. I'm very grateful to Susan Russo for bringing it to my attention. Let's try it again with one more example: factorise 12x2 + 11x - 15. Here's the massive list of 24 options to consider:

(12x + 15)(x - 1)
(12x + 1)(x - 15)
(12x + 5)(x - 3)
(12x + 3)(x - 5)
(6x + 15)(2x - 1)
(6x + 1)(2x - 15)
(6x + 5)(2x - 3)
(6x + 3)(2x - 5)
(3x + 15)(4x - 1)
(3x + 1)(4x - 15)
(3x + 5)(4x - 3)
(3x + 3)(4x - 5)
(12x - 15)(x + 1)
(12x - 1)(x + 15)
(12x - 5)(x + 3)
(12x - 3)(x + 5)
(6x - 15)(2x + 1)
(6x - 1)(2x + 15)
(6x - 5)(2x + 3)
(6x - 3)(2x + 5)
(3x - 15)(4x + 1)
(3x - 1)(4x + 15)
(3x - 5)(4x + 3)
(3x - 3)(4x + 5)

Removing those with a common factor in one or both brackets gives us this:
(12x + 15)(x - 1)
(12x + 1)(x - 15)
(12x + 5)(x - 3)
(12x + 3)(x - 5)
(6x + 15)(2x - 1)
(6x + 1)(2x - 15)
(6x + 5)(2x - 3)
(6x + 3)(2x - 5)
(3x + 15)(4x - 1)
(3x + 1)(4x - 15)
(3x + 5)(4x - 3)
(3x + 3)(4x - 5)
(12x - 15)(x - 1)
(12x - 1)(x + 15)
(12x - 5)(x + 3)
(12x - 3)(x + 5)
(6x - 15)(2x + 1)
(6x - 1)(2x + 15)
(6x - 5)(2x + 3)
(6x - 3)(2x + 5)
(3x - 15)(4x + 1)
(3x - 1)(4x + 15)
(3x - 5)(4x + 3)
(3x - 3)(4x + 5)

So this time we eliminated half the possibilities. It's not as time-saving as in the first example, but still helpful. My next step would be to try the less extreme numbers (ie not those involving a 12x or a 15) so that gives me only four options to test initially. For an experienced factoriser it's fairly quick to see that (3x + 5)(4x - 3) works.

Of course, in reality we never really list out all the options and then decide what to eliminate. What most people actually do when faced with 12x2 + 11x - 15 is write down (3x      )(4x      ) and then (often in their head rather than on paper) try some numbers that multiply to give -15. So it's helpful to remember that there's no point putting and 3 or a 15 in the first bracket.

This isn't a big game-changer and it doesn't help with every quadratic, but I like things that save us time. When solving a long, complicated problem at A level, it's good to able to factorise quadratics efficiently.

If you hadn't realised that you can quickly eliminate options in this way then I hope this was helpful.

If you want to have a play with this, there are lots of non-monic expressions to factorise here.






22 December 2018

2018 Highlights

Last weekend I recorded a podcast with Craig Barton to celebrate my 100th gems post. I love the way @boss_maths described it: "So informative and entertaining, listening to this felt uncannily like listening to TMS as a cricket fan"! You can listen here and see what you think. The conversations we had in the podcast made me realise how much happens in a year. In this post I look back at 2018 and list some of my personal highlights, and look ahead to what's coming up in 2019.

The start of 2018 saw the publication of Craig's book How I Wish I'd Taught Maths. I can't believe that was only a year ago! Having read the book in advance I knew it was going to be a huge success, but I couldn't have predicted how much impact it would have on the maths education community. It's not just the teachers of Twitter who have told me how much their teaching has changed since reading Craig's book. I go into lots of different types of schools and see both new and experienced teachers trying example-problem pairs, silent teacher and other techniques that I probably wouldn't have seen at all in 2017. These teachers are keen to tell me how much Craig's book has made them more reflective, and how entire departments are now taking more interest in research and seeking to improve their practice.

Thankfully, opportunities for maths teachers to take control of their own professional development have continued to grow. We still live in times where most schools are unable to support requests for term-time subject specific CPD, but increasingly we are able to attend CPD at the weekends if we choose to. Of course weekend CPD is not suitable for everyone, so thankfully it remains entirely optional. I adore being part of the community of hundreds of maths teachers who participate in these events and am very grateful to the organisers for regularly bringing us all together.

In 2018 I attended three of La Salle's national maths conferences and loved every minute. If you're a maths teacher and you want to try some Saturday CPD for the first time, do check out the 2019 events (visit mathsconf.com for details). The next one takes place in Bristol on Saturday 9th March.

At the Manchester conference I presented on indices, and at the Birmingham conference I presented on quadratics.
If you missed these presentations then you  might be able to catch me presenting them again next year. I'm presenting Indices in Depth at the ATM/MA London Branch event on 19th January and How to Solve an Adfected Quadratic at the #HabsGirlsConf on 23rd March.

I will also be presenting new material at a number of events in 2019, including Educating Northants on 30th March, the ATM/MA conference at Easter, and both ResearchED Rugby and the MEI conference in June. There are loads more maths education events happening in 2019 - check out my conference listings here.

In addition to the La Salle conferences, I was fortunate to attend a number of excellent events in 2018. It was an honour to deliver the keynote presentation at the BBO Maths Hub secondary conference, and I thoroughly enjoyed the second JustMaths conference which took place at Alton Towers in the middle of the summer heat wave.
David Faram, me and Craig Barton on the rapids

I also attended my first ever residential maths education conference at Easter. BCME (the British Congress of Mathematics Education) only takes place every four years so it was quite a big deal. I loved it - not only for the CPD, but also for the social programme (did I mention that we won the quiz?!). I also very much enjoyed recording a daily conference podcast with Craig in which we reflected on the sessions we'd attended that day. I can't wait for the upcoming ATM/MA conference which takes place in the Easter holidays - there's a ceilidh, a quiz and a disco! And the daily podcast will be back. 

2018 was the year that I became a bit braver. I often turn down exciting opportunities, normally because of family commitments but sometimes because I think I won't do a good job. After turning down the opportunity to appear in an advertising campaign for Mazda at Easter, I kicked myself for weeks and resolved that I should stop saying no to things. So when I was invited to take part in the Big Internet Math Off, I said yes. And later in the year I also said yes to presenting at the MathsJam Annual Gathering, and to contributing to Craig's 'Slice of Advice' podcasts. In all three cases women were underrepresented, not through the fault of the organisers but because more women did not take the opportunity to participate. This made realise how important it is to keep saying yes, even to things I find a bit scary. I can't complain about women being underrepresented if I say no to everything!

Another first for me in 2018 was having two articles published in print for the first time. My article on indices published in Teach Secondary magazine in October, and a month later my article on the order of operations was published. I'm still chuffed about these articles.

My blog posts have been increasingly influenced by the research I have been doing through old maths textbooks. Blog posts I am particularly proud of from the last year include my posts on ratio, bounds, surds, algebraic LCM and HCF, and Year 7 maths activities. Check out my blog archive to see the whole collection.

Every year I host a social event for maths teachers. This year it was LateMaths - a big party in London to celebrate the launch of More Geometry Snacks by Ed Southall and Vincent Pantaloni. It was a great night and I am very grateful to everyone who helped me make it a success.

I have lots of ideas for events I'd like to run in future. In July I'm hoping that Rob Smith and I will run an event which (fingers crossed!) will involve a trip to the amazing MA archive at the University of Leicester. I'd also love to run a two day residential maths education conference at the same venue as the MathsJam Annual Gathering. It's a shame I don't have the time and money to run events more often because I really enjoy it.

What will 2019 bring? If you haven't already read Craig's book, perhaps give it a go. If you've never been to a La Salle maths conference, maybe 2019 is the time to try one. If you've not done one of the big Easter conferences, this might be the year to come along. If you've never listened to a podcast, have a go and see if you like it. If you're not on Twitter, consider joining. We're a very welcoming maths community, and we're stronger together.

We live in exciting but incredibly challenging times for maths teachers. I can't wait to see what 2019 brings.

I'll leave you with some of my favourite photos from 2018.

With my old PGCE buddy Colin Hegarty
 at GLF's first annual maths conference

With ex-colleagues Lizzie, Amelia and Sarah at prom 

Recording a conference podcast with Craig

At MathsJam with friends Mariana, Ed, Tim and Joe

Summer drinks at Dr Frost's house. 


With Megan Guinan at a Chalkdust Magazine Launch Party

Celebrating three new books and one new job with my Twitter besties
Craig, Ed and Tom at #mathsconf14 in Kettering

On the MA bookstand with Rob Smith
 at #mathsconf15 in Manchester

At BCME with Ed, Craig and Hannah Fry

At LateMaths with Matt Parker and Ben Sparks


Have a wonderful Christmas and New Year everyone!







8 December 2018

5 Maths Gems #100

Welcome to my 100th gems post!

This is a big milestone for me. I've published 327 posts since I started writing my blog four and a half years ago. One hundred of those posts have been part of my 'Maths Gems' series - each one has featured a selection of news, ideas and resources for maths teachers.

When I joined Twitter I couldn't believe how many ideas and resources were being shared by maths teachers everyday that weren't being seen by the hundreds of thousands of maths teachers who aren't on Twitter. I remember trying to convince a colleague to join Twitter and he said 'I just don't have time for it. I wish someone could just summarise the ideas for me'. So that's what I try to do.

I used to write one gems post a week (I was on maternity leave!) but now I work full-time I only manage one or two gems posts a month. Twitter still provides a constant stream of material to pick from, so I continue to summarise and share some of the best ideas, in the hope that I can get these ideas into classrooms all over the world.

To celebrate the fact that this is my 100th gems post, I'll be recording a special podcast with Craig Barton next weekend. In preparation for this podcast Craig wants you to choose your favourite gem (there are 500 to choose from, all indexed here). Tweet, DM or email Craig (or comment below) to explain why you chose it, and it could end up on the show.

On with the gems...

1. Mastery Learning Cycle
Over the course of the last two years Mark McCourt (@EmathsUK) has published a series of posts on mastery. You must read these excellent posts if you haven't already! Oliver Caviglioli (@olicav) and Mark have worked together to create a poster which visualises Mark's model of the Mastery Learning Cycle.
This is just an extract - download the poster to understand what it's all about. This is definitely something to share with all trainee maths teachers (and probably all experienced maths teachers too).

No doubt Mark's book 'Teaching for Mastery', due to be published in Spring 2019, will be a must-read too.

2. Manipulatives
If you want to use manipulatives in your teaching but don't know where to start, Craig Barton and Bernie Westacott have recorded a video podcast that you will find very useful. You can access the videos through Craig's Youtube playlist. For example here Bernie explains how to use manipulatives to teach negative numbers:



I've blogged before about Jonathan Hall's (@StudyMaths) amazing library of virtual manipulatives. It has continued to grow.
One of the new additions is a bar modelling tool. It's very easy to use and I'm sure lots of teachers will find it helpful.
3. Indices Tasks
Miss Konstantine‏ (@GiftedBA) shared a task for exploring indices. Students sort the cards and find the odd one out.
Peter Drysdale‏ (@pwdrysdale) made a Desmos version of this card sort.

I can't keep up with all the ideas and resources that Miss Konstantine‏ (@GiftedBA) has been sharing lately! For example I enjoyed her recent perimeter problems. Check out her Twitter feed and blog for lots more great stuff.
Speaking of indices, I made an indices task for a recent Teach Secondary article. This resource is designed to be used with a Year 7 class after spending some time on index notation, but it would work with other year groups too. The full resource is here - it contains four introductory indices activities.
4. Area
Here's a nice idea to help students develop an understanding of what area is. Ilona Vashchyshyn (@vaslona) challenged her students to write their name so that it covers an area of exactly 100cm2. Read the thread for ideas on how to extend this activity.


5. Assessment and Questioning
Mrs Budak (@mrsbudak) tweeted an interesting idea from ⁦‪@teacher2teacher‬⁩ that could work in every subject. At the end of an assessment students are given the opportunity to write down everything else they know about the topics on the test. It stops students being frustrated when a test doesn't cover the things they revised, and it's probably a good use of time to retrieve stuff from one's memory and write it down (it definitely beats sitting there waiting for the test to end!).

Finally, for some reason this reminded me of another gem that I've been meaning to share for ages...


It such a simple idea little change, and so easy to do! It's worth reading the thread for discussion and ideas. Credit to Howie Hua (@howie_hua) for first tweeting about this back in May. Here's another of Howie's ideas:


Update
I've had a busy few weeks visiting a number of different schools, including one where I saw silent teacher in action for the first time.

I helped to run the first day of a new London-wide Maths Hub Work Group on developing A level pedagogy, which is led by Carlos Karingal. We were fortunate to have a fantastic group of teachers attend and I look forward to seeing how our A level teaching develops throughout the year. In my session I talked through some of the ideas in this excellent piece written by Chris McGrane about approaches to teaching calculus.

Next week I'll be supporting Chris Reilly in running another Maths Hub Work Group - Challenging Topics at GCSE. I'll blog about this soon.

My second Teach Secondary article is now available to read online. It's about order of operations, and opportunities to interleave this topic with fractions, decimals and algebra.
Did you see that Pearson have a new series of maths textbooks coming out? It's called Purposeful Practice and you can view sample pages here.

Finally, Christmas is fast approaching so you might find a use for my collections of seasonal resources (here and here) - some are topic based and some are for enrichment. I've written various posts about Christmas presents for maths teachers over the years (here is last year's post on TeachWire if you're looking for inspiration). If you want to treat yourself during December, the MA has a Christmas advent calendar where you can get daily discounts on MA books.

I'll leave you with this lovely problem shared by James from MathsPad (@MathsPadJames). There are a range of solutions in the comments (spoiler alert!), but it can be solved in a matter of seconds without any workings using GCSE level maths.







24 November 2018

5 Maths Gems #99

Welcome to my 99th gems post. This is where I share some of the latest news, ideas and resources for maths teachers.

1. Non-Examples Quizzes
I blogged about the new website nonexamples.com from Jonathan Hall (@StudyMaths) back in Gems 95. There are now some great new features on the website including Frayer Model templates and Multiple Choice Quizzes.
The multiple choice quizzes come with a QLA allowing instant identification of misconceptions.

On Twitter Bernie Westacott (@berniewestacott) described how he used the multiple choice quizzes with an intervention group:

2. Sum Fun
I had an email from a maths teacher looking for books by the author of this A level resource:
It turned out the original books are out of print but Twitter came to the rescue and thanks to Hans Stroeve (@stroevey) we now have the full collection of books scanned in and available to download here. They remind me of Maths with Pizzazz resources and I know they won't appeal to everyone! They include resources for topics from Key Stage 3 right up to matrices and polar coordinates! Warning: always check that the joke is appropriate before using these resources with students.

3. A Level Questions by Topic
Thank you to Chris Ansette (@mransette) who has collated old Exexcel exam questions for Pure and Mechanics and organised them for the new A level. You can download them here. These well formatted collections of exam questions with answers are really helpful for A level maths teachers.
4. Calculator Poster
In Gems 97 I featured a link to a poster of an A level calculator. Casio Maths (@CasioMaths) have also shared a set of high resolution posters of the fx-83GT Plus, which is commonly used at GCSE. You can download the posters from the Casio website.
On the subject of calculators, read this thread from @literallyjustq for some calculator tips.

5. Times Table of the Week
I see a lot of Year 7s really struggling in lessons (on topics like multiplication, division and fractions) because they don't know their times tables. I have long been a big fan of Times Tables Rock Stars to help fix this. I like @DynamicDeps's idea for a times table fact of the week. The suggestion is to use the Times Table Rock Stars heat maps to identify a multiplication fact that students struggle with, and to put up a poster of that fact everywhere in the maths department, and in fact all over the school.
Bruno Reddy has now made a set of 'Times Tables of the Week' posters for all multiplication facts which you can download here.
Perhaps maths teachers and form tutors could regularly quiz individual students on the weekly multiplication fact. Given that there are only 21 facts to memorise (assuming students already know their 1, 2 and 5 times tables), you can easily get through the whole lot in a school year if you do one a week.
The 21 Facts from Kangaroo Maths
Update
I had an absolutely wonderful time at the MathsJam Annual Gathering last weekend. Thank you to the organiser Colin Wright and to everyone else involved. I absolutely love everything about the weekend and would really like to run a maths education event with the exact same format. Maybe next year!
Me, Mariana, Ed, Tim and Joe at the MathsJam Annual Gathering 2018

If you like the idea of social puzzling, do check out the monthly MathsJam events, and also Puzzled Pint's monthly social puzzle event in pubs all over the world. You can download Puzzled Pint's awesome puzzles for school maths clubs too.

I had another article published in Teach Secondary this month. It's about order of operations, and opportunities to interleave this topic with fractions, decimals and algebra. It comes with a free algebraic order of operations resource!
I also presented on order of operations to Harris Heads of Maths this week. The idea was to show that 30 minute CPD sessions on specific topics that are coming up on the scheme of work are a good use of maths department meeting time.
Hannah Fry has agreed to become the 2020 President of The Mathematical Association, which is very exciting news for all MA members.

Next month I will publish my 100th gems post (I have some cracking gems lined up!) and will record a celebratory podcast with Craig Barton. Craig will be asking listeners to get in touch with him in advance to share their favourite gems from over the years. So if there's something you use in your teaching that you found out about through a gems post then do let Craig know! Check out my gems index to see the whole collection!

I'm not normally one for motivational posters, but here's a quote that I'd have up by my desk if I had a desk. Often attributed to CS Lewis, this is a great message for a Year 11 class getting mock papers back. Thanks to Jen McMillan at Harris Greenwich for this!