31 May 2016

Useful GCSE Questions from Linked Pair Papers

If you attended any training on the new GCSE last summer then you may have been advised to look through Linked Pair papers for questions on new GCSE topics. It's a nice idea, but what teacher has time to trawl through past exam papers?

A year later, I've now taught Linked Pair (for the first and last time) so I have a better idea of whether the Linked Pair papers are actually helpful. Before you start searching through papers, here are a few caveats:
  • There are loads of topics in Linked Pair (spreadsheets, flowcharts, AER, linear programming, moving averages etc) that are not in the new GCSE.
  • There are some new GCSE topics that are not in Linked Pair such as functions, iteration and quadratic inequalities.
  • There are a few topics in Linked Pair that are in the new 9 - 1 GCSE - so this is where the papers are helpful (ie Venn diagrams, quadratic sequences, gradient of a curve and area under a graph). 
  • There are also some lovely challenging questions in Linked Pair papers - on familiar topics such as bounds, angles and forming equations - which might be helpful in lessons. I've shared some examples below. 
The easiest way to access past exam questions - rather than trawling through papers - is to use a test building tool (AQA's Exampro, Edexcel's ExamWizard, OCR's ExamCreator or Eduqas's Question Bank). I think these tools are really useful for creating resources such as homeworks and end of year exams, so a worthwhile investment for a maths department.

Density
The topic 'compound measures' has grown in the new GCSE. It can be hard to find resources for teaching density so you'll be pleased to hear that there are some good questions in Linked Pair exams. There's a nice example below. I've put a worksheet on TES containing this question and similar density questions.
Applications 2 Higher, Edexcel, June 2015, Question 16

Bounds
Compound measures links really nicely with bounds - it's good to see an exam question that combines these two topics.
Applications 2 Higher, Edexcel, June 2013, Question 17

Forming expressions
Linked Pair GCSE papers contain a lot of questions in which students have to form expressions. This question takes some thinking - it really stumped some of my students:
Applications 1 Higher, Edexcel, June 2014, Question 20

Angles
This question tests understanding of angles in polygons:
Methods 2 Higher, Edexcel, Specimen Paper, Question 7


My class struggled with this angles question in their mock exam this year:
Applications 1 Higher, Edexcel, November 2015, Question 2


Probability
Did you like Hannah's sweets? Try this one!

Methods 1 Higher, Edexcel, November 2015, Question 24

Percentages and Ratios
The Applications module in Linked Pair contains quite a lot of wordy questions that EAL students may struggle with. Here are a couple of examples. These might be worth trying with new GCSE classes.
Applications 1 Higher, Edexcel, Specimen Paper, Question 15

Applications 2 Higher, Edexcel, Specimen Paper, Question 7


I have loads more examples of interesting Linked Pair questions, but in order to keep this post to a manageable length I'll leave it there!

What are your favourite GCSE questions? I'd love to see them.






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26 May 2016

5 Maths Gems #56

This is my 56th update from the world of Maths EduTwitter. If you're not a tweeter, or if you're wondering whether you've missed anything, here's a summary of some of the latest ideas and resources for teaching maths.

1. Euro 2016 Maths
@dooranran makes lovely maths resources. I think teachers will really like the activities he has prepared for Euro 2016. Topics include vectors, Pythagoras, trigonometry, angles on parallel lines, time, pie charts and estimating the mean.

2. Pythagoreanmath.com
I discovered a fabulous website, pythagoreanmath.com, which has lots of cool content including an amazing section on Euclid's Elements. Do check it out. I also really like their 'Complete Explanation for Area of a Circle Formula'.
3. Find someone who can
@rondelle10_b shared an interesting idea which Phil Bruce (@pbrucemaths) adapted for maths. In 'Find Someone Who Can', students ask other members of the class to answer questions using the sheet pictured below. This develops students' mathematical communication skills as they are required to explain solutions to classmates. You can download the PDF from Phil's page of revision resources.
4. Colin Foster's Activities
I discovered Colin Foster's 'Instant Maths Ideas' books a while ago. I enjoy browsing through them every now and then - they're packed full of excellent tasks and questions.

For example, in Possible or Impossible? students are asked to decide whether each statement in the table below is possible or impossible. If it’s possible they are asked to give an example and if it's impossible they have to say why.
Another great activity, this time from Colin's chapter on rounding, is this task which looks at various scenarios in which students have to calculate 17 ÷ 5. In each case they have to think carefully about how to round their answer.
5. More from MathsPad
Another awesome free resource from MathsPad: Using a Calculator - Odd One Out. This activity addresses lots of common errors and misconceptions.
Updates
I've written quite a lot of blog posts since my last set of gems. Here they are in case you missed them:

I've also added some A level revision resources to TES - check out my TES Shop to download these for free.

There's loads going on in June and July - see my conferences page for details. First up for me is researchED Maths and Science in Oxford on 10th June - the programme is excellent so I'm really looking forward to it.

Bookings are now open for my session at LIME Oldham on 20th June where I'll be talking about quadratic methods. I also recommend that you book a place at Edexcel's Warwick Conference where I'll be presenting a session on 'The Wonderful World of Maths Resources'

Finally, I'll leave you with this set of maths exam meme posters - I put these up in my maths corridor a couple of weeks and they went down really well with students in every year group. They were created by Paul Collins (@mrcollinsmaths) - you can download them here.


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23 May 2016

GCSE reform - will it work?

Nine months into delivering the new GCSE and I'm starting to wonder if these reforms are going to work. The Government wants to raise standards in maths education so that England can 'win the global PISA race'. But global league table dominance is not our country's only aim. The Government is also trying to increase the quality and quantity of students taking maths at A level. This, apparently, will make the country 'more productive' and increase our students' earning potential. These aims do not sit well with teachers, but we all agree that there is room for improvement in maths education. We want what's best for our students, and for future generations.

The Government's mechanisms for raising standards in mathematics education are:
1. Supporting teachers to improve the quality of teaching.
2. Increasing the amount of time spent teaching maths.
3. Increasing the amount of content on the GCSE specification.
4. Increasing the level of challenge in GCSE exams.

So is it working?

Quality of teaching
The best way to raise standards in mathematics education is to improve the teaching in classrooms across the country. Although there's lots of brilliant teaching, if you look at the bigger picture we're actually seeing a lowering of teaching standards as schools become more and more desperate to recruit. Vast numbers of students are being taught by teachers who lack the subject knowledge to teach maths effectively. There's also many classrooms where behaviour management comes before maths. Sad but true. The current landscape is not conducive to good teaching.

Many of us find that our busy teaching timetable often gets in the way of preparing high quality lessons. The only initiative that would actually make any significant difference to the quality of teaching across the country would be a reduction in contact time, giving teachers more opportunity to develop their subject knowledge and pedagogy. Of course, a reduction in contact time will never happen because of the costs involved.

 The Government has made some investment in the Maths Hubs initiative, and a number of hubs are doing fantastic work, but it's definitely not enough. Not by a long way.

As Anne Watson says, reported in today's Schools' Week article, there has been “little support provided for this very radical shift of focus in teaching".

Timetable allocation
I welcomed the Government's drive to increase the amount of time spent teaching maths, which was incentivised by double weighting maths on Progress 8. But some schools have not adjusted their timetables. This has resulted in a huge mismatch in teaching time across the country, with students in some schools getting 5 hours a week compared to 3 hours a week in others. This disparity really adds up across the course of a school year. It's a maths education lottery for children.

New content
I taught Linked Pair GCSE this year, as part of a pilot in which students take four exams, leading to two GCSEs in maths. My students were taught a lot more content than students in most other schools. So did learning more topics in Linked Pair produce better mathematicians? I don't think so. Just because my class can calculate AER and (on a good day) estimate the area under a curve, it doesn't mean that they are better prepared for A level maths than your class.

If we want our students to be better prepared to embark on A level maths, we want them to be fluent with algebra, indices, fractions and surds. Strong reasoning and problem solving skills are important too. Adding new GCSE content like frequency trees and iteration doesn't achieve this.

The worst thing about the GCSE reforms, in my opinion, is the increase in breadth when in fact all we needed was more depth. We already had too many topics on the GCSE syllabus and now we have even more.

Harder exams
Making GCSE exams harder is only an effective mechanism for improving the quality of maths education if it is accompanied by a corresponding shift in teaching quality.

Vanessa Pittard of the Department for Education says, “As a country and culture we do need to reform our whole approach to mathematics, our expectations, our teaching, our attitudes to maths”.

This huge cultural shift won't happen overnight. It certainly won't happen by next summer. It's going to need investment, strong leadership and patience.






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22 May 2016

#mathscpdchat - Celebrating Don Steward

Please join me for #mathscpdchat at 7pm on Tuesday 24th May to explore Don Steward's fantastic resources.

Don's blog Median has recently passed its millionth view so this seems like a good time to share our favourites from his vast collection of rich tasks. Join the chat to discuss which resources you've tried and which have worked well.

To start us off, here are three of my favourites.

1. 'One incorrect simplification'

I love this set of tasks. When I took over my current Year 11 class in October, I gave them this activity in the first lesson. At the time they were working at GCSE grade B or C and it was important for me to know how fluent they were with algebra. This activity is really engaging - as my students got stuck in, I had the opportunity to circulate, assess their understanding and discuss common misconceptions. They found the task accessible but quite challenging, which set the tone for what their maths lessons with me would be like.

This expression caught most of them out:
I'm sure you can see what the common mistake is here - most students incorrectly simplified this to 3 + 5n. This raises a useful discussion about grouping and brackets, or lack of brackets.

This activity also works brilliantly as a warm-up on A level induction day.

 2. Difference of Two Squares
Recognising and being able to factorise a difference of two squares is a useful skill throughout GCSE and A level.

Give a student an algebraic fraction to simplify and you'll often find that they have no idea what to do with a 4x2 - 9 in the numerator, even though they seemed to understand how to factorise a difference of two squares when you previously taught it.

Don Steward has some great activities for teaching this topic, culminating in this awesome set of challenging questions. I love these.
This reminds me of another Don Steward task - 'Mega hard powers questions' which offers stretch and challenge for students learning fractional and negative indices. This task works well at A level too.

I like it that both of these tasks help students realise how much easier it is to use improper fractions rather than mixed numbers or decimals.

3. Form and Solve a Quadratic
Forming equations comes up a lot in GCSE exams (particularly in Linked Pair GCSE, which is what I've been teaching this year). I'm not sure our students get enough practice of this - which is partly why so many were stumped by Hannah's Sweets last year. Don Steward has a lovely set of tasks for forming and solving quadratics.

Students often find it really hard to know where to start on problems like this so careful questioning and scaffolding may be needed.

In this post I've only shared algebra resources, but bear in mind that Don's resources are awesome for shape, measure, number, proportional reasoning, data and probability too. I will share many more resources during the chat on Tuesday. See you then.





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20 May 2016

C2 Revision Resources

This is a quick post to share some resources for Edexcel C2 revision.

  • Revision Lesson Activities
Your students might enjoy my C2 Revision Relay.
I've made a C2 Revision Clock and Andy Winterbottom has made one too. See my previous post for more on revision clocks.
I've also made a Quick Facts Quiz which would work well as a revision lesson warm-up. The questions are taken from my C1 and 2 Revision Cards. 
I've made a C2 version of Stuart Price's 'Correct Answer Only' activity.

  • Topic Focus
If your students need to practise a specific topic then try the topic papers on Maths Genie. Solutions are provided.
The topic assessments from Oxford University Press are also helpful for topic-focused practice. 

  • Papers
There are loads of C2 practice exam papers online, including past papers, Solomon papers and tiered papers.
Fantastic challenging papers are available from madasmaths.com.
Additional C2-style questions can be found on m4ths.com, StudyWell and mathshelper.co.uk. 


I hope this is helpful.



C2 question from madasmaths.com




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13 May 2016

Revision Clocks Galore

In my last post I wrote about revision clocks - an idea from @teachgeogblog that was shared by @Just_Maths back in October. Check out the hashtag #revisionclock to see these in action in numerous subjects. They are now all the rage in maths. No wonder, given that they are easy to prepare and do a great job of keeping students focused during revision lessons.

The idea is that you set 12 five minute questions that students answer on an A3 clockface. I haven't yet used a revision clock with Year 11 (though lots of people have done so with great success) but I've used revision clocks in a number of A level lessons and have found them to be really effective. In these lessons I set a buzzer to go off every five minutes and at that point I write an answer on the board.


I've received so many tweets about revision clock activities that I thought it would be a good idea to share them here so that everyone can access the resources. This post contains revision clocks for both GCSE and A level

GCSE

The resource for this tweet is here.








The resource for this tweet is here.






A level






And finally...
Here are template clockfaces for various combinations of timings - for example you might want to do 15 two minute questions followed by 6 five minute questions.


If you make a new maths revision clock resource then please upload it to TES or an online drive and tweet me a link so I can add it to this post. This should save teachers a lot of time in planning revision lessons. Thanks to all who have contributed! The final exam countdown is on...





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8 May 2016

C1 Revision Activity

The revision clock idea has become incredibly popular now that it's revision season. It originated from @teachgeogblog back in October and was introduced to the maths world by Mel (@Just_Maths) in her post 'Keeping Time'. I shared the idea at my school's weekly staff briefing on Tuesday and it's now being used in a number of subjects across the school.


If you teach Year 12 then you might like to borrow my C1 revision clock which I have uploaded to TES. I've made two versions. The easier version took some of my students 30 - 40 minutes to complete. Others were working on it for the full 60 minutes.

I felt that I probably hadn't made it challenging enough for students aiming for a top grade, so I've now made a harder version which draws questions from MadAsMaths.com's IYGB papers. This one should take the full hour.

Question from MadAsMaths.com IYGB C1 Practice Paper X

(By the way, thanks to @icecolbeveridge, I now know what IYGB stands for. I wonder if you can guess. It's a reference to the difficulty of the papers...).

Both versions of my C1 Revision Clock are editable so you can tweak the questions if they're not suitable.

The revision clock activity allows students to practise working under timed conditions and keeps them on task and engaged throughout the revision lesson. It's worth trying if you haven't already - it works for any age group.

All my other resources can be viewed through my TES 'shop' - they are all free, of course. If you're looking for other revision ideas for A level and GCSE then check out my blog posts:

Not long to go! Less than two weeks until C1... eek.







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7 May 2016

See you there...?

I'm looking forward to speaking at four maths education events in the coming months.

Warwick 2016
Edexcel's conference 'Excellence in Mathematics: Into the Future' is in Warwick on Saturday 2nd July. I'm incredibly excited about this event because Hannah Fry is the keynote speaker. You may have seen Hannah on TV recently (on Horizon and Gogglebox!) - she is a lecturer at University College London and author of 'The Mathematics of Love'. I saw Hannah speak at a Mathematics in Action event a couple of years ago and it was outstanding - she's a brilliant speaker and I can't wait to see her again.

The rest of the conference promises to be excellent, including the pre-conference dinner which looks like fun (there's a pass the parcel!). Delegates will be able to choose three workshops, including sessions from my Twitter pals Mel (@Just_Maths) and Emma Bell (@El_Timbre). I'll be presenting on 'The Wonderful World of Maths Resources' - I've enjoyed planning this presentation, it's a bit different to anything I've done before.

The cost of this conference is £185 (or £220 if you want to stay the night before). It's worth asking your school to fund this, it's a good price for a whole day of quality CPD and because the conference is on a Saturday you won't miss a day of school.
Two events for A level teachers
On Friday 8th July I'll be speaking at the FMSP's annual London KS5 Network Day. This is a popular event for A level maths teachers in London. For FMSP registered schools it's only £50 for two teachers. In my session I'll be focusing on resources and ideas for teaching the core A level modules. There will also be sessions on statistics and mechanics and an update on the new A level (by then we will have seen specifications and sample material).
Tom Bennison, Tom Wicks and Ria Symonds are hosting the East Midlands Key Stage 5 Mathematics Conference in Nottingham in the summer holidays. It's on Tuesday 9th August and costs a mere £25. I'll be speaking about A level resources and I'm looking forward to attending the other sessions too.
LIME Oldham
I'm very impressed by Lindsey Bennett's brilliant work supporting maths teachers. Her free LIME (Leaders Improving Mathematics Education) events are held after school in Oldham - recent speakers include Don Steward, Colin Hegarty and Craig Barton. I'll be making my way to Manchester on Monday 20th June to speak about mathematical methods. I did a workshop on methods at #mathsconf2015 - my session at LIME will be similar but I'll be focusing on new GCSE topics, including alternative methods to find the nth term of a quadratic sequence and solve a quadratic inequality. Come along to explore and evaluate which methods and explanations work best.
There are a number of other events happening over the coming months, including researchED Maths and Science on 11th June (which has now sold out), the MEI Conference (I went last year and loved it - read about that here) and La Salle's Complete Mathematics Conference in Leeds on 25th June (I'm disappointed that I won't be able to attend - these conferences are always good).

All upcoming conferences for UK maths teachers are listed here. Have I missed anything?

See you at an event soon!








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1 May 2016

Animations for A level

Last week I presented on A level resources at Stuart Price's 'Maths in the Sticks' event. I spoke briefly about how we can use animations to support our explanations of mathematical concepts. Many teachers already make use of programmes such as Geogebra, Autograph and Desmos, but here I'm talking specifically about animated gifs that teachers can simply paste into a PowerPoint. Gifs run on a loop so students can watch them for a while, providing 'thinking time' in the lesson and allowing new ideas to click into place.

I use gifs alongside physical demonstrations where possible, for example when I teach Volume of Revolution I show animations and use paper props too (see Gems 45).

So where can you get animated maths gifs? A Google Images search is normally sufficient but there are a few websites you might like to check out:
Here are some examples of gifs suitable for A level. You can copy them directly into PowerPoint. Some are more helpful than others - watch each animation for a minute and decide whether you think it adds any value.

Definite Integration. Source: 0a explains
The Trapezium Rule. Source: Vivaxsolutions.com
Radians. Source: LucasVB

Tangent to a curve. Source: Calculus in Motion


Completing the Square. Source: LucasVB


Product Rule. Source: mathwarehouse.com

Quotient Rule. Source: mathwarehouse.com

Logs. Source: Purplemath.com


Normal Distribution by Robert Ghrist. Source: Gizmodo



If you're looking for animations for Key Stage 3 and GCSE have a look through my blog posts tagged 'animations'.



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