23 November 2016

GCSE 9 - 1 Revision Resources

I published a post in March 2015 about Higher GCSE revision resources. Although the GCSE specification has changed, the resources in that post are still helpful. Today's post contains additional resources which are specifically for GCSE 9 - 1.

Practice papers
All four awarding bodies have published sets of practice papers. My school is using AQA for GCSE - we plan to use Practice Set 3 for our December mock exams and Practice Set 4 (due out soon) for our March mock exams. That leaves us with Practice Sets 1 and 2 and the specimen papers. I've already issued a couple of these for homework over the last few weeks, so that doesn't leave many papers for revision lessons in May (particularly when compared to previous years, when students had access to hundreds of past exam papers).

So what else can we use? Given that the differences between exam board specifications are minimal, we can use 9 - 1 practice papers from other exam boards. Old GCSE papers are still helpful too. So things are not as bleak as they first seem.

Thanks to @Maths_Master for drawing my attention to the practice papers produced by Churchill Maths. Much like Solomon Press products, these papers are reliable and high quality. I will certainly be using their free sample papers which are available here. My school is thinking about purchasing Churchill Maths's practice papers (£180 + VAT provides 15 practice papers for each tier) - we will issue these to our students in a booklet before the Easter holidays.

For £6 students can buy a pack of 6 practice papers from CGP. Practice paper books are also available to buy.
Revision by topic
Topic tests provided by AQA and Edexcel (through All About Maths and the Emporium respectively) are really helpful.

Maths Genie continues to be a very user-friendly website (I recommend it to my A level students). It has been updated for GCSE 9 - 1 so you'll find exam style questions on new topics.

Corbett Maths also has exam style questions, including new GCSE topics.

Also, don't forget that Mel at justmaths.co.uk has pulled together GCSE 9 - 1 specimen questions by topic. I use these a lot in my teaching at the moment.

Resources to purchase 
There are loads of resources that your students can buy through Amazon. I imagine that schools might buy some of these resources for their Pupil Premium students. CGP have summarised the content of their extensive range herePearson has a range of revision products too, as does Collins. A new set of revison books are due out in February, from publisher Scholastic.

Revision cards
9 - 1 revision cards are available to buy from the following sources:

Flash cards can be downloaded for free from tannermaths.co.uk.

Aimed at Grade 9
Around 4% of the cohort will get a Grade 9. My school is fairly large (we have 240 students in Year 11), so that equates to nine or ten Grade 9s. I can't help but think of all the grammar schools, and all the top private schools - each of these schools is likely to get dozens of Grade 9s. That leaves less for us... I think one or two Grade 9s might be a more realistic outcome.

I totally agree that there should be a grade that identifies the country's best mathematicians, much like the A* at A level. To achieve a Grade 9 students will need to know every topic inside out. They will also need a high level of accuracy and brilliant problem solving skills - the ability to think laterally. They need to be better than 96% of students in the country, and that's a big ask. In my top set Year 11 I have a handful of particularly hardworking students who I'm trying to push towards Grade 9. I have absolutely no idea if they'll get it. Here are some resources I will be asking these students to look at:
  • There are revision workbooks for 'Grade 9 targeted exam practice' here
  • There are three 'Grade 9' booklets here at Bland.in.
  • Pixi Maths has a Grade 9 booklet here.
  • m4ths.com has Grade 9 resources here.

More resources
Here are some more general revision resources that I've collected:

Have I missed anything? Please share your resources in the comments below.

14 November 2016

New GCSE: Trigonometry Questions

I've been teaching trigonometry to my top set Year 11 over the last couple of weeks. The content is much the same as it was on the old GCSE but the exam questions may now be considerably more challenging.

The only new trigonometry content in the Higher tier is 'exact values' (ie non-calculator trigonometry), which requires sound knowledge of surds.

I wrote a blog post about Teaching Trigonometry a couple of years ago and I have loads of resources listed in my shape library so I won't repeat it all here, but I just wanted to mention a few interesting GCSE trigonometry questions that I found when looking through the questions collated by Mel (@Just_Maths) here and here. If you teach Year 11s who will be taking the higher tier exams then you might find these questions helpful in your lesson planning.

1. Ambiguous case
I always teach the ambiguous case at GCSE but I've not seen many exam questions on it before. It's interesting to see this three mark question in AQA's higher Specimen Paper 3.

At first glance it seems like a straightforward Sine Rule question but we're told that the angle is obtuse, meaning students have to subtract their initial answer from 180.

I've spotted a couple of questions in the specimen papers that refer to acute and obtuse angles so I do think it's important to teach the ambiguous case.

2. Quadratics and surds
I recommend that you have a go at this question to see how challenging it would be for the vast majority of Year 11s.
It's from WJEC Eduqas's sample assessment materials (the last question on the higher non-calculator paper). It requires knowledge of the value of sin60 and cos60. It requires students to solve a quadratic equation and work with surds. They also have to recall the formulae for the Cosine Rule and area of a triangle using sine.

They get eight marks (and in my opinion deserve an automatic Grade 9!) if they get this question right.

3. Angles in parallel lines and similarity
Here's a four mark question from WJEC Eduqas's sample assessment materials.
There are two common approaches here: the first is to use angles facts to find the angles in triangle ABC, then use the Sine Rule to find side AB. The second approach is to use the Sine Rule to find ED, then use scale factor 1.5 to find AB.

4.  Angles of elevation
My students always struggle with trigonometry questions where they're not sure which angles are being referred to in the wording of the question (they find this particularly tricky when bearings are involved).

This four mark question from Edexcel's Specimen Set 1 just requires right-angled triangle trigonometry and use of a scale factor. So there's nothing particularly advanced here, but the challenge for some students will be knowing where the 52o goes.
5.  Long!
This five mark question from Edexcel's Specimen Set 2 isn't particularly exciting but there's a lot to do here. Four steps in fact. It seems like a test of resilience at the end of 4.5 hours of maths exams.
In order to tackle this challenge, exhausted students need to remember and accurately apply all three of the trigonometric formulae that used to be provided in the GCSE exam. Harsh.

I don't want to scare anyone! There are plenty of straightforward questions in the sample materials too. See the questions by topic on JustMaths for more examples of new GCSE questions, ranging from simple to complex.

I've written a similar post about Pythagoras here.

I hope your students enjoy having a go at some of these interesting questions.

13 November 2016

5 Maths Gems #66

Welcome to my 66th update from the world of Maths EduTwitter. This is where I share some of the latest ideas and resources for teaching maths.

November is always one of the hardest months for teachers. I'm drowning in workload at the moment and I bet many of you are too. It's relentless. At times like this I'm grateful for the Twitter community and my lovely colleagues for their ongoing support and encouragement. I plan to write a blog post soon with some thoughts and ideas on workload. In the meantime, here are five slices of mathematical loveliness to cheer us up...

1. 3Blue1Brown
Thanks to ‏@johngreen for sharing YouTube channel 3Blue1Brown. I'll be using their Vectors video when I teach this topic in C4 later this year.

If you teach logs then you might be interested in their video 'Triangle of Power'.

2. Classroom Display
Thanks to Clarissa Grandi (@c0mplexnumber) for sharing this beautiful classroom display 'The Faces Behind the Formulae' which she made for an A level classroom.

I've added it to my displays page

3. Pinpoint Learning
Last year I featured Pinpoint Learning in Gems 45. It's a good time to mention this website again because most schools run mock GCSE exams in November or December. Pinpointlearning.co.uk provides students with personalised question booklets based on exam results. There's a sample booklet here. You (or your students) simply upload mock marks by question and the website automatically produces individual booklets featuring questions on the topics that students need to work on. I'm told that students love receiving their personalised booklets! I hope to try it out with my Year 11s next month.
Edexcel and AQA mock QLA sheets are on the website and you can currently upload results for all three mock papers for free during a one month trial. If you subscribe during the trial period then you get an annual subscription for £300.

Follow @pinpntlearning for updates.

I'm teaching an interesting Year 7 class this year. Having not taught Year 7 for a number of years, I'm taking a fresh look at resources and approaches. I recently rediscovered SMILE worksheets. Here are a couple of examples:
Powers of Ten Flags
Coordinate Messages

Also, SMILE cards are available through STEM Learning - these are pretty old now so the quality of the copies vary. I remember learning maths from SMILE cards when I was in Year 7. Thanks to Martin Colley for arranging the cards by topic here.

5. Pythagoras with Blokus
I love this stop motion video from ‏@JoelBSperanza.
If you want to see more of Joel's stop motion videos or find out how to make your own, check out his blog post Stop-Motion Education.

La Salle have announced some more dates for their conferences (including Wales and Scotland for the first time). I've added these to my conference listings and will try to attend as many as possible.

In case you missed it, my most recent post was the third in my series '5 Websites You Should You Know'. It featured Jonathan Hall's websites MathsBot.com, Flashmaths.co.uk and Formtimeideas.com.

I've also updated my recent post about Corbettmaths.com. Since writing it I discovered how good his textbook exercises are! I've found them so helpful for teaching Year 7 this week.
Extract from CorbettMaths.com 'Collecting Like Terms

I've sold 91% of my Christmaths tickets now (there are only 12 left!). I can't wait!

I'll leave you with one of Don Steward's latest resources, puzzle square. This one is for directed number practice.

6 November 2016

5 Websites You Should Know... #3

This is the third in my series of posts about five maths teaching websites that you may not be familiar with. My previous posts were about Corbettmaths.com and MrCarterMaths.com.

Today I'm featuring MathsBot.com, a wonderful website packed full of tools for busy teachers. MathsBot.com is one of a set of websites from maths teacher Jonathan Hall (@StudyMaths).

Jonathan is constantly adding helpful new features to MathsBot. In this post I'll highlight a few of these features, but do visit MathsBot.com to explore the website yourself.

MathsBot holds a huge bank of questions which can be filtered by topic and displayed in numerous helpful formats:
  • timed mini-whiteboard or starter questions
  • differentiated questions (red/amber/green)
  • GCSE style questions, displayed individually (example below) or in a revision grid
  • printable practice GCSE papers (you choose the length, topics, difficulty etc)

There's also a worksheet generator where you can produce printable worksheets for a large range of topics.

MathsBot also has activities such as Four Operations Puzzle and Number of the Day.
Form Time Ideas
Formtimeideas.com was also created by Jonathan Hall. If you're a form tutor and you don't know this website, go and look at it right now! With this user-friendly website you can easily fill a 20 minute form time with quality activities - it works well with any year group, from Year 7 right through to Year 13. My Sixth Form tutor group enjoy it, and I often click on 'Name the Flag!' so they can do more of them! The content changes every day so form times require no planning whatsoever - it's a huge time saver for form tutors. It makes me sad that there are form tutors who needlessly worry about how to fill their daily form times because they've not heard of this website.
Flash Maths
I know you've already heard of FlashMaths.co.uk, but it's always good to be reminded of the classics. This website is another of Jonathan Hall's creations. There are so many great activities on Flash Maths, it's hard to know which ones to feature here.
Flash Maths includes activities that students can come up to the interactive whiteboard to complete, such as Drag and Drop Venn Diagrams.
It also includes tools that are helpful for teacher explanation, such as this Rotational Symmetry Demonstration.
Flash Maths has activities which students complete in their books or on mini-whiteboards. Memory Maths is one of my favourites - it works well with any age group. 

Shape Shoot is fun!
I have also used Equation BalanceRounding Numbers and Substitution Grids in the past. Helpfully, Jonathan has made all the Flash Maths content available to download and run without an internet connection.

I really think that there should be a proper annual award ceremony for people who make outstanding contributions to maths education. The type of event with bow ties and sparkly dresses where people are properly thanked and congratulated for their successes... Until such a thing exists, this will have to do: Thank you Jonathan - your websites are brilliant, and a huge help to thousands of maths teachers and form tutors. We really appreciate all your efforts.

Look out for the next post in my websites series, coming soon...

29 October 2016

5 Maths Gems #65

Welcome to my 65th update from the world of Maths EduTwitter. This is where I share some of the latest ideas and resources for teaching maths.

1. New GCSE Revision Resources
I'm always on the lookout for resources for the new GCSE.

I'm pleased to see that Ben Tanner (‏@tannermaths) has updated his free revision flashcards.
Also, Steve Blades of m4ths.com has created a 9 - 1 GCSE helpbook which is packed full of facts and examples. 

If you've got any students working towards a Grade 9 then you'll like Steve's Grade 9 resources too. I'll be recommending these to my top students at Year 11 Parents Evening next week. I've also spotted Grade 9 Targeted Exam Practice workbooks on Amazon that they might want to buy.
2. Puzzle
Thanks to @Mr_Mathematics for sharing this nice number puzzle. My Year 7s enjoyed it. I also used it as the "Parents' Puzzle" in my half-termly Year 11 newsletter.
3. Visualiser Challenge
I went to a TeachMeet last week where teacher Ryan Foster talked about WAGOLLs ('What a Good One Looks Like'). He described how his school models the expected standard of work.

When I return homework to my classes I often display photos of the best work on my interactive whiteboard. I did this recently with my Year 12s after marking a disappointing set of homeworks. The example below was particularly difficult to mark.

I was pleased that the quality of most students' work improved after I shared good examples.

Thanks to my PGCE buddy Heerpal Sahota ‏(@MrHSahota) for sharing this idea for improving the standard of presentation:
"I use 'visualiser challenge' in many of my lessons, where I randomly select two or three pieces of work to project. The work should speak for itself, and we have a class discussion focusing on specific praise and constructive criticism".
What a lovely idea.

4. Marking Crib Sheets
This idea isn't going to work for everyone but is worth a look. To save time during marking, history teacher Mr Thornton (@MrThorntonTeach) created a template to record his comments and observations. He uses this sheet to give feedback to students collectively rather than individually. He shared this marking crib sheet on his blog and now it's become quite popular. Read his blog post to see how he uses these crib sheets with his classes.
Check out Twitter for more examples and discussion. This would work just as well in maths as in other subjects, particularly if your school expects you to do book marking - writing thirty separate (often near identical) comments is not a good use of your time.

Here's an example for A level maths from Katie Pollard (@takepi21). Her template is here. Katie handed out copies to her students for them to attach to their work. They each highlighted the sections relevant to them. 
5. Twinkl
Twinkl is a website full of lovely maths resources, including a huge range of activities for primary school children. They have recently started expanding their secondary maths collection, including resources for GCSE. The nice people at Twinkl kindly gave me free access to their resources so I could explore. Note that these resources require a subscription (they have various subscription packages ranging from £29.99 to £69.99 per year).

I'll share a few examples of their resources here to give you an idea of their style.
Extract from 'Shape at Home: Surface Area and Volume PowerPoint'
Extract from 'Budget at Home: Compound Interest and Depreciation PowerPoint'

There are a lot of resources that might work well with low attaining Year 7s, such as the 'KS3 Maths Addition and Subtraction Catch Up Resource Pack' and the 'KS3 Maths Place Value Catch Up Resource Pack' (extracts below).

I look forward to seeing Twinkl's secondary collection continue to grow.

Hurrah for half term! It came just at the right time. I've been even busier than usual this term because I'm a Year 13 form tutor and 27 of the students in my form are applying for university - UCAS is taking over my life! A break was much needed.

In case you missed them, my recent posts were:

My #christmaths16 tickets are selling really well. I've sold over 100 tickets so far so if you want to come then please book now before they sell out! I have less than 30 tickets left. Many schools are using this as their maths department Christmas night out.

Finally, I'll leave you with this Halloween problem from puzzle website expii (@expii). For more Halloween maths resources, see my Seasonal Maths page. 

The small town of Halloweenville was founded with a population of 1000 people. Each resident lives for about 30 years and each woman has an average of 4 children over her lifetime. After 300 years, what is the approximate ratio of the number of people who have died, to the number of people who are alive?

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.