# Mathematics Revision Resources

I wrote recently on Revision Time 2017, noting several updates as well as checks of the revision series of pages. In this post – some more additions:

For GCSE, from Steve Blades on his excellent m4ths.com, have a look at his Right or Wrong Challenge, a series of 10 quick questions for Foundation GCSE students. Steve Blades has designed and written this section to test students understanding of the concepts involved in GCSE topics. Watch the video as Steve works through 10 questions and work out which answers are correct. It strikes me that many of these questions would make an excellent revision resource for younger year groups too – a great starter for my Year 9s I think! Note that Steve has very helpfully provided a pdf document with all the questions, (scroll to the bottom of the page).

I have mentioned reources from m4ths.com elsewhere, on the exam questons and solutions page I have included Steve’s eBook GCSE Higher wordy questions. On the GCSE page Steve has a section (near the end of the page) of eBooks, and one of those is on GCSE Higher wordy questions. See also Steve’s Think like a problem solver and mathematician book. And of course don’t forget his GCSE Help Book, included here for students.

PixiMaths

On Danielle Moosajee’s piximaths.co.uk you will find an extensive collection of outstanding resources for teaching and learning and revision. The Revision Resources are very clear and comprehensive revision booklets, packed with things to remember and examination questions by topic, answers are also provided. Five booklets are available for students aiming at grades 1, 3. 5, 7 and 9.

PixiMaths Problem Solving

Also from PixiMaths resources I really like the set of Problem Solving Booklets by curriculum area, all with very clear fully worked answers. Danielle has created these using collated Edexcel questions that will be on both higher and foundation tiers so can be accessed by most students. Like the first resources from Steve Blades mentioned above I think there are many useful questions here for younger year groups. We should clearly be looking at problem solving skills with all our students.

From Danielle Bartram, on Miss B’s Resources see her GCSE Maths Passports Grades 1 to 9 Revision. Five different passports are available.

For A Level I have two pages in the Revision series, MadASMaths with it’s excellent series of revision questions and solutions increasing in challenge and UK A Level (16-18) Exam Quesions and Solutions with resources good for all examination boards.

From Underground Maths, to challenge students I find the Review Questions excellent, so many excellent questions from old A Level papers clearly organised and with very full solutons.

Calculus meets Functions

From the Underground Maths team have a look at the Bundle Tying it together, which looks at effective mathematics revision. To quote Underground Mathematics “The resources in this bundle encourage students to bring together their experiences in multiple areas of mathematics, helping to reveal and reinforce connections between a variety of mathematical ideas and problem solving strategies.” Note the associated recorded webinar. I particularly like the fluency exercise Pick a Card which will be a great way to revise Quadratic Functions, linking together many student experiences in Algebra, functions and graphs; this is also useful for high ability students. What’s the shared area for these two circles? another resource  in this bundle illustrates so well how a good diagram can help.

Revision pages for students.

# Revision Time 2017

That quote from Robert Collier seems so appropriate when it comes to revision. Once again, this academic year I have used the day in, day out approach even more with my students, frequently reviewing earlier work even for short sessions. I am convinced this is important in our teaching and help makes things stick for our students.

mathsbot.com – Jonathan Hall

Once again we are in the final run up to examinations, so, an annual job I have checked and made many major updates to the series of revision pages. There are two new pages, one is GCSE Questions by topic – I thought it would be useful to collect together resources which allow for revision by examination topic; the other is Chasing the highest grades?

Before mentioning the resources though we should think about how best to use them.

The first page in the series ‘Highlighting is a waste of time’ links to what I believe is a very important report on how students learn effectively; having used testing – even very short ‘self checks’ or ‘mini tests’ as they have come to be known in my classes I am convinced like the authors that this is very effective and we will be using testing in our revision classes, often short with immediate feedback so students can see if they can recall and apply information. When I asked my Year 9 students about good Maths teachers, one said:

A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.

On Study Strategies, note the very valuable set of resources from The Learning Scientists. See their blog for more information and note the excellent downloadable materials on study strategies including Retrieval Practice. Note the blog on meta-analysis of 217 Retrieval Practice Studies.

So before we worry about amazing revision resources we must consider how we will use them so our students learn effectively. According to research learning strategies with high utility include distributed study sessions (last minute cramming is not effective) and practice testing.

So bearing these learning strategies in mind, many of the resources found on the series of revision pages could be used as mini tests with immediate feedback or several topics mixed up within a lesson and perhaps the trickiest topics revisited several times over the last weeks, even if briefly.

The revision activities can be found on the series of revision pages:

For students, I have added the revision and examination questions to Mathematics for Students.

Resources in the collections allow for a mix it up approach but also provide questions by topic. A huge thank you to the teachers who so willingly share their resources – you are helping students everywhere. Correct attribution has been given wherever possible with the resources. All resources are free.

Wishing your students everywhere success in their examinations.

By Colleen Young Posted in Revision

# Mathematical Miscellany #3

Mr Westwater – TES Resources

With revision still in mind, for some excellent PowerPoint resources with A Level questions and mark schemes by topic try Mr Westwater’s resources on TES. (Twitter @westiesworkshop). Though Edexcel questions these are clearly useful for other examination boards also. There are six of these PowerPoint files available:
Core 1   Core 2
Statistics 1  Mechanics 1
Core 3
Core 4

Diagnostic Questions

Craig Barton’s and Simon Woodhead’s Diagnostic questions site includes some excellent question collections for revision; as well as GCSE questions, there are quizzes for AQA’s excellent Level 2 Further Mathematics specification and for Core 1 at Advanced Level. Questions from the Oxford University Mathematics Admissions Test are also available.

From AQA this set of revision tests and mark schemes is very useful and from Oxford University Press a lovely set of free revision resources is available. Under Mathematics Revision Guides, choose the ZIP file Worksheets. Note that these are headed New GCSE – this is the old new specification, not the new new specification! These are clearly perfect for UK students taking exams this year but still excellent for future years.

For many more revision resources note the Revision Activities series of pages.

GCSE Problem Solving: Steve Blades’ site www.m4ths.com has many excellent resources; on the GCSE page Steve has a section (near the end of the page) of eBooks, and one of those is on GCSE Higher wordy questions. See also Steve’s Think like a problem solver and mathematician book.

For more Problem Solving Resources, see Problem Solving and Problem Solving 16-19.

Alec McEachran’s Furbles – a large data set!

Statistics – thinking about large data sets which we will need to for the new A Level specification – for an amusing large data set, how about the Furbles?! The images generated here are from the original 2003 version which is still available on Alec McEachran’s ptolemy.co.uk. Talk to students about summarising this data, perhaps ask for their impressions as to which colour is the most or least common. Data can be presented as a bar chart or a pie chart and you can choose to categorise in various ways. It is also possible to vary the number of Furbles, the maximum and minimum number of eyes and sides. The illustration here show the largest data set possible.

Alec McEachran’s Furbles

Visual Patterns – Fawn Nguyen

From Fawn Nguyen comes the brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who’ve used visual patterns in their classrooms.

By Colleen Young

# Revision Time

That quote from Robert Collier seems so appropriate when it comes to revision. Once again, this academic year I have used the day in, day out approach even more with my students, frequently reviewing earlier work even for short sessions. I am convinced this is important in our teaching and help makes things stick for our students.

Once again we are in the final run up to examinations, so I have checked and made many major updates to the series of revision pages. Before mentioning the resources though we should think about how best to use them.

The first page in the series ‘Highlighting is a waste of time’ links to what I believe is a very important report on how students learn effectively; having used testing – even very short ‘self checks’ or ‘mini tests’ as they have come to be known in my classes I am convinced like the authors that this is very effective and we will be using testing in our revision classes, often short with immediate feedback so students can see if they can recall and apply information. Earlier this academic year when I asked my Year 9 students about good Maths teachers, one said:

A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.

So before we worry about amazing revision resources we must consider how we will use them so our students learn effectively. According to the report the two learning strategies with the highest utility are distributed study sessions (last minute cramming is not effective) and practice testing.

So bearing these learning strategies in mind, many of the resources found on the series of revision pages could be used as mini tests with immediate feedback or several topics mixed up within a lesson and perhaps the trickiest topics revisited several times over the last weeks, even if briefly.

The revision activities can be found on the series of revision pages:

For students, I have added the revision and examination questions to Mathematics for Students.

Resources in the collections allow for a mix it up approach but also provide questions by topic. A huge thank you to the teachers who so willingly share their resources – you are helping students everywhere. Correct attribution has been given wherever possible with the resources. All resources are free.

Wishing your students everywhere success in their examinations.

# MadAsMaths

MadAsMaths

One of my students told me recently about MadAsMaths by Dr Trifon Madas. She likes the Practice Papers, particularly the way the papers are rated according to their difficulty, see C1 for example. All papers come with full solutions.

(Post also added to Mathematics for Students).

MadAsMaths question & solution

Not only do all the questions come with full solutions but most have very clear mark schemes too.

MadAsMaths mark scheme example

The papers cover the Pure Mathematics content of the UK A Level course. Note the Special Papers designed for extremely able students; ideal for students capable of the top grades. This is a really valuable collection of questions.

There are further questions and solutions available in the large collection of booklets, originally samples they are free to use. These are pdf files, if you zoom you will see a clear solution as illustrated in the image here. Some of these booklets are aimed at undergraduate students.

# Aural Test – Statistics

My post on using mental tests for revision seems to have interested many readers so I thought I would follow this up. Having looked back in time to GCSE many years ago when an aural test was actually part of the exam (10%) I shall in future refer to these as Aural Tests. It was these tests that started me using the idea of an aural test on anything any time! They can be short and make ideal starters or plenaries or in the case of revision aural tests can last a lesson with lots of associated questions and discussion.

Looking through some old resources I came across a cassette (!) recording of myself reading the questions for a GCSE aural test I recorded for a correspondence college. I intend to transcribe that and will write a post on these old style tests in the near future.

Having successfully given my Year 13 students two aural tests on the Pure Mathematics C3 and C4 modules (after the first they requested the second) my wonderful colleague who teaches the group with me joined in the venture and gave them a third aural test on their  Statistics module. We and our students feel we have done some really useful revision in their last lessons for all three modules on their Advanced Level course.

So this week I have my last lessons with Year 11 (UK age 15-16) who are preparing for their GCSE. I want to look at their Statistics unit with them and have decided that an aural test should work well. Looking at various papers I have extracted some diagrams and asked questions around those. These are topics that I feel my particular class needs; I want to review various statistical diagrams. In case this is of interest I have made all the resources available here. Students need the answer sheet only. The teacher reads the questions and they have to listen very carefully and answer the questions. They will need to write answers in their exercise books or on paper as well as using the answer sheet. With these longer revision aural tests it is sometimes appropriate to give feedback after each question as opposed to waiting till the end to mark all questions. I use both techniques.

Creating the solutions reminded me once again of how useful colour can be to make solutions clear.

I would be interested to hear from teachers who try aural tests with their students; I find them useful for all ages.

# Last Revision Lessons

Study leave is approaching fast for our examination classes so it’s time to think about those last lessons. I will be using a few mental tests with all my examination students as I find these work very well indeed. Last week with Year 13 we had a C3 (an A Level module – OCR MEI) mental test; at the end of the lesson they said that was really useful and requested a C4 mental test for this week. I think my favourite kind of lesson feedback is when students make requests like this!

Note that the ideas here can be used all year round – not just for last revision lessons.

These tests are simply short questions that test recall of the basic skills needed for the module; so for example some standard derivatives and integrals, graph sketches, changing the subject of the formula for expressions involving exponential functions and so on. Note that another possibility is to ask students to write down the expressions / calculations needed for a question (they can always come back and complete it later).

### Basically, sit down with the syllabus in front of you and cover as much as possible. Although informal this is making the students individually recall material they will need – see Highlighting is a Waste of Time.

CIMT Teacher Resources

For some inspiration for mental tests have a look at the Centre for Innovation in Mathematics Teaching resources for GCSE (and for younger students note that mental tests are supplied for all the Key Stage 3 (UK age 11-14) units). In fact the GCSE resource shown above would also apply to AS level.

For the Teacher Resources scroll down to the end of the GCSE Resources page and you will find resources for each unit.

CIMT Mental Test – Using Graphs

For A Level students, questions such as Mohammed Ladak’s Essential Skills pack for Core AS or Corbett Maths A Level 5-a-day could be used / adapted. Questions do need to be short, recall type questions where just a short time is needed for any working out. I do find that because I use this idea regularly, I can just ask questions by looking at the specification and using my experience of what I know students forget!

Looking at the CIMT resources I noticed some more valuable revision resources; note the GCSE Revision pack; this has quick checks at Foundation, Intermediate and Higher Level and example papers with answers and mark schemes.

CIMT GCSE Quick Checks

CIMT Higher Paper example

For revision tests by topic, each unit of the GCSE course has a revision test with answers. Whilst the vast majority of the material on the CIMT site is freely accessible, a few documents such as these revision tests are password protected. The password can be obtained if you send a request using your educational institution email address; CIMT also give the password to home educators.

I have added the CIMT GCSE Revision pack to the examination resources page which is part of the Revision Activities series of pages.

# Final Revision

That quote from Robert Collier seems so appropriate when it comes to revision. This academic year I have used the day in, day out approach even more with my students, frequently reviewing earlier work even for short sessions. I am convinced this is important in our teaching and help makes things stick for our students.

Once again we are in the final run up to examinations, so I checked the various revision resources I have highlighted on this blog earlier this year and created a series of revision pages which I hope makes resources easier to find. I have recently updated these again. Before mentioning the resources though we should think about how best to use them.

The first page ‘Highlighting is a waste of time’ links to what I believe is a very important report on how students learn effectively; having used testing – even very short ‘self checks’ as they have come to be known in my classes I am convinced like the authors that this is very effective and we will be using testing in our revision classes, often short with immediate feedback so students can see if they can recall and apply information. Earlier this academic year when I asked my Year 9 students about good Maths teachers, one said:

A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.

So before we worry about amazing revision resources we must consider how we will use them so our students learn effectively. According to the report the two learning strategies with the highest utility are distributed study sessions (last minute cramming is not effective) and practice testing.

Interestingly, interleaved practice: though rated as just moderate utility gets a special mention for students’ learning and retention of mathematical skills. William Emeny has written on this see this post and a follow up on Great Maths Teaching Ideas.

So bearing these learning strategies in mind, many of the resources found on the series of revision pages could be used as mini tests with immediate feedback or several topics mixed up within a lesson and perhaps the trickiest topics revisited several times over the last weeks, even if briefly.

The revision activities can be found on the series of revision pages:

There have been recent updates, in particular to the examination questions page. I will certainly be using all the resources I have mentioned on that page. Resources in the collection allow for a mix it up approach but also provide examination questions by topic. A huge thank you to the teachers who so willingly share their resources – you are helping students everywhere. Correct attribution has been given wherever possible with the resources.

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Wishing teachers and students everywhere a successful final revision period.

# Revision Time Again

Algebra Snippets – select image for details

I recently created a new page ‘Revision Activities’ as I could see from my WordPress statistics that posts on revision are popular.

Time to say a little more on the first item on the revision page. I am a huge fan of Corbettmaths 5-a-day. I have been using these regularly with my Year 11 GCSE class; they like them and have come to expect these at the beginning of many lessons. I print the questions for them and hand them out as they come into the room so they can get straight to work. I find that using the Windows snipping tool I can easily fit two sets on an A4 landscape page making them economical to print or copy; this is a size that can easily be stuck into exercise books which my students choose to do.

Corbettmaths 5-a-day

The above image shows, appropriately the higher questions for January 31st. I tend to hunt the collection looking for sets that include particular topics. Following their earlier mock exam we decided that we needed more trigonometry practise so I made sure that a trigonometry question appeared in each day’s set for several sessions; it has been very rewarding to see the speed and confidence they now seem to have on for example the sine and cosine rules. I have also sought question on topics that we have not met for some time.

I do believe that asking students to recall topics regularly is very valuable, see my earlier post  “Highlighting is a Waste of time”. Using short GCSE questions like this fits in with the distributed practice idea. Short tests can be useful too – on Monday Year 11 will be getting 10-a-day under timed exam conditions!

Thank you so much Mr Corbett from myself and my students!

# Algebra Snippets

Year 11 (UK age 15-16) have mock examinations starting next week so we have been revising.
I have written before on ‘Here’s the diagram …what’s the question? and having studied Trigonometry recently

Here’s the diagram….

the selection of various triangle diagrams worked very well and prompted some good discussion on unknowns we could work out in the various diagrams and what methods we could use.

I thought I would extend the idea to Algebra and rather than a diagram just use what I have termed Algebra snippets where I have given for example only algebraic expressions, equations and so on from questions. (Very economical – you can get a lot on an A4 page!) All the vocabulary (which students often ignore!) has been stripped out. So rather like the diagrams idea students have to work out what the question might have been. With the vocabulary missing it is interesting to ask students what terms they think were used in the question. Following our discussions I also showed the students the complete questions. On the subject of vocabulary there are some excellent resources on this page including the very useful guide to exam terminology (I have seen this document around the web – I believe the original is from AQA).

Resources like the above can be fast to create – I created a table in Word then used the wonderful Windows Snipping tool to select my images and copy them to the table. If anyone wants the complete sheet: Word Algebra snippets or pdf Algebra snippets (you’ll see I snuck in a backwards percentage question as well).

I find these are worthwhile exercises and do get students thinking about the various question types and was pleased that some students started commenting on the differences in types of questions.

One last diagram! Having asked these students if they wanted any particular topics, some asked for equations of lines so in one lesson we started with this diagram and managed to revise equations of lines, simultaneous equations and inequalities as well!

I gave them a copy of the diagram each and used a flipchart to give them some information and ask questions as we went along.

In case this is of interest the complete document is here: Lines & equations revision

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The diagrams here were very easily created with Desmos, note that you can turn of numbers and/or the grid if you wish on Desmos from the Tools menu.