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.
m4ths


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.

UKMT Maths Challenges

The UK Maths Challenges provide a wonderful library of multiple choice problems; note the past papers where you will find questions and full solutions. Check also the Individual Challenges pages where you will find details of the challenge and see sample materials. Check the Junior Challenge for example. Note the extended solutions.

As well as a full solution which does not use the multiple choice answers further ideas are given for investigation.

UKMT Extended Solutions


Maths Challenge questions are an excellent resource at any time – not just for preparation for the competitions, particularly with the increased requirement for problem solving skills at all levels. On the outstanding Diagnostic Questions site you can choose Junior Maths Challenge questions by topic by choosing the Themed Quizzes option. These quizzes consist of sets of four or five questions grouped by topic. (Log in to Diagnostic Questions to use the link.)

UKMT Diagnostic Questions


Another way to access Maths Challenge questions by topic for Junior, Intermediate and Senior is from Dr Frosts’s wonderful website full of outstanding resources.

DrFrostMaths.com

DrFrostMaths.com

Very conveniently it is possible to download zip files of questions by topic.


UKMT Skills Builders Topics

From UKMT, try their free Skills Builders, on-line problem solving questions for both junior and intermediate level. Note the user guide, which applies to both Junior (age 11-13) and Intermediate (age 13-16); this offers clear step by step instructions with screenshots.

jmc

UKMT Maths Challenge – Junior


Another possibility, generate a random quiz, using Mathster’s UKMT Mathematics Challenge Online Quiz. Choose Junior, Intermediate or Senior and one of three difficulty levels; you can also choose the number of questions, a time limit and the order the questions are presented in – random or in order of difficulty.

UKMT Mathster

UK Maths Challenge Online Quiz – Mathster


Team Challenge

Links for students, including advice for young mathematicians are provided on Mathematics for Students. Further outstanding resources from UKMT include the Team Challenge resources.

The UK Maths Challenges are included on the Problems & Activities page.

For more sources of multiple choice questions see this post.

Daisy C Multiple Choice

Daisy Christodoulou on Multiple Choice Questions


Mathematical Miscellany #11

Desmos Geometry
An exciting space to watch! Chancing upon this tweet I saw that indeed we have an exciting possibility here as Desmos does Geometry! Early days right now and this is still in early beta.

Have a play – it’s very easy to use. There are some examples to investigate. Excellent to have vectors as an option in the line tool and I like the way that once a line or segment is drawn construction options are available.

See the Desmos blog post The Desmos Geometry Tool. Such a thoughtful post. Reading it reminded me why this is one of the few websites I use on a daily basis to help my students learn.

First, our goals are different than those embodied by most of those other tools. When we design products, we design first for students who struggle with math and we assume they may also struggle with technology. We strive for a student’s first creation with our tools to feel effortless and joyful. For that reason, our geometry tool has a far shorter list of features than some of those above. We will carefully expand that list over time, never trading power for ease-of-use.

I have always said that what I like about Desmos is the ease of use. A young student can just ask for a graph of a straight line and my Year 13s can play with Polar Curves for example.


With revision for examinations very much in mind at this time of year, have a look at Tying it together, a bundle from Underground Mathematics which looks at efficient revision for mathematics; 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”. (And note the free webinar on April 19th looking at revising effectively and sharing resources for AS revision.)


Being very conscious of our first students aiming for grade 9 GCSE 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. What’s the shared area for these two circles, another resource  in this bundle illustrates so well how a good diagram can help.


Pick a card is a Fluency Exercise, Note that you can search resources in many ways including by type.
(More on Underground Mathematics).


Staying with the subject of exam revision, The Learning Scientists have an important post here on studying with Retrieval Practice. For further valuable resources to support study techniques see the excellent downloadable materials on study strategies. Note how each strategy is backed up by research.
study-strategies-research

retrieval-practice-learning-scientists


MEI Maths Item of the Month example

From MEI this curriculum mapping for their Maths Items of the month resources is a great resource, both for GCSE and A Level. (This has been added to the A Level Resources page.)


See all Mathematical Miscellany compilations.


A Level (16-18) Resources – STEM Learning

STEM Learning hosts hundreds of Mathematics resources, resister free here. Log in to STEM Learning to download any of the resources here.

For the new A Level Specifications from STEM Learning comes this A level mathematics resource packages. To quote STEM Learning “Each resource has been hand-picked to cover key subject content in Pure, Mechanics and Statistics, as well as meet the overarching themes of mathematical argument, language, proof, problem solving and modelling.”

The package includes resources covering all the sections in the subject content given for Pure, Mechanics and Statistics in the Department for Education’s document: Mathematics AS and A level content. The references I have added to the images are those used in that subject content document.

STEM Learning A kevel mathematics resource packages

STEM Learning A kevel mathematics resource packages

Indices – Odd one out. Susan Wall

Each section begins with a reminder of the subject content and leads to several resources selected by STEM Learning, Have a look at Algebra: Indices, linear and quadratic functions for example.

Marking from Further Indices

I see some resources from Susan Wall’s excellent resources. (Resources from Susan Wall can be found in this Active A Level Mathematics collection on STEM Learning.) I do like marking activities such as the one illustrated here and have used many such resources successfully.

Exploring these resources I see familiar excellent resources such as those from the Standards Unit; note the Mostly Calculus resources and I have been happily side-tracked looking at some less familiar collections, Exponential Graphs for example which is part of the Exponentials and Logarithms collection comes from the Core Maths Support Program resources.

The collection includes a great variety of resource types, we have for example Michael Bawtree’s Prove It Algebraically

Prove It algebraically – Michael Bawtree

If you like this resource then take a look at the Virtual Textbook Secondary collection.

Turning to Mechanics and Statistics examples, we have a great variety of resources including some great use of Excel. I like this Descriptive Statistics resource very much, a combination of Excel sheets and work cards this should really help understanding. This and some of the other resources could be adapted for use with younger students too.


I see a Mechanics resource which is a link to one of the PhET smulations; I would recommend the HTML5 collection as this will work across platforms and devices.

Moments – Revision

These resources have been added to the A level resources page.

Revision Time 2017

Revision
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.

Examinations, Twitter Lists…

… can be so very useful!

For example, try this list of just the UK Examination Boards Maths teams; you don’t even need to sign up to Twitter, just follow the list for updates and resources from the exam boards.

For some samples from these tweets:

For a more general examinations list which includes more organisations associated with assessment, see this list which includes all the examination boards including WJEC, who I see also have a Question Bank tool which allows teachers of Maths, Computing, Science, Electronics, Business Studies, Food & Nutrition and Physical Education to create a paper at either Entry Level, GCE or GCSE.  I can confirm the Question Bank tool is very easy to use and works brilliantly;  I searched for GCSE Maths filtered by Algebra and Problem and created a paper with mark schemes and examiners’ comments in minutes.

The list also includes Ofqual, the Department for Education and the Chartered Institute of Educational Assessors.

WJEC Algebra problem

WJEC GCSE Algebra problem

 

 

 

Mathematical Miscellany #10

For any of your students studying for STEP direct them to this excellent portal from stepmaths.co.uk which has (all free) access to STEP questions and solutions. Create an account, login and you have access to a complete library of resources.

The resources are very clearly presented. For each question you have access to a pdf with the question, Examiners’ Report and both an Official and thanks to Peter Mitchell a fully worked handwritten solution.

Note that you can also download a copy of  Stephen Siklos’ Advanced Problems in Mathematics and Core MathematicsAdvanced Problems in Mathematics is excellent preparation for ANY undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 43 problems. Each problem has been given a title and a rough indication of the mathematical content which means you can pick out questions by topic.

See also, from Cambridge University, their STEP Support Programme and from Nrich, Prepare for University.

These details are also available on Mathematics for Students.

On the subject of challenging questions for older students and with revision on our minds, perhaps a good time to remind everyone of the excellent MadAsMaths site.

MadAsMaths mark scheme example


ofqual-April

The AQA Mathematics AS and A Level specifciations have now been accredited. Watch the AQA website for further resources on the new specification. Checking Teaching Resources we see that AQA are developing their route maps; I have always found the GCSE route maps very helpful indeed.

AQA Route Map

Something I have used a great deal with my GCSE teaching for both the current and previous specifications is AQA’s detailed and very clear teaching guidance.

AQA Teaching Guidance

An A Level Teaching Guidance extract is available.

We can also see Command Words which reminds me a little of the Exam Terminology document so useful at GCSE. There seem to be versions of this document in various places, I believe the first time I used it was back in the days when there were more Examination Boards, this may well have come from the then Southern Examining Group!

Under Assessment resources we find Specimen Papers and mark schemes; also an Assessment Guide on using a large data set. On the subject of large data sets, for information on all the Examination Boards and large data sets, read Bruce Hampton’s clear and detailed comparison.

I have added an AQA page to the A Level Reform series.


Royal Statistical Society Problem Solving

Eduqas will not be offering AS / A Level Mathematics specifications, but note their Level 3 Statistical Problem Solving Using Software. See also  the International Centre for Statistical Education (ICSE) with Plymouth University and you can follow @IntCSE on Twitter. It may be that some of the resources here will be useful for our teaching of Statistics.

Educas state: “The objective of this qualification is to assist the understanding of the problem-solving cycle of planning, collecting, processing and discussing in meaningful contexts and to use statistical software to process real data sets. It has been specifically designed to be taught in schools and colleges to equip learners aged 16-19 with a broad range of skills empowering them to successfully negotiate statistical problems in Higher Education or the world of work.”

Staying with the subject of Statistics AQA and Edexcel have accredited GCSE specifications; note that coursework is no longer a requirement of GCSE Statistics.

See more in the Mathematical Miscellany Collection.

Women In Mathematics

March 8th 2017 is International Women’s Day.
We’ll start with an image I shared this time last year that I think still says it all! Thank you Steve Lomax who shared this wonderful response to the task ‘Describe a mathematician’ from Mansfield Green E-ACT Academy.

Capture

Describing a mathematician – Mansfield Green E-ACT Academy

Some useful references on women in Mathematics:

And for some History

 

 

 

 

Examination Resources

With changes to examinations at both GCSE (UK examination taken at age 16) and A Level (UK examination taken at age 18) all the examination boards are offering help and support for teachers and students. Many excellent resources are available with several published very recently.

For example we have Edexcel’s very helpful resources for teaching new content. For each topic, information, examples and exercises (with answers) are given.

edexcel-new-content-resources

 

 

edexcel-iteration

Edexcel – New Content Resources

More helpful Edexcel resources include the Exemplification of the New Sample Assessment Materials and the Topic Tests, note the Show More button which will take you to more resources including for example posters of formulae that students need to know.

From AQA and OCR too we have many excellent resources to support the teaching of the new specifications. Given so many new and useful resources I have separated the UK Assessment pages further and now have pages for AQA, Edexcel and OCR. Whichever board you are using it is well worth while looking at resources from all the boards, the specifications are all based on this content.

I have also been updating (this is a work in progress) the A Level pages, noteable additions to the A Level documentation are Interactive schemes of work from Edexcel and OCR MEI. From MEI – look at this excellent scheme of work for the new specification. Each of the 43 units is based on a topic and includes a commentary of the underlying mathematics, a sample resource, a use of technology, links with other topics, common errors, opportunities for proof and  questions to promote mathematical thinking. The schemes of work is freely available. And from Edexcel for each unit of work you will find Specification References, Prior Knowledge including GCSE Specification References and Key Words. For each sub-unit you will find Objectives, Teaching Points, Opportunities for Reasoning / Problem Solving, Common Misconceptions / Examiner Report Quotes.

MEI Interactive Scheme of Work

MEI Interactive Scheme of Work

Note also the addition of a Use of Technology page.

MEI on Integrating Technology

MEI on Integrating Technology

Mathematical Miscellany #9

ukmt-diagnostic-questions
Now on the outstanding Diagnostic Quesions site – United Kingdom Mathematics Trust Quizzes – choose a theme or a quiz with random topics. To use the resources will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.” (See this post for Diagnostic Examination Questions).


aqa-ao3From AQA, on their ‘All About Maths‘ site see their Further Guidance and Practice Questions for the AO2 and AO3 requirements of the new 8300 GCSE. The 120 questions in this resource have been selected from legacy specifications which, to quote AQA “exemplify each of the strands of these Assessment Objectives and would therefore be suitable questions for the new GCSE as well.” AQA have arranged the questions in approximate order of difficulty andhave also divided them into those suitable for Foundation tier only, common to both tiers, and those suitable for Higher tier only, as well as by Assessment Objective. To

Remember fAQA 90 Problemsrom AQA we also have the excellent, GCSE Mathsematics: 90 maths problem  solving questions. These problems have been designed for use in supporting the teaching and learning of mathematics. There is a helpful intruductory section for teachers and note also the helpful Classification Tables by Strategy and by Content Area. Em,  has a brilliant PowerPoint with all the questions and answers – see it here.

AQA


Staying with problem solving, on TES Resources cchristian’s Multi-Stage Problem Solving is an excellent resource. These problems could make great starter activities.
cchristian-multi-stage-problem-solving

Also, remember the GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Hub Team, @WRMathsHub available on TES Resources.

White Rose Maths Hub problems

The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided. Also from the team, their mastery schemes of learning now includes Year 7 material (UK age 11-12); an assessment is also available.


scooby-mysteryFrom author Captain Loui a TES resource, BIDMAS – Solve a Scooby Doo Mystery! Note that answers are provided in the author’s description of the resource. The theme is engaging but doesn’t get in the way of doing plenty of Mathematics!  Captain Loui’s resources are all free to use and as you can see have very favourable reviews.


Splat - Steve Wyborney

Splat – Steve Wyborney

A resource that caught my eye recently is Steve Wyborney’s Splat! Definitely a resource I wnt to explore further; you can read Steve’s blog post and download the lessons here.

Thursday 2nd March is World Book Day; we could bring books and Mathematics together with some Statistics (at any time); have a look at this resource from TES, World Book Day Maths Data Investigation where students analyse word length and sentence length in some book extracts. UK readers who remember Statistics coursework, this brings back memories of AQA’s coursework task ‘Read All About It’ where students considered various newspapers and magazines for readability. Note too the launch of a new website, MathsThroughStories.org is an international research-based initiative which sets out to explore various aspects of integrating stories reading and writing in mathematics instruction.

AQA - Read All About It

AQA – Read All About It

The extension task for the TES resource above considers the reading age of a text, you may wish to consider further readability formulae; if you paste some text to this site, Readability Formulas you can easily check statistics for your chosen text and generate a reading age according to the various tests.

WolframAlpha can be used for Words and Linguistics, note the various examples given, including number names.and document length.

Analyze My Writing

Alternatively, try Analyze My Writing. Simply paste in some text for a comprehensive analysis including basic statistics, word and sentence length and readability. It is also possible to create Cloze tests.  You can read more about this resource on Richard Byrne’s always impressive “Free Technology for Teachers”.

It seems appropriate to check some world records on books!

On the subject of books see the free books information and note in particular Colin Foster’s Instant Maths Ideas – lots of ideas you can try in the classroom.

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