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.
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.
The UK Maths Challenges provide a wonderful library of multiple choice problems; note the these 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 addition for 2015 of extended solutions.
As well as a full solution which does not use the multiple choice answers further ideas are given for investigation.
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.
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
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.
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.
Jane Hart is the Founder of the Centre for Learning & Performance Technologies and as you can see from her blog, 2016 marks the 10th year of her annual Top 100 Tools for Learning list.
The 2015 slideset is shown here.
Voting is now open for the Top 200 Tools for Learning 2016 and will close on Friday 30 September 2016, and the 10th annual list will be released on Monday 3 October 2016. You can find all the voting guidance and forms here. Note the 200, not 100; as you can see from Jane’s description she is making some changes to celebrate the anniversary.
From the voting guidance you can see that there are three methods of voting, my choice is:
3 Write a blog post about your choice and send the link to Jane Hart.
So these are my own 2016 choices as top tools for learning because these are tools I use all the time in my job, both in my teaching and in my role as a senior leader. Note that we are not discussing subject specialist resource sites here (that’s another whole (updated) story), but tools for education generally; I think it is very useful to remind ourselves of Jane Hart’s own definition:
“Any software or online tool or service that can be used for your own personal learning or for teaching or training”.
|CY 2016 votes||Education||Personal Learning & Productivity||Place in Top 100 2015|
Looking at Jane’s alphabetical list of ALL the tools which have appeared on any of the lists, I thought it would be interesting to see which tools have been on all nine lists to date and also at popular tools from the last 5 lists, 2011-2015. I used a favourite tool, Excel to create these, the file is available if of interest: Jane Hart Top 100 Tools – Colleen Young analysis Note the tabs at the bottom, the first three worksheets show the tools which have been in every list, 2007-2015, the last two look at the longer list of tools which have been in the list for the last 5 years. You can read Jane’s fascinating analysis of trends for work place learning.
To elaborate further on my choices
Evernote – an outstanding note-taking tool and something I use every day. I have a notebook for each of my classes to which I upload any resources I want for that class; I also jot down any ideas I have for each class. I can use it on any PC, tablet or my phone. It is also a good way to share for example a list of websites with students – using a shared notebook. I have many notebooks both for my job and life generally; the search facility in Evernote is awesome and the ability to link from one note to another, very powerful. (Blog post on Evernote).
WordPress – obviously – you are reading a WordPress blog right now! I have several other blogs, Games, Starters and for students I have created Mathematics for Students and something I am very pleased with is a blog I use to give the details of homework for each of my classes. I created ‘What was that homework?’ as a result of a survey of students across several schools where many students said that they would like homework details online. No student can ever say to me that they didn’t know what their homework was! I also have blogs on useful tools for students and teachers generally. (The very first post on this WordPress blog – which includes some useful WordPress links).
Twitter – great for professional development – I have contacts in education all over the globe and have been led to many useful resources by my virtual colleagues! See Mathematics Conversations. and this post on Twitter.
PowerPoint I can’t really have Slideshare without including PowerPoint in my list because that’s where I start with my presentations, often with a little help from the interactive whiteboard software. It is interesting to see how popular PowerPoint was last year at number 5, other presentation software such as Prezi is also useful, but it’s so important to remember that it’s the content that matters! See this post, Presentations for some reading and resources on presentations.
Excel is something I use everyday in my job to analyse and present data; I also use many spreadsheets for teaching. Of all the applications in the Office suite this stands out for me, the changes from Excel 2003 to 2007 with the massive improvements to conditional formatting for example make this one outstanding application. There are also many Excel spreadsheets out there too to help in Maths lessons – see Maths Files for example.
Moodle We have a Moodle course for each year group in school; each course has links to any websites that we use in class so students can investigate further themselves if they wish. VLEs are sometimes criticised for being no more than ‘filing cabinets’; I would argue what useful filing cabinets they are – containing resources chosen by teachers for their students all in one organised place. For example we see that in the run up to examinations the relevant Moodle courses receive hundreds of hits as everything students need was available, not only syllabus information and papers but worked examples that we have uploaded. It is also of course possible to use forums and quizzes on a VLE and being a secure site for the school we can include information intended for our students only.
WolframAlpha. WolframAlpha is not just all about Maths, it covers so many subjects and even though they would love us to pay for WolframAlpha pro, the free model still offers unlimited queries everyday!
Desmos, the outstanding graphical calculator deserves a vote in my opinion, it is wonderful for learning mathematics, accessible for young students yet has the sophistication required for university students. Brilliant. It is entirely free, very simple to use even for young students and brilliant for projecting in lessons. There are also free apps for both Android and iOS.
So that concludes the voting from Colleen as 10 tools are needed for a valid voting entry!
I thought it would be useful to collect the information on A Level reform in one place so have reorganized the existing pages under UK Assessment which will provide, I hope, easier access to information. The various pages, which you can see on tabs near the top of the page have been developed from areas which have proved popular.
The series of pages includes the following
- National Curriculum UK
- Assessment Without Levels KS3 (11-14)
- GCSE Reform
- GCSE New Content
- GCSE New Content – Resources
- A Level Reform
- Results 2015
From MEI comes this excellent presentation relevant for any new specification whichever examination board is being used. A strength of this presentation is its clarity. Simple statements of fact are given in very clear language and as well as stating what we know we also have a very important reminder of what we don’t know!
Further references and reading
Note that the documents mentioned in the presentation above are included here.
From the Further Mathematics Support Programme:
2017 A Level Mathematics and Further Mathematics
This is really helpful – clear and simple statements. Note the link to the very helpful document on changes to AS/A Level Mathematics & Further Mathematics.
GCE Subject Level Guidance from DfE, this guidance is intended to help awarding organisations understand how to comply with the GCE subject-level conditions and requirements for mathematics. The guidance includes further information on the use of Technology and large Data sets. Making Statistics Vital from Jonny Griffiths has some tasks which could be excellent, look at the this task on World Wide Statistics for example which includes the task with answers and a spreadsheet with data for 191 countries. Census at School is an excellent source of data and you can generate data for your own school too.
How demanding are questions in the new A level maths? Ofqual is planning to conduct a research study to support the accreditation process for new A level maths qualifications. Taking place in July this year, the research aims to compare the level of difficulty of exam boards’ sample assessment materials by having judges compare pairs of exam questions. An interesting method of comparison and something I have come across before – see No More Marking on Comparative Judgement.
The A level mathematics working group report is a very valuable document and one I referred to in a presentation on GCSE Problem Solving – I do believe we should always look both backwards and forwards to inform our teaching; where have our students been and where are they going? I have also created a new version of the problem solving presentation: Problem Solving 16:19.
The Cambridge Mathematics Education project (CMEP) mentioned in the presentation has now been renranded as Underground Maths, a superb site which will I feel be very important in our work with our Mathematicians students.
Twitter (quite rightly!) suggested I might like to follow IsThatABigNumber. The aims of the site are as follows:
- Put numbers in context
- Promote numeracy
- Share number facts
- Develop Number Sense
Exploring the menu at the top, note as well as the home page, we have other options, we could ask for example how big is 5km? The question returns a very comprehensive answer with comparisons to many other numbers! I do like the various quotes that appear randomly, as I was exploring I saw (very appropriate for someone responsible for Assessment) from Charles Babbage: “Errors using inadequate data are much less than those using no data at all”.
Other options as you can see include conversion, we could convert 1cm to 1 m (though I can already do that with WolframAlpha which returns rather more comparisons, and can also do it myself, I hasten to add!). Alternatively look at some random Number Facts or an interesting option – try a quiz.
On the home page we can the site is in its early stages, (the authors welcome feedback). Numbers in the News is a good idea; always looking for other sources too I discovered the BBC’s #bbcgofigure. Some links on the home page currently seem to link to simply a Google search page; I suspect this is a work in progress and I wish the authors well – promoting numeracy just has to be a good thing!
On the subject of big numbers, I have recently completely checked and made major updates to my post on Standard Form resources.
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:
- Highlighting is a Waste of Time
- MadAsMaths (16+)
- UK A Level (16-18) Exam Questions & Solutions
- UK GCSE (14-16) Exam Questions & Solutions
- Aural Tests
- Corbettmaths 5-a-day
- Multiple Choice Questions
- Loop Activities / Treasure Hunts
- Dynamic Maths
- Diagnostic Questions
- Other Revision Ideas – a collection
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.
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).
Not only do all the questions come with full solutions but most have very clear mark schemes too.
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.
I know from my blog statistics that people are still searching in vain for Wisweb Applets that work as Java seems to have many problems these days.
Such a happy discovery on Twitter this evening – a conversation with Christian Bokhove of Southampton University led me to a new home for those wonderful widgets! Try the Digital Mathematics Environment from the Freudenthal Institute.
To access the resources mentioned here:
- Choose Open DME for student
- Login as guest.
- The DME Widget list has all these old favourites which will work in modern browsers.
A guest login is clearly restrictive but you will be able to use several of the widgets.
Algebra Arrows illustrated above is excellent for exploring functions. Form inputs, operations and output by dragging them onto the main workspace, connect them up and optionally connect to a graph. Click inside any of the elements to change the content.
Algebra Trees also works well.
. I am very happy to see widgets such as Building Blocks again (check Geometry under the DME widget list). This is useful for demonstrating plans and elevations. I discovered I could clear a block by selecting both left and right mouse buttons simultaneously.
Statistics and Probability includes the widget illustrated here on the Normal Distribution; try experimenting with the various variables.
(For an an excellent Normal Distribution calculator, see the last calculator on this page.)
Probability Trees could be useful for creating diagrams as the basic diagram is very easy to set up – simply enter the number of branches you require.
The Digital Mathematics Environment has much more than the original Wisweb applets I used – a quick glance at Secondary Education shows we have resources to explore.
Choosing Secondary Education/Algebra/Exercises – Equations/Linear equations led me to another favourite. A whole series of these exercises is available. I like the way the steps and working are clearly shown
There are useful demonstrations that could work well in class:
How to use Algebra Arrows
(I used Screencastomatic to create the thrilling video! This is very easy to use.)
I’ll return to these again, for now – happy exploring!
From the University of Cambridge comes Underground Mathematics which started in 2012 as the Cambridge Mathematics Education Project (CMEP). The site provides a library of rich resources for age 16+ students with the aim of “Enabling all students to explore the connections that underpin mathematics”. Underground Mathematics is being developed by the University of Cambridge, funded by a grant from the UK Department for Education. The resources are free for all users; you can read more about the team and their philosophy here. Follow Underground Mathematics on Twitter or Facebook.
Note that you can also select individual elements on the map. Try Quadratics for example and check the station guide for information. Looking at the guide led me to Name that graph; as with all the resources on the site more than just the problem is provided, we also have printable resources, solutions and teachers notes.
I thought I’d have a look at Review Questions on Algebra – so much to choose from! How about an A Level question from 1975?! As you can see, not only do we have the question, but a suggestion, then a solution. And if that’s not enough let’s take it further and generalise, exploring on GeoGebra as we do!
I’m tempted to try that one with my very able Year 10 set studying for the new Mathematics GCSE qualification. In fact I suspect we can find other useful questions here for our most able GCSE students.
Prepare to lose yourself for some hours / days in this treasure trove! This resource is frankly incredible and I applaud the team behind this. The site I know will be on my own go to list of places where I know I will always find high quality resources to make my students think and more than that has suggestions for exploring further on a given area and of course explore connected areas.
I predict rich and happy travels around these lines for students and teachers!