Mathematical Miscellany #31

Underground Mathematics Review Questions
A project started recently to look at the various review questions available on Underground Maths to support teaching of the A Level specification now has further review questions added.
Underground Maths Mapping Review Questions

Logs laws review question

Read about the use of Review questions in the classroom on this Teacher Support page. The fact that these questions are designed to test understanding of one or more topics, exercise problem-solving and proof skills and help students make connections make them ideal for use in the A Level classroom. They can be used to introduce a topic or are also ideal for review, something which should be a regular part of linear courses.

For further questions to challenge your older students, see Challenging Mathematics Questions.

Mr Men Ed SouthallPosters and Displays

Looking at my blog statistics, I see the poster collection is very popular, it’s that time of year I think! I realised there were some missing gems and have added Ed Southall’s wonderful Mr Men collection (Note the two posts with poster packs and his delightful colouring book!

Also added is Clarissa Grandi’s display suggestions on her wonderful Artful Maths. Linking these two together, I do like the “Today I’m feeling…” collection!

Whilst there is much debate about classroom displays, see Mark Esner’s thoughtful TES article on the subject, we still may have corridors we would like to add some displays too or events where posters can be helpful. Many of the resources in the poster collection such as the Nrich collection  or Joey Kelly and Xi Yu’s Play With Your Math display very well on the whiteboard.

Transum & Mathisfun

Earlier in the holiday I noted some puzzles in the post Puzzle Time; to add to those puzzles, some further puzzles for consideration from two favourite websites, Transum Mathematics and Mathisfun. Many of these would work as lesson resources.

For those still on holiday (the numbers are diminishing I know!) remember the #SummerMathsPuzzles from the Isaac Newton Institute for Mathematical Sciences. Each weekday throughout August the Institute publishes a maths-based puzzle.  Whilst the puzzles do not require sophisticated maths to solve, they are not be easy. A new puzzle becomes live each day in August and answers will be provided at the end of the month.

Mirror Writing  mirror
Visiting the Leonardo Da Vinci A Life in Drawing exhibition one sees many examples of his mirror writing. Curious to learn a little more, I came across information and additionally a lesson plan from the Museum of Science, Boston. Something a little different when teaching reflections perhaps?

UK Examination Results
I am keeping my Results 2019 page updated. The page includes links to all the results statistics and grade boundaries as well as links to ofqual’s apps and other news items.
Ofqual A Level app 2019

Mathematical Miscellany #30

To begin this collection, two items where you need to act swiftly!

Jonny Griffiths Further RISPS

Jonny Griffiths investigative activities for the pure A Level Mathematics classroom are well known. He has now published Further Risps, forty rich tasks for the pure Further Mathematics classroom.

For just a few days, Jonny Griffiths is halving the cost of the Further Risps pdf ebook from £7.50 to £3.75.

I thoroughly enjoyed his excellent session for London Maths, ATM and MA London Branch on Saturday 11th May, where teachers enjoyed working on these activities. Two editions are available – a hard copy or pdf version. On this page you can see two trial activities, Further Risps 1 and 2.

The pdf not only provides the forty problems but also full teachers notes for each. The notes for each task begin with the topic or topics covered, identify the type of task, for example, introductory and state any preliminary knowledge required. This is a valuable resource for teaching Further Mathematics.

For A Level mathematics, Jonny has a wonderful collection of free RISPS, the details are included in my series of pages on A Level reources.

The second act swiftly item – a remnder from last week on A Level resources that you have until July 10th if you would like to download the 2019 AS & A Level Question Countdown sheets from crashMATHS, See AS Level Question Countdown and/or the A Level Countdown. Each set provides 10 worksheets of mixed questions with 7 questions on each sheet, 5 are pure questions and 2 are applied. The pure section of the worksheets includes a mix of basic, problem and modeling questions.Whilst written in the style of Edexcel, the subject content is the same for all examination boards.

CrashMaths Countdown

Jonathan Hall has added an Arithmagon generator on his wonderful Mathsbot site. As always with Jonathan’s resources you have choices to create the resource you want.
Jonathan Hall Mathsbot
This has been added to my Arithmagons collection where you will find all the Arithmagons you could ever want from the simplest to complex numbers and Calculus for older students!

From Ontario Math see these HTML5 mathies tools which  are designed for use in desktop or mobile browsers. A search on Google Play apps for mathies found them all. Mathies are also available on ios.
mathies apps

On the mathies tools site you will find full details and tips for use. With Notepad for example you can sketch diagrams, import pictures, create graphs on one of four backgrounds: grid, isometric dot, lined or blank. The app includes built-in line, shape and text annotation objects, including number lines, rulers, grids and polygons. It is possible to copy and rotate any annotation object. A tip sheet provides a clear summary of  all the features.

mathies Algebra Tiles

Mathies – Algebra Tiles

The Algebra Tiles app comes with support including a series of examples, this page provides complete documentation.

Penrose Triangle

A lovely activity for the end of term perhaps, try a lesson on Impossible Objects from  Clarissa Grandi on her marvelous Artful Maths (scroll down  to the third lesson, Impossible Objects).

All the Resources you need are provided, including a presentaion containing a selection of images of ‘impossible objects’; and very clear printable instructions for constructing three different types. The instructions are taken from the 1985 SMP 11-16 booklet ‘Impossible Objects’ a direct link to the instructions is provided.

Note that you can access SMP materials through These materials certainly bring back memories, I have SMP O and A Level Maths!

Workers of Zen

Workers of Zen

Speaking of the end of term, fast approaching for UK schools, there are several suggested activities on this page.


Mathematical Miscellany #29

With Exam season already started, an exam themed miscellany this week…

Command Words GCSE EdexcelFrom Edexcel – I do like this recently added Teacher’s Guide to Command Words, not only do we have commentary on what is expected from students when a particular commonly used command word is used but examples of questions to exemplify the use of the word.

All the examination boards have very clear resources illustrating command words, something we can incorporate into our teaching.

On Naikermaths you will find several new A Level Mathematics Practice Papers. These papers are based on legacy Edexcel Exam Papers, but they have been edited to reflect the new A Level Specifications and include new questions to make them suitable for the new specification. Full solutions are provided.

What a treasure trove Edexcel’s Emporium is, log in and look for example at the themed practice papers for GCSE. This includes one mark questions and mark schemes (scroll down the alphabetical list), a good idea for any final revision sessions. Talking of one mark questions has given me an idea for Maths and Further Maths A Level revision sessions;  the very old Multiple choice papers I began my career with could be a very useful source of questions. Scroll down this post for an example.
Multiple Choice Example

Note the comment from Graham Cummings below, papers are available in Edexcel’s Emporium:

The Emporium has some 17 multiple-choice question papers from the period 1988-1992 – by no means a complete set, but they range across the Mathematics, Further Mathematics, Pure Mathematics and Applied Mathematics syllabuses. You can find them in the “Pre-C2000” cabinet within GCE AS/A Level.

A recent post from The Calculator Guide blog has very useful advice from AQA on the use of calculators in A Level Maths. I have recommended the Calculator Guide before and have shown many of the very helpful videos in both Maths and Further Maths classes. Check the resources here. Certainly, calculator use at A level needs to be taught explicitly. Note section 3 on Calculator Use from AQA’s excellent A-Level Maths The thinking behind great assessment.
Note my page here on Classwiz tutorials.

Crashmaths AS Countdown
With common content for all the examination boards at A Level, we have many resources for our students. On Crashmaths, see the AS and A Level Countdowns. The first AS exam was 15th May – all 10 worksheets are available.

CrashMaths Countdown

crashMATHS – A Level Countdown

The A Level countdown leads up to the first A Level Maths Exam on 5th June 2019 with the first worksheet published on 26th May. Each question sheet has 5  pure questions and 2 applied, one Mechanics and one Statistics; I like the way the pure section includes a mix of basic, problem and modeling questions.

From crashMATHS I have successfully used all the AS key skills checks this year with Year 13 and will do so again; they make great lesson starters. I see a section on End of Unit Tests under development, with a good set of Proof questions available now; certainly a space to watch.



Mathematical Miscellany #28

MEI Calculator Crunch

MEI – Calculator Crunch

This coming June MEI’ summer challenge, the Calculator Crunch will be helping Year 6s get ‘calculator-ready’ for secondary school, and additionally provide extra practice for Year 7s.

Note the dates – from 10 to 20 June, on each school day, MEIMaths will tweet a question a day for students to work on. PDFs of the questions will also be available from MEI’s page for display on whiteboards and to print as hand-outs. MEI has designed the problems not only to practise using a basic or scientific calculator but to develop mathematical thinking skills. Lesson plans will also be provided.

On the subject of MEI and Primary Maths, don’t forget their latest wonderful Sumaze! Primary app, one of a series of three apps in the series. All highly recommended, these problem-solving games cover a wide range of ages. Sumaze! which explores arithmetic, inequalities, the modulus function, logarithms, powers and primes is a problem-solving puzzle game suitable for A level mathematicians and above. Its sequel, Sumaze! 2, which explores fractions, decimals, percentages, primes and digits is suitable for those studying GCSE Mathematics and above.

For some more practise with calculators, perhaps try this calculator exercise from ADA Maths. Students can check that they can key in all the calculations correctly by answering the questions and checking their answers. ADA Maths is a free Mathematics Question Bank with no login required. The creator is Sam Powell, a mathematics teacher from the UK, working in Australia. All questions have answers, some have a fuller solution and a video explanation. Several categories of questions are available; look at Algebra for example and we see some nice use of colour in presenting a solution to a problem expanding double brackets (select Show Solutions) These examples could be helpful for students when revising.
ADA Project Algebra

Desmos AQA LDS Cars
In February of this year, I was very pleased to see that we can use Desmos for Statistics. Tom Bennison has written a large data set (AQA-Cars) resource using the Desmos statistics visualisation functions. It really is very easy to copy and paste into Desmos and display boxplots. Tom’s resource includes questions for students. It strikes me we should use the large data sets with younger year groups, using Desmos (or GeoGebra) makes it very easy to investigate such data when we are teaching boxplots and other Statistics topics.

Tom Bennison A Level Question a day

Tom Bennison – Year 13 Exam Question a Day

Tom has been busy, see also his Year 13 Exam Question a Day with questions up to June 13th. Tom has used Sample Assessment Materials from the awarding bodies’ websites so students can find mark schemes using the reference for any question. This will be a very useful resource for revision now and also in future. I do like the way we can easily see the topic for each question.

TeachItMaths Proof review

TeachitMaths Proof review sheet

Following my post on Proof resources, looking further through TeachIt Maths proof resources, I see many gems. Rather good for year 11 Higher GCSE students is this Higher Level Proof review sheet.

Maths Week London
In June we have for London teachers, Maths Week London. You can still register for this event, there are a limited number of welcome packs remaining.

Coming in November 2019, we have Maths Week England.

Mathematical Miscellany #27

From Access Maths, a brilliant selection of 90 Algebra Questions, Progressive Overload-Algebra is ideal for revision.

Have a look at all the other Access Maths revision resources too.

TES Resources
From one of my favourite resource authors, try Building Blocks from Andy Lutwyche.

Building Blocks for Bearings

A great idea, Andy!

A Level Practice Papers

CrashMaths gold

CrashMaths Edexcel Practice AS paper – gold

A recent addition from CrashMaths, Gold Edexcel AS Practice papers.

ATM Open Resources
For, activities, videos and more, have a look at ATM’s Open Resources. ATM provides many free resources on their website for teachers to download or use online in the classroom. There are many free resources available, note the menu on the right, these are excellent in their own right and also provide an excellent way of seeing what ATM has to offer. I do like GeoBoard tasks, try for example Board Task 3B.

If you like GeoBoards, see GeoBoard Activities, where I have given information on free online GeoBoards and resources.

Try ATM’s Puzzle Page, where you will find many examples of their puzzles, or get some free posters for your walls.

On the subject of Geometry, have a look at Don Stewards great slides from his recent London ATM/MA session.

I’m looking forward to attending the next session, Jonny Griffiths on Further Maths RISPS,

A Level (16+) Examination Materials
A very popular page is the Edexcel page in the A Level reform series; this has been updated and checked.

Edexcel new teaching materials

Edexcel frequently publishes new material, keep an eye on new publications by changing the Sort By filter to ‘Latest’. Check Teaching and Learning materials.
also Exam Materials and Specification and Sample Assessments.

Edexcel Model Answers for Sample Assessment materials

Edexcel Model Answers – Core Pure Further Mathematics

Looking at the latest Teaching and Learning materials we see for example recent February and March publications including very welcome Model answers for Further Mathematics Sample assessment materials. The content of Core Pure for Further Mathematics is common to all the examination boards, so a very useful document for any Further Mathematics teacher.

The latest Exam Materials include, for teachers, A Level Mathematics Mock papers and with common content for all examination boards, a very useful source of questions. (The same is true of course for AQA and OCRA and OCRB).

GeoGebra Scientific Calculator App
See the Calculators page for further information on Casio and Texas Instruments calculators.

Geogebra Scientific Calculator

GeoGebra has announced the release of their new free GeoGebra Scientific Calculator apps for tablets and phones.

The online calculator is here and you can get apps for iPhone & iPad: Scientific Calculator in App Store and Android: Scientific Calculator in Play Store.

There are several Scientific Calculator tutorials available.