Mathematical Miscellany #82

The new Casio Calculators are appearing, here’s Jack Brown’s first look at the Casio FX-991CW.

And from an absolute favourite Calculator guide author, The Calculator Guide, Inequalities On A Number Line On A Casio fx-83GTCW | fx-85GTCW. I am looking forward to more from the Calculator Guide, keep an eye on these playlists on The Calculator Guide YouTube Channel.

The Calculator Guide.

You can see further details on the calculators from Casio here and the manuals can be found here, fx-570CW | fx-991CW User’s Guide, and fx-83GT CW I fx-85GT CW User’s Guide.

View a QuickStart video from Casio to help get you started with New ClassWiz.

I have added a page for easy reference to the Calculator series of pages.

Some great resources that have caught my eye recently:

The word problems are available on All About Maths. The booklets have been designed by shadowing past exam questions to help students gain ample practice in answering such questions. Two levels of difficulty are available: basic and multi-step. For students who need a little extra support, note the booklets with ‘starter advice’ which could be useful to provide scaffolding.

AQA’ s all about Maths is a resource site for teachers with numerous excellent resources. The resources are for teachers who offer, or are considering offering AQA maths qualifications; see How to get access to AQA All About Maths and register here.

From NCETM, have a look at these new resources on Algebraic Thinking.

These materials for exploring algebra with KS3 students are all freely available to download from the NCETM website. The 6 resources include PowerPoint slides and very helpful notes for teachers including the rationale behind each topic, useful language for teachers to model, how to address misconceptions, and how the topic might be explored in the context of KS2 to KS3 transition..

NCETM Balance Beam

The notes suggest that this Checkpoint activity could be used to introduce the Balance Beaam resource. A reminder that you can find all the Checkpoint activities on the NCETM webste.

NCETM Checkpoint Activity

From the brilliant Nathan Day Calculate Cleverly, Trigonometry, and Mathematical Quotations :

What a lovely task from Miss Konstantine on Quadratics.

GCSE Revision 2023

See Exams Weeks 2 and 3 for recently created practice papers and checklists given that paper 1 is complete.

We must start with Corbett Maths – GCSE Maths – Summer 2023,

Note the latest addition – Ultimate Revision, currently available for Foundation GCSE and Higher. This incredible resource includes a video and accompanying booklet (answers also available) with 400 questions!

Corbett Maths – A Bit of Everything practice papers

On Corbett Maths choose your examination board from GCSE Maths – Summer 2023 and you will also find Revision checklists, a collection of Practice Papers, and A Bit of Everything Papers; the papers with questions provide very comprehensive syllabus coverage! Each paper includes a contents list with the relevant teaching video.

CorbettMaths revision checklist

Mr Neill

From Mr Neill, a brilliant resource, all Edexcel, AQA and OCR GCSE maths questions categorised by topic with answers from June 2017 to Nov 2021 (9-1), available all on pdf, PowerPoint or Promethean.

On ExamQ from Mr Watts you can quickly search for Edexcel Maths GCSE and A-Level exam questions. You can choose from GCSE Foundation or Higher, AS or A level, you can also select by exam series, paper, area and topic.

The interface is very clear indeed, easily display the questions or mark schemes.

Dr Austin Maths – Revision Grids

From DrAustin Maths under Revision note the new revision grids, further grids will follow.

On Maths Genie you can revise by topic, or access exam papers and mark schemes for Edexcel, AQA and OCR. For AQA and OCR these are simply the papers and mark schemes, the Edexcel papers additionally have worked video solutions

On Mr Morely Maths you will find a wonderful collection of GCSE resources, including Video tutorials, worksheets to match, exam question packs with mark schemes, starters, full lessons, revision guides, CPD sessions and methods road maps.

Mr Morley Maths Revision Work Books

Note the latest resources – Revision Work Books. These booklets contain at least one past paper question on every topic split into grades 1-3, 4-5 and 6-9. Each has a contents page with QR code links to relevant videos.

I do like these excellent revision guides – notes jotters to accompany the videos.

Mr Morely Maths

From White Rose Maths, GCSE Practice Papers (scroll down) for AQA, Edexcel and OCR. Whilst based on the November and June 2022 advance information these papers and mark schemes for all three boards and also the excellent pre-exam workshops provide very useful revision resources.

White Rose Maths

Third Space Learning

From Third Space Learning, papers for AQA and Edexcel have been created for 2023 (OCR to follow).

1st Class Maths

On 1st Class Maths, new practice papers and video solutions are being created for Edexcel and AQA. The publication dates are here.

From GCSE Maths Tutor we have practice papers and worked solutions.

From Gareth Westwater, see GCSE (and IGCSE) questions by topic, on, or on TES, a massive (be patient, there are over 5000 slides) PowerPoint of IGCSE examination questions organised by topic, combining all the individual PowerPoints of exam questions, this is very simple to navigate.

On BBC Bitesize you will find GCSE Maths – exam practice, 5 quizzes of 10 questions each, with fully worked solutions.

Also from Bitesize, try these GCSE maths – quick-fire quizzes, each quiz has 10 quick-fire questions that should take approximately 5-10 minutes to complete. You can take the quiz again and answer a new set of questions. Answers are all explained.

BBC Bitesize quick-fire quizzes

From Dave Taylor, we have these very useful GCSE Higher Revision Booklets for OCR.

Transum Mathematics – Refreshing Revision

This Custom Starter from Transum, is one I have featured before, it allows teachers to select the number of questions and the topics to include; scroll down the page and choose the topics you want from the Concept Selection. It is possible to save a particular selection of topics as the URL for your selection will be generated. It is also possible to drag the panels so your questions are displayed in the desired order. The beginning of a lesson can be an ideal time to review previous learning.

On the subject of starters – short questions can make ideal revision starters – a reminder of some great resources:

Transum has an extensive library of self-checking exercises, so we could easily provide examples on inequalities for example. On Transum, there are several ways to search for resources, for example, try:

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Unlimited Edexcel GCSE 1 mark questions

On TES, from SNO, this Excel spreadsheet generates an endless supply of 1 mark questions with the option to display the answers, making an ideal starter. Two versions are available, you can choose 5 or 10 questions to display.

Check this great resource from Mr Kingsley, an ideal starter, there are 80 sets of 10 1 and 2 mark questions in this file.

We start every foundation lesson with a booklet of ten 1&2 mark questions, aimed at repetition. Builds up in difficulty in both calc & non-calc topics. 80 pages worth. Seems to help reduce errors at the start of papers. Feel free to take a look.— Mr Kingsley (@KingsleyMaths) February 12, 2021

Edexcel’s Practice Papers include freely available Foundation Tier one mark questions. There are calculator and non-calculator paper questions and mark schemes from June 2017 through to June 2019 (non-calculator) and to November 2019 for the calculator questions.

We also have:

See also: Knowledge Organisers – Mathematics

Mr Chadburn – Calendars

I do like Wayne Chadburn’s monthly calendars that provide regular, varied practice – a little bit of maths each day. Calendars for the 2022-23 academic year are available here. Note the three versions including crossover questions (these appear on both Foundation and Higher papers so great practice for the more challenging Foundation questions), Foundation, Foundation plus and Higher; answers are provided.

From Jake Gordon, try his Skills grid creator – customise exactly as you want from 90 skills, and answers are included.

Jake Gordon – Skills Grid Creator
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Jake Gordon – Skills Grid Creator

On Jonathan Hall’s Test Maker on MathsBot we could create a test to test many of these skills. Choose the skills you want from the menu, the number of questions, and the initial and final difficulty of the questions on a scale of 1 to 10, also note the Paired Solutions option to show one example with an answer then one to try. An Answer Key is provided for any test you create.

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MathsBot – Test Maker

We could also use the many brilliant GCSE resources from MathsBot.

Maths White Board – Revision Boards

See on Maths White Board: Revision Board – generate a starter based on the Advance Information

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Interactive Maths Generators – Dan Rodriguez-Clark

On Interactive Maths Generators from Dan Rodriguez-Clark (@InteractMaths), design your own sets of questions on more than 50 maths topics for your students to practice a variety of skills. There are many customisation options, generally as well as for individual topics. Full instructions are on Dan’s site.

From TeachitMaths an AQA Maths partnership resource: GCSE mathematics-small things make a big difference includes many really useful and important reminders for students.

AQA / Teachit Maths

Fill in the blanks…

Inspired by Jonathan Hall’s (@StudyMaths) excellent session on Completion Tables at Maths Conf31, I have been reminding myself of all the excellent fill in the blanks type resources available and have updated my original post on this. Now available as a page, Fill in the blanks can be found as part of the Problems & Activities Collection. Several new activities have been added to the original.

Trigonometry (Area) – Fill In The Blanks, Andy Lutwyche

There is also a good deal of evidence that the use of worked examples can
be helpful in introducing new ideas (Booth et al., 2017; Sweller et al., 2019).
Particularly effective are ‘completion problems’ where students are given
partial solutions and required to complete them
. These can help students to
focus on the examples but also manage the difficulty level while retaining
authentic tasks

Great Teaching Toolkit – Evidence Review, June 2020 Rob Coe, C.J. Rauch, Stuart Kime, Dan Singleton

Check the galleries here for images of some of these great resources, all the details are available on the page Fill in the blanks…

Women in Mathematics

March 8th 2023 is International Women’s Day.
We’ll start with an image I have shared before that I think still says it all! Thank you, Steve Lomax (Photo courtesy of the wonderful children of Mansfield Green E-ACT Primary, @mgeact  @EducationEACT) who shared this wonderful response to the task ‘Describe a mathematician’…


Some useful references on women in Mathematics:

From Lucy Rycroft-Smith, see this wonderful collection of books about Maths by women. Lucy has chosen 13 books, I like the way she has categorised the books, a book for the artist, for the rebel…. Brilliant – I can see some in there I want!

From the Advanced Mathematics Support Programme, Find ways to encourage girls to study Mathematics. Note the free resources here, including (for girls and boys!) Maths, Opening the door to your future, a leaflet which explores the post-16 maths qualifications available to students, to help them decide which one is best. 

Note too the 30-minute presentation, Why Study Maths, for students and parents/carers which is about the importance of studying maths post-GCSE. It outlines the options available and provides compelling reasons for choosing to take an advanced maths qualification. Slides and speaker notes are available to download. These resources could be an excellent way of helping Mathematics Departments link curriculum learning to Careers, for all students, helping to meet the Gatsby Benchmark on this. 

And for some History

Questions by Topic – Maths A Level

The A Level Maths series of pages features many resources for teaching A Level Maths. Following last week’s post on Worked Examples – A Level Maths and Further Maths, I thought it would be useful to include a page in the series of sites which are easy to search for questions by topic for Maths A Level.

It seems appropriate to begin with this brilliant resource from Transum Mathematics. I have often recommended GCSE Refreshing Revision, just like the GCSE version this Advanced Level version allows teachers to select the concepts required; the questions will change instantly to show your choices. It is also possible to drag the panels so that the questions are ordered as you choose. Refresh the page and you will get different revision questions on your chosen topics. The ability to save the web address for a chosen selection is very useful indeed.

This resource like all the Transum resources is free to use, an extensive collection of resources such as the various KS3 and KS4 self-checking exercises provide answers for any user. Answers for some resources such as examination questions and this Refreshing Revision resource are provided for subscribers; extremely good value for money in my opinion.

AQA Topic Tests for Maths and Further Maths

OCR A Delivery Guides and Check In Tests

OCR B Delivery Guides and Check In Tests

OCR Maths Section Check In

On Doctor Oliver Mathematics you will find an extensive library of worked examples, access these via examination papers or choose questions by topic. It is so valuable that the question and solution are presented together. At A level you will find both Mathematics and Further Mathematics.

MathedUp! Maths Takeaways

MathedUp! A Level Maths takeaways

Maths Genie
Maths Genie

From Maths Genie, we have A Level worked examples; videos and questions by topic are available for both AS and A Level.

Andy Lutwyche – Erica’s Errors series
Stoke Maths

Stoke Maths MEP Starters are very attractively presented high-quality resources. Looking at the Spot the Mistake PowerPoints for example, as you can see in the image below there are a great collection of questions that include full answers. It’s great to see Mechanics and Statistics collections. The revision question starters provide very useful question sets.

From Ben Bently, comes a collection of low stakes quizzes by topic using questions from Diagnostic questions.

Westie’s Workshop – Past Paper questions by topic

From Physics and Maths Tutor – see Maths Revision which includes GCSE, Maths, Further Maths and International A Levels questions by topic.

From A Level Maths Exam questions by topic. The questions are legacy questions but are chosen for relevance to the new specification. See also:

On ExamQ from Mr Watts you can quickly search for Edexcel Maths GCSE and A-Level exam questions. You can choose from GCSE Foundation or Higher, AS or A level, you can also select by exam series, paper, area and topic.

The interface is very clear indeed, easily display the questions or mark schemes.

On MadAsMaths, hover on Maths Booklets for a dropdown menu of questions available by topic. Basic Topics – Various includes several topics from Pure Maths quoted as suitable for:

  • providing enrichment material for very able G.C.S.E students. (most booklets)
  • covering the typical first year non calculus material, of a two year course in A Level mathematics.
  • introducing/revising various non calculus topics to undergraduate students in degrees not requiring A Level mathematics.

Note the inclusion of the solution – increase the magnification to view these:

CIMT – A Level

On CIMT, the A Level course materials include activities, examples and exercises by topic.

On Dr Frost Maths, we can select examples by topic, there is an extensive collection of Key Skills examples, all with fully worked solutions.