November – Barvember

White Rose Maths – Barvember

It’s Barvember from White Rose Maths. Barvember, from White Rose Maths, was created to encourage the use of the bar model. Bar models can really help children visualise and then solve maths problems. You could solve the problems using this great digital tool from White Rose Maths, Bar Model

Further resources on Bar Modelling:

For an Introduction to Bar Modelling have a look at the NCETM Secondary Professional Development Materials  Choose the section on Using mathematical representations at KS3 for 10 different guidance documents including Bar Models. This 17-page document for professional development provides a very comprehensive introduction to Bar Modelling and includes example problems.

On the subject of White Rose Maths have a look at this brilliant resource from Ben Gordon: Representations through the Curriculum shows the progression of bar modelling from Year 7 to Year 11 with examples for each topic and some video support.

Thinking Blocks – Math Playground

The section on Further Resources in the NCETM guidance document includes Thinking Blocks, an outstanding resource that I included in a post on Ratio and Proportion. The relevant information on using the resource is included for completeness in this post. Further resources for Bar Modelling are also given.

Thinking Blocks from Colleen King’s site Math PlayGround – is a wonderful way to visualize Ratio and Proportion problems. This works on all devices.

Models like this really help students to visualise problems. Note the numerous videos showing how to model problems (scroll down the page). You can use the Thinking Blocks Tool to model your own problems; watching the videos will help you learn to use the tool. There is a very clear help section also.

Thinking Blocks Modeling Tool

I have used the tool here to model a problem from Andy Lutwyche’s Clumsy Clive on Ratio resource.

Thinking Blocks Modeling Tool – use for your own problems

Also featured in NCETM’s resource section is The Mathenæum from Ken Wessen which includes Modelling Word Problems and Fractions, Decimals and Percentages.

The Mathenæum – Ken Wessen
The Mathenæum – Ken Wessen

See also:

Sybilla Beckmann paper

Sybilla Beckmann’s paper, Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4–6 Texts Used in Singapore is an interesting read on the subject of the use of diagrams.

Note Pearson Edexcel GCSE Maths Networks on YouTube; for an excellent introduction to Bar Modelling watch Naomi Bartholomew-Millar’s session.

MathPad – Using Bar Pictures to Solve Equations


Wayne Chadburn

The start of November is a good time to remind readers of Wayne Chadburn’s monthly calendars. He writes these calendars to provide regular, varied practice – a little bit of maths each day. Three versions of each monthly calendar are available, Higher, Foundation Plus, and Foundation; answers are provided.

November Examinations 2023

MathsBot – GCSE Countdown

With November examinations fast approaching, a reminder that many useful revision resources are available in this collection.

Corbett Maths – Revision Resources
Corbett Maths – A Bit of Everything practice papers

On Corbett Maths, try the Ultimate GCSE Revision Videos; use the GCSE Revision resources available for Edexcel, OCR, AQA, and CCEA, 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

On 1st Class Maths, the Edexcel Revision page offers questions and solutions by topic and difficulty, note the final column in the table which shows the Edexcel past series percentage correct up to and including the June 2023 exams. The Ultimate Revision Booklets for Foundation (114 questions) and Higher (106 questions) have one question on every topic and accompanying video solutions.

1st Class Maths Ultimate Revision Booklet

Practice papers and video solutions were created for the June 2023 exams for Edexcel and AQA.

Edexcel GCSE 9-1 Key Topics

From Edexcel, GCSE 9-1 Mathematics Key Topics, a series of 30 very short videos reviewing essential GCSE skills.

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 June 2022 (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 look at the very useful revision grids.

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 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).

From GCSE Maths Tutor we have practice papers and full video solutions available for Higher and Foundation tiers.

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. The 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.

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 2023-24 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.

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

Knowledge Organisers – Update

This post on Knowledge Organisers is very popular – this has now been reorganised so that organisers for KS3, GCSE and A Level can easily be located. Do have a look at this post on Knowledge Organisers from Durrington Research School, it is not about the knowledge organisers themselves but how they are used for planning, teaching and testing. Note the example shared of a Maths Knowledge Organiser, Year 10 Expressions, Foundation. I like the fact that key vocabulary is included here, the few key facts needed and of course by far the largest section – key concepts with examples.

Mrs D has now completed her excellent set of Year 2 Pure Mathematics Organisers, these are clearly indexed in the A Level section where you can also find Pure Year 1, Statistics and Mechanics Knowledge Organisers.

Mrs D Maths – Knowledge Organisers

Oak National Academy

Oak National Academy has begun sharing its new interactive curriculum plans and early release units. See the Oak update on the new curriculum plans for further details.

Ed Southall is the subject lead for Maths, for some background read the Oak Update – Maths curriculum partners and subject experts – March 2023.

Oak National Academy – Secondary Maths Curriculum Plan
Oak National Academy early-release units.

The new curriculum plans and early release units include primary and secondary maths resources produced in collaboration with MEI. For secondary Maths and available to look at now, we have:

Looking at the series of 12 lessons on Surds, each lesson includes a slide deck (slides used in the video), lesson details, a worksheet. 2 quizzes – a starter and exit quiz, and a video.

Oak National Academy – Simplifying Surds, slide deck example

The worksheet on Simplifying tasks includes the activities from the video/slide deck. The answers are all included in the slide deck.

Oak National Academy – Simplifying Surds, exit quiz examples

The Oak Update includes this comment on what is new about the teaching resources:

As well as being designed specifically for use in the classroom, the resources have been built around the latest evidence on how pupils learn, including SEND best practice. Plus, they’re editable, so you can tailor them to your pupils’ needs.

They’re created by teachers, rigorously checked by experts, and tested in classrooms. All so you can feel confident in the resources you use.

Oak National Academy

We will be able to see more lessons and teaching resources over the current academic year with access to everything or these first subjects (English, history, maths and science from key stages 1-4, plus primary geography and secondary music) available by Summer 2024.

STEP Support – A Level Notes

From the STEP Support Programme from The University of Cambridge, I do like these A-level notes; currently available are notes on Algebra, Coordinate Geometry and Introduction to Calculus.

Also available are notes on the parts of the STEP specification not included in the prescribed DfE content for A-level Maths and Further Maths.

The Algebra notes, for example, include the following topics: manipulation, surds, quadratic equations, inequalities, polynomials, rational functions, logarithms, and binomial expansions.

Cambridge University STEP Support – A-level Algebra Notes

The notes link to many excellent problems from Underground Maths and Nrich, for inequalities we have from Underground Maths Inequalities for some occasions, a brilliant way to practice inequalities. and When are these quadratic inequalities true together?

When are these quadratic inequalities true together is one of the Review questions I have often mentioned from Underground Maths.

On the Underground Maths site you can find resource suggestions clearly mapped to the subject content for the A Level specification. This is an Excel spreadsheet; for each content statement, Underground Maths has suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of Mathematical modelling have been highlighted.

These, of course, are suggestions. There are so many outstanding resources on Underground Maths.

An ongoing project, I do find the Review Questions can be excellent for either introducing ideas or for review and have created a spreadsheet of my own for just the Review Questions which lists the questions by title rather than by number. Excel File: Underground Maths Mapping Review Questions August 19 or the same file in pdf format: Underground Maths Mapping Review Questions August 19

Underground Maths Mapping Review Questions
Nrich – Power Match

To look at another extract from the Cambridge Algebra notes, on Logarithms, we see the suggestions Power Match from Nrich for investigating logs base 10, and from Underground Maths

On logs, I have to mention the brilliant Underground Maths resource – To log or not to log? I have used this resource many times and it has always resulted in some great discussions and highlighted some misconceptions.

To log or not to log – Underground Mathematics

This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. I have always found that in addition to working on indices and logarithms, this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!

This problem is classified as a Problem Requiring Decisions.

Students are often used to problems being posed in such a way that they have all the information that they require in order to start, and no more. Problems (especially from the real world) are very often not like this, and so resources of this type will give students the opportunity to develop the skills needed to deal with this. Some problems might not contain enough information, so students may need to decide on classifications, make assumptions or approximations, or do some research in order to move forward. Some problems might contain too much data, so that part of the challenge is to identify the useful information.

Here’s what my students said:

See also: