Mathematical Miscellany #71

I really like the grids from Jonathan Hall on MathsBot, try his updated linear sequences grid. Note Jonathan’s reference to Amanda Austin’s brilliant Linear Sequences Fill In The Blanks activity. Remember you can keep an eye on new resources from Amanda Austin, I see a fill in the blanks circle geometry activity for Year 12. For lots more fill in the blanks activities from a variety of sources see this Fill in the blanks post.

Andy Lutwyche – Careless Casey

Talking of new resources, see Miscellany #63 which includes examples of sites with clear ‘What’s new?’ type sections or are easily searched for recent additions and/or have a subscription to a newsletter. Looking at the latest resources from Andy Lutwyche on TES I see Casey continues to be very careless with her Level 2 Further Maths!

Maths Sandpit blog

On Maths Sandpit from @Ms_Kmp, A-level Exam misconceptions 2022, a presentation about her thoughts on the Edexcel A-Level Maths papers, from the perspective of reviewing students’ papers. 

DrFrostMaths is such a goto website and an excellent example of a website which is easy to navigate, perhaps try the Question Explorer. A brilliant feature (well one of the many brilliant features) of Dr Frost Maths is the extensive collection of key skills for UK KS2 to KS5 (ages 8-18), practice as many examples as you want, and perhaps watch a video on this key skill.

DrFrostMaths Key Skills

Note this latest work – diagrams for Key Skills are now done using Desmos.

DrFrostMaths Key Skills

From Mark Willis, try his Video site, a comprehensive set of Maths questions ordered according to topic and level with video solutions from KS3 to A-Level FM with interactive GeoGebra apps. Also available are IGCSE quizlets.

From Tom Sherrington, a post providing links to his Five Ways To series including one-page summaries produced by David Goodwin.

A place for everything…

“A place for everything, everything in its place”

Benjamin Franklin

Where do we put things so we can find them again?! I have been organising posts and pages in an attempt to make things easier to find – an ongoing mission, still in its early days! Just a few examples of recent organisation:

Added to the A Level (16+) series of pages is a page for GCSE to A Level Transition. One of the A level pages is on University Admissions Tests, added to that page is Mr Bowler’s Problem Solving Booklet for University Preparation which contains 151 questions to help prepare students for undergraduate admissions interviews in mathematics, answers are also available; the booklet is available on Dr Frost Maths.

Stephen Siklos – Advanced problems in Mathematics, see University Admissions Tests

The A level series includes A Level Teaching resources, and I have added Advanced Level Starters to that collection.

Andy Lutwyche – Erica’s Errors

On the subject of Starters, added to the Collections category, is Julia Smith’s (@TessMaths), wonderful collection of Mathematical Hooks. The Starters library can be found on the first of the top menus – Lesson Planning.

Also added to Lesson Planning is a page for Misconceptions in Mathematics.

Nevil Hopley’s excellent Classic Mistakes site.

George Stone (@DrStoneMaths) is producing one slide summaries of interesting educational research papers, this information has been added to both Research – Learning and Teaching and Research – Mathematics Learning and Teaching, both part of the Reading series available from the top menu.

National Strategies – Exemplification Examples: Geometry and Measures

Older, but still with many useful examples – see these Exemplification Examples which were written by the National Strategies for the then Secondary Framework for Teaching Mathematics. The examples illustrate what students should be able to do within a particular strand of objectives by the end of each year. Examples are in the four categories number, algebra, statistics and geometry and include examples for Year 7, 8 and 9. There are many excellent examples here still relevant for KS3.

These can be found on the KS3 page, also in the Collections category, part of the Starters library, the Starters Library can be found on the first of the top menus – Lesson Planning.

Mathematical Miscellany #70

Thinking about November exams – in the Summer, 1st Class Maths created excellent resources based on the Advance information, watch for foundation papers for Edexcel/AQA.

Mr Chadburn – calendars

Whether or not students are taking November examinations, Short questions can make ideal starters – see this Revision post for many suggestions including collections of 1 mark questions, recently updated with Wayne Chadburn’s great monthly calendars which provide regular, varied practice – a little bit of maths each day. Calendars for the 2022-23 academic year (so far up to December) 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.

Unlimited Edexcel GCSE 1 mark questions

Show that….
A reminder of this post with resources to encourage students to show their working.

My post on Transition includes the excellent free Transition resources from Sparx Maths, also available free from Sparx Maths is a free formative baseline assessment for Year 7 with a supporting Question level analysis resource (QLA) providing student, class and year group performance on individual questions. The QLA also provides a topic-level analysis of students’ performance in the topics they will need to be fluent in to access the Key Stage 3 curriculum.

Sparx Maths – Fluency Quiz

Not only have Sparx Maths provided the test and accompanying documents but fluency quizzes with answers provided.

Ben Sparks – Circle Theorems

From Ben Sparks on GeoGebra – interactives for all 8 circle theorems discussed at GCSE maths.

Tim Devereux

On the subject of Circle Theorems, see also Tim Devereux’s GeoGebra appletsYou can access each theorem from the menu on the left which includes a useful summary of all the theorems. From the menu, we can see that proofs are also available.

Transum Yohaku Puzzles

To finish with a puzzle, try Transum’s Yohaku Puzzles. For numerous Puzzles and Games – see this collection.

Back to School

Some useful posts and pages for the start of term…

Examinations – Mathematics November 2022

MathsBot GCSE Countdown Timer

This page – which is currently easily accessible from the menu on the right-hand side has links to the advance information from the exam boards and some resources to support revision for these exams. I will keep the page updated as new resources are added.

Transition Time

Edexcel Transition Vidoes (11 Sections)

This recent post has resources for transition from Year 11 to A level and for students beginning Year 7.

Don Steward – sum and product

The Starters collection includes many ideas for starting lessons including starters for older students.

Index of starters:

This series of GCSE pages is currently undergoing a major update to include many more resources. Number, Ratio, Algebra, Geometry, Probability and Statistics, all include a list of sites where it is easy to search by topic, and all include the old but still useful exemplification examples for Years 7, 8 and 9. On the subject of Years 7, 8 and 9, see the KS3 page which includes the excellent guidance from NCETM.

Number and Algebra currently have the most resources and links to popular posts on these areas.


Exemplification examples – Geometry
Edexcel GCSE GeoGebra resources

The GeoGebra pages include many resources from Edexcel for GCSE and A Level Mathematics.

Your Year 12 students may be taking University Admissions Tests. This page includes many resources for these tests.

These resources for University Admissions Test preparation provide challenging questions for students anywhere studying Mathematics beyond age 16.

See also – No Calculators Allowed which includes information on the BMAT test, and also useful resources for students of all ages to work on estimating skills.

The A Level (16+) series of pages accessible from the top menu includes University Admissions Tests and many other useful pages.

The A Level page includes many teaching resources.

GCSE and A Level Science includes much mathematical content, it strikes me that is important for Mathematics Departments to be aware of the mathematical requirements for these qualifications and where appropriate use resources which will support Science as well as Mathematics; see Mathematics for Science

From Transum Mathematics, Back to School includes many activities to start the year.

Mathematical Alphabet – Sarah Carter

In case you want somethimg for your walls, some Posters.

Transition Time

Edexcel’s transition to A Level Maths videos and worked examples are a very comprehensive set of free resources designed to help the transition from GCSE to A level Maths. The content focus is on the overlap between GCSE Maths and the first year of the A Level Maths course making the resources useful not only for initial transition but also for the first year of the course.

From Sparx Maths, have a look at their Transition Booklets, one for Year 6 to 7 and one for GCSE to A Level; these booklets are free whether you have Sparx Maths or not. The Year 6 to 7 booklet with over 130 questions is based on the Year 6 DFE/NCETM ‘ready to progress’ guidance from June 2020. The GCSE to A Level booklet uses over 120 questions taken from 11 key topics on Sparx Maths. Answers can be obtained by completing a form with your school details.

OCR Transition Algebra Fractions
OCR- Bridging the Gap – A Student Guide

For students going on to A Level then a really useful publication is use OCR’s brilliant guide for students Bridging the gap between GCSE and AS/A Level Mathematics – A Student Guide. With sections on Algebra, Trigonometry and graphs including examples, question practice on key topics and suggested reading before starting the A Level this is so valuable for students.
pdf format: bridging-the-gap-between-gcse-and-as-a-level-mathematics-a-student-guide

Hegarty Maths

Free lessons from Colin Hegarty recorded on YouTube are available to help GCSE students prepare for A Level Maths.

From TL Maths GCSE to A-Level Maths Bridging the Gap is a series of videos looking at some of the basics of GCSE Maths Higher Tier that students should be proficient in before they start A-Level Maths.

You could also look at Step Up to A Level Maths from The Centre of Innovation in Mathematics Teaching which helpfully lists skills you should be confident with and provides resources to support your study of these skills.

AMSP – Transition To A Level Mathematics – Essential Skills

From AMSP – check Transition to A Level Mathematics – Essential Skills.

These Transition Takeaways from Mohammed Ladak have been specifically chosen to help with A Level Maths preparation.

Transition Resources

The many useful resources from OCR have already been mentioned; also available from OCR are transition guides. See for example this Equations Transition Guide which is very clear on the differences in the demand and approach at the different key stages. Each transition guide includes the relevant checkpoint tasks, in the Equations transition guide these activities focus on solving equations in one variable including those that require some rearrangement.

OCR Transition Guide

For the transition from KS2 to KS3 see MEI’s transition resources including an excellent series of webinars. The webinars explore curriculum and pedagogical continuity across the KS2 to 3 transition and look at the Primary Maths Guidance Document. The guidance for Year 6 is a valuable document for looking at the transition from Year 6 to Year 7 and includes example assessment questions for each of the ready-to-progress criteria.

Primary Guidance – Year 6

NCETM has produced an extensive library of resources offering support with the Primary Guidance documents. This includes 79 PowerPoints, these focus on the ready-to-progress criteria in the DfE maths guidance for KS1 and KS2. These can usefully be viewed by topic or by year.

You can find NCETM guidance videos on YouTube.

NCETM – Checkpoint sample

NCETM’s Checkpoints are diagnostic activities designed to help teachers assess the understanding students have on leaving primary school. You can see three examples of Checkpoints activities and teachers of Year 7 can download the first Checkpoints activities using their school or organisation name and email address. There will be further Checkpoint activities published, enough for three Checkpoints a week across the school year.