Mathematical Miscellany #80

A compilation post, featuring:

New on BBC Bitesize are GCSE exam-style quizzes; the quizzes have been designed for students working on GCSE maths, biology, chemistry, physics, combined science, computer science and geography studying any awarding body specification. For each subject, you will find 50 exam-style questions, these are arranged over five activities of ten questions each. The questions are multiple-choice and students can see a fully worked solution for each question.


Rob Southern

Rob Southern has created a very useful document linking sections from the Pearson A level textbooks to his videos, where they exist. Rob’s YouTube channel is Maths in an empty classroom. Do check Rob’s site for his collection of A Level Maths and Further Maths resources. I mentioned his Coordinate Geometry exercise, part of the A Level Pure 1 Year 1 collection in this Fill in the blanks post. Note Rob’s questions to consider to get students thinking hard. You can also find a version on Transum, Coordinate Geometry Table which allows answers to be checked.

Rob Southern Coordinate Geometry Table – on Transum

I do like Amanda Austin’s latest inequalities resources, these linear programming style resources would be very helpful for Decision Maths.

For resources for Linear Programming, see these pages in the A Level Further Mathematics series.


From MEI, comes excellent support for investigating the A Level large data sets. You will find help videos with useful techniques for using Excel and GeoGebra for statistics in GCSE and A level, also, from The Advanced Mathematics Support Programme (AMSP) look at these workbooks that show how to use Desmos to investigate the large data sets. Desmos could be used to support Statistics at GCSE also.

Desmos classroom activity

Here’s a Desmos activity on Interpreting Box Plots.


Staying with Statistics, an activity I have always liked is S4 Understanding Mean, Median, Mode and Range.
(All Standards Unit resources).


Mathematical Miscellany #79

Looking ahead to summer examinations, this year there will not be advance infomation as there was last year, but in GCSE Mathenatics students will again have formaule sheets; the exam boards have now published these. This page, Examinations 2023, includes links to infomation and the formulae sheets for each exam board. The page also includes the series of revision pages with many ideas and resources for revision.

Formulae sheets 2023

OCR formulae test

OCR additionally have formulae sheets top tips, and GCSE formulae tests.


Mathsbot – Directed Number

I often use Jonathan Hall’s wonderful Completion Tables so was delighted to see that these are all in one place on MathsBot, a personal favorite is his Directed Number.

(See Fill in the Blanks for many such exercises, and Negative Numbers for more resources on Negative Numbers.)


Regular readers will be aware a favourite website of mine is Transum, two recent additions are Algebraic HCF with Algebraic HCF and LCM exercises over 5 levels and Gradients now with a new level 2 which features straight lines drawn on axes where the vertical scale is different from the horizontal scale, soe labels are obscured for an additional challenge.


From Chris McGrane on Starting Points Maths, have a look at this lovely task on Integration which provides much needed practice on deciding on the integration required to determine the areas shown. Students are required only to write down the integrals with limits.  

It struck me that the questions could be checked and illustrated on WolframAlpha.


Both MathsBot and Transum featured in my Enduring Websites collection, websites started between 1997 and 2013, and still there! MathsBot and Transum are regularly producing such excellent resources after many years. I believe Starting Points Maths will be included in the next Enduring websites collection!

These slides are from a session I presented at last year’s MA Conference.

Mathematical Miscellany #76

MathsBot GCSE Countdown Timer

With two GCSE papers done and just one to go, see November Examinations for resources including papers from 1st Class Maths.


From Mrs Jagger, @Jaggersmaths

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

Fill in the blanks worksheets can be so good – for many more examples, see my post, Fill in the blanks…


From Brooke Hunter, why not practice rearringing formulae to support your Science colleagues?


Thinking about misconceptions in Algebra recently I came across “2b or not 2b: Misconceptions in algebraic reasoning” from Barbara J. Dougherty. This has been added to my page on Misconceptions.

Something Dan Meyer said at the MEI Conference 2021 really struck a chord with me, he said “There are no mistakes or misconceptions, just takes and conceptions.” Dan Meyer mentioned WW Sayer who said:


Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong’. Rather he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole art of teaching.

WW Sayer

In case you missed it, Mathematical Miscellany #75 on some brilliant resources has proved very popular.

Jake Gordon – Worked Examples

Mathematical Miscellany #75

A collection of impressive resources…

Jake Gordon – Worked Examples

Jake Gordon has been rather busy! Have a look at his “monster of a PowerPoint”. These detailed worked examples are based on the book Teaching math with examples by Michael Pershan.

Also inspired by Michael Pershan’s book and her research on self-explanation, have a look at Karen Hancock‘s journey into worked examples.


From Nathan Day – a brilliant collection of resources on Distributivity: Partitioning, Grid Method, and Expanding Brackets The 15 tasks increase in demand. Note the complete thread.

Nathan Day

Also from Nathan Day – a wonderful collection of Starters – again, note the complete thread.
I have added this collection to my Starters page, a collection that includes Advanced Level Starters.

Andy Lutwyche – Erica’s Errors series

Andy Lutwyche’s collection of Erica’s Errors where students must identify errors in solutions can be an ideal starter for either retrieval practice for an earlier topic or to consolidate learning for a current topic.


Added to my Primary page – curriculum mappings from NCETM

Also added to the Primary page:

On DrFrostMaths there is a growing collection of Key Skills for Primary students.


I have mentioned DrFrostMaths more than once recently, a new instruction manual for teachers is now available.

DrFrostMaths Key Skills – Algebra

From the GCSE/IGCSE/L2 Further Maths page, the pages for individual topic areas all include Sites with clear resources by topic, see the Algebra page for example. These resources by topic include links to the relevant DrFrostMaths key skills.


Mathematical Miscellany #74

Back in Mathematical Miscellany #46 revisiting some of the much older Miscellany posts to remove broken links I was reminded of some resources still available after many years.

For today a small selection of some resources from older posts. From 2011, we have a dance for teachers of Decision Maths – Dancing the Bubble Sort! I see AlgoRythmics celebrated its 10-year anniversary in 2021.


Math Open Reference

From 2011, Math Open Reference, I have used this many times – I particularly like the constructions, see this on Bisecting an angle for example.


Mike Hadden – Excel Files

Also from 2011,  Mike Hadden’s Excel Maths Files are all still there.


In 2011 I wrote about the weekly problems try the challenges from the University of Mississippi.
Four problems are set every week.

…still going strong!


I’ll finish with slides from a session I presented at last year’s MA Conference on Enduring Websites – some sites that have been with us for many years and all still there!