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.


Solving Linear Equations

GCSE Content
17. solve linear equations in one unknown algebraically (including those with the
unknown on both sides of the equation); find approximate solutions using a graph

A variety of resources to use:

Enigma Maths Hub: under Key Stage 3 Mathematics Core Concepts see Solving Equations – Small Steps

Enigma Maths Hub

For each of the above you will find suggestions and resources including NCETM checkpoints activities.

Desmos – Solve equations bar models

Maths White Board

On Matt Woodfine’s Maths White Board, from the home page use the filter to choose Algebra and search on linear equations.


Math Whiteboard

On Math Whiteboard start a new board. On the right-hand side of the top menu select the three dots for More and then Highlight equivalence.

You can type expressions on a whiteboard and equivalent expressions will be highlighted in the same colour – brilliant. (For more on this feature – see Highlight Equivalence.


PhET Interactive Simulations, University of Colorado Boulder, https://phet.colorado.edu

The ability to display or hide the variable and to take snapshots means working can be clearly shown using this PhET Sims Equality Explorer.
Math HTML5 PhET sims by topic see PhET Sims – Index.


Andy Lutwyche – Clumsy Clive On Solving Equations

From Andy Lutwyche one of the Clumsy Clive series is on Solving Equations. Andy has many other Equations resources including Building Blocks – Solving (Linear) Equations.


SERP – Algebra by Example

On the SERP website before see MathByExample and AlgebraByExample which is a set of Algebra 1 assignments that incorporate worked examples and prompt students to analyze and explain. These resources can provide prompts for discussing common misconceptions.


Transum Mathematics

Using the KS3 Index on Transum, we can see many activities on solving linear equations these activities include equations with fractions.


On Dr Austin Maths you can find many resources on linear equations.

The practice strips are wonderfully efficient for photocopying.


On Corbett Maths we have videos, practice questions and textbook exercises.


Dr Frost Maths

On Dr Frost Maths we can use any of the reosurces here on linear equations or perhaps try his full coverage resource – if you want a compilation of GCSE questions.


I think this ‘cover up’ method seen here on Don Steward’s Median can be helpful for many students, something I have used sometimes in class where students are finding solving equations challenging.

On Don Steward’s Median, you will find resources labeled linear equations, linear equations cover up method, and linear equations x both sides.


CIMT Year 7 Interactive Resources

CIMT have a tutorial on Linear Equations in their Interactive resources for Year 7 and on Linear Equations with Brackets in the Year 8 resources.


Graspable Math – Solving Equations


Graspable Math is easy to use, I decided I would solve an equation and wanted to show all the steps. To start, go to a blank canvas and choose Insert / Math Expression, I have used the method of selecting and holding the = sign to start as you can see illustrated in the video above; I was then able to enter an operation to apply to both sides of the equation.

equation to solve
Graspabale Math - Solve Equation
mathisfun balance when adding and subtracting

From Phil Bruce – Linear equations with algebra discs.

Phil Bruce – Linear equations with algebra discs

On Jonathan Hall’s Mathsbot, in the Manipulatives collection, we have Algebra Discs.

BossMaths Algebra Discs.


Using my GCSE Algebra page which includes the GCSE subject content and resources, note also the sites easily searchable for algebra resources by topic. Several examples from these pages are given in this post for further resources from other sites on that list:

Colin Foster – Expression Polygons

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!

Mathematical Miscellany #73

A compilation post this week…


November exam revision

Added to the revision collection for November exams are the papers and mark schemes from White Rose Maths (scroll down) for AQA, Edexcel and OCR.

White Rose Maths

GCSE Practice Papers can be found for November 2022 exams, also still available are the papers for Summer 2022.

The pre-exam workshops were created for the Summer examinations, but these can make excellent revision resources at any time.

White Rose Maths

Multiple Choice questions

MathsHKO – Multiple Choice

From Helen Konstantine on MATHSHKO a lovely page of Multiple Choice questions. There is quite a collection here, these can make ideal starters.


My Revision Notes – Worked Examples

Hodder examples
Hodder – Solutions for My Revision Notes (Pure)

On my page on A Level worked examples, I highlighted the My Revision Notes books from Hodder. Many books are available in the My Revision Notes series, most with a free document of worked examples; questions and fully worked solutions for each section of the book are provided, whilst the documents refer to the books, they are complete in themselves. It’s good to see a book with this document for the International GCSE Mathematics from Pearson. I have added this to the IGCSE page.


Visnos Visual Numbers

Visnos Visual Numbers

A recent interesting online discussion recently on some students using only digital devices for telling the time made me wonder about resources for telling the time using a clock face. Looking at the KS2 programme of study, I see references to clocks, including tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times. Have a look at this demonstration, Time Angle and Fractions from Visnos Visual Numbers. I was happily distracted by many of the other demonstrations!


To log or not to log

Talking to a group of students recently about logs we used a favourite (I have many favourites!) Underground Maths resource – To log or not to log?

Underground Mathematics

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:


Mathematical Miscellany #72

Continuing with my reorganisation of pages and resources I have updated the page on resources for Level 2 Further Maths (AQA).

Dr Austin Maths

A new page has been added for IGCSE information and resources including Gareth Westwater’s very useful PowePoint resources.

Westies Workshop

From Gareth Westwater, see IGCSE questions by topic, on westiesworkshop.com, 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.


Another page with a new section is the A Level (16+) resources page from the A level series where I have added a section on sources of exam practice papers.


MEI – Ritangle

A reminder that MEI’s Ritangle competition begins on Monday. Do have a look at the questions from previous years (scroll down), full solutions are provided, these are a great source of questions for students studying A level Mathematics, the International Baccalaureate, Scottish Highers, or any qualifications with equivalent content.