I have enjoyed books for as long as I can remember and have several Maths books on my Kindle, some of which were free or very low cost. Now you don’t have to own a Kindle to read Kindle books as the Kindle app is free to download for any device you may own: PC, phone or tablet.
Looking at the free offerings, these include Henry Ernest Dudeney’s – Amusements in Mathematics a puzzle collection (with solutions). The first set of puzzles will offer a trip down memory lane for those who remember money – pre-decimal! There are several categories of puzzles available.
Note GMAT Foundations of Math – 900+ Practice problems and explanations of fundamental math concepts.
Further free books include some Open University eBooks including some titles on Mathematics, see for example Using visualisation in maths teaching, Starting with maths: Patterns and formulas, and Working on your own Mathematics.
Published in 2023, Mathematics Curriculum Reforms Around the World, the 24th ICMI study is an Open Access publication which can be downloaded for free.
Colin Foster’s KS3 Instant Maths Ideas (3 books) are freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is a Reader in Mathematics Education in the Mathematics Education Centre at Loughborough University.
From the Shell Centre for Mathematical Education, you will find some free pdf downloads, such as The Language of Functions and Graphs and Extended Tasks for GCSE Mathematics.
From Hodder see these brilliant worked examples for the new Advanced Level Specification, see Advanced Level – Worked Examples for details.
Jonny Griffiths’ investigative activities for the pure A Level Mathematics classroom are well known (details are included in the A Level resources pages, see RISPS. He has now published Further Risps, forty rich tasks for the pure Further Mathematics classroom. Jonny has generously made the pdf version available free from www.further-risps.co.uk.
The pdf not only provides the forty problems but also full teachers’ notes for each. The notes for each task begin with the topic or topics covered, identify the type of task, for example, introductory and state any preliminary knowledge required. This is a valuable resource for teaching Further Mathematics.
ATM is providing some free resources. More from Jonny Griffiths – a free resource for KS5 is a complete publication, The Proving Ground – an introduction to mathematical proof. This e-book offers forty easy to understand problems classified by one of three levels, level 3 has problems that have not been resolved. The book is very clearly structured, a notes page is provided for each problem, best accessed after trying the problem first. There are also Learning Pages that introduce different proof techniques. The home page is the contents page with links to all parts of the book.
For GCSE try:
Complete GCSE Maths Revision text from CLCnet. Don’t be put off by the 2007 date – this is still useful. The text includes numerous sets of questions for each topic by (legacy!) grade with solutions for all the examples.
‘Street Fighting Mathematics‘ by Sanjoy Mahajan, with the excellent sub-title ‘The Art of Educated Guessing and Opportunistic Problem Solving’.
Street Fighting Mathematics is available as a course from MITOPENCOURSEWARE. The course includes Problem sets and solutions.
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Nix the Tricks by Tina Cardone and many other contributors discusses how the use of ‘tricks’ can lead to misconceptions.
The complete Cockroft Report, Mathematics Counts is available online. You can use the menu on the left to navigate to the various chapters, alternatively, download a pdf of the complete report from STEM Learning.
Any discussion on free Maths texts should include of course all the free texts available on the wonderful CIMT site (Centre for Innovation in Mathematics Teaching).
Problem Solving is an open access (free) book which looks at research on Mathematical Problem Solving.
Project Gutenberg includes numerous Mathematics books, including classics such as Flatland. (Mark Twain’s comment on “Classic’ – a book which people praise and don’t read.” always amuses me!)
CK-12 provides an extensive range of open-source content and technology tools for students and teachers. See for example the algebra resources here; click on FlexBooks Textbooks to see the available books. Books such as CK-12 Algebra – second edition can be downloaded free in various formats, PDF, mobi and ePub. To download books you will need to sign in (free); you can create an account or sign in with Google, Facebook or Twitter.
You could even write your own by publishing your own Kindle eBook.