More free books and Iterative Techniques again

World Book Day last Thursday inspired me to update the page on free books page; working further on that page has inspired me to create a further page.

Nelson Thornes GCSE Texts

Nelson Thornes GCSE Texts

STEM LearningSTEM learning has an extensive library of free resources for Mathematics (and also for Computing, Design and Technology and Science) including textbooks; you can search the collection in various ways, a search for textbooks for ages 11-18 returns these results. You will find a real treasure trove in this collection hence this new page. which can be found on the Reading Menu. Do have a look at all the goodies available, although some of the books are old many have chapters on topics such as Venn Diagrams; GCSE books developed for Intermediate students could be rather useful as the new Foundation course looks more like the old Intermediate level!

PorterSome resources will take older readers on a trip down memory lane – anyone for Porter’s Further Elementary Analysis!

Several books are available – answers included. Perhaps these will be handy when we get the new A Level specifications!

Checking some of the Nuffield National Curriculum books proved a distraction as the following activity in one of the texts (Number and Algebra) reminded me that I wanted to revisit iteration for a revision session with my Year 10 GCSE students.

Nuffied text




. I thought these questions would provide a way to revise several topics – simultaneous equations, solving equations graphically and iteration. Graphical solution to equations is something that seems to puzzle students and it does not come naturally to them that you can solve an equation by rearrangement.

I decided we will look at question IV, first we can use algebra to form a cubic equation in x, then solve the cubic by trial and improvement – a familiar method that seems more intuitive to students than rearrangement.

Then we can rearrange the equation – plot the graphs and show that we still get the same result. The next step is to impress them with using the rearrangement in the form of an iterative techniques question – it’s a lot quicker than trial and improvement. This is a particularly able set of students so I have gone well beyond what we need here; I checked the rearrangement on Autograph hence some of the additional slides in the file I have included below in case it is useful to anyone.

I thought I would include this AQA practice question for the new GCSE as when we looked at iteration earlier this year the subscripts really bothered students; my colleague said exactly the same of his set.

AQA question

Desmos illustration In case it’s useful this pdf file shows the examples fully worked with the graphs to illustrate: Solution of equations graphical & iteration 

Desmos illustration

pdf file








Returning to a Nuffield text I mentioned earlier, I found this question in one of the exercises (an isolated question, I couldn’t see any more). Now what’s the probability of that?!
Nuffield NC

Mathematics Books

Maths texts

Image – Klara Kim on flickr

I have enjoyed books for as long as I can remember and have been enjoying myself today organizing all the books I have in my Kindle library into collections on my new Kindle Paperwhite. I have several Maths books on my Kindle, many of which were free. 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. It is possible to search Kindle books by price, so a search on Mathematics books by price from lowest to highest will give all the free entries (worth keeping an eye on as these can change) first. It is worth noting that currently 50 mathematical ideas you really need to know is available on Kindle for £1.54 UK $2.52 US.

Looking at the books currently on offer for free, these include some books from CK-12 (for more information on these see below), Mind Hurdles: Mystery Number – a set of ‘number mysteries’, one or more of which would make a good lesson starter and 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.

Having downloaded a CK-12 book I discovered another whole collection. 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 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. Looking at the Algebra books, this looks useful: Algebra Explorations for Pre-K through Grade 7 (so age 3 to 12)

There are many other free Maths books online as you will discover with a little searching, see these for example. A couple of free books I have mentioned before but I think are worth another mention:

GCSE text1

GCSE text from Clear Creative Learning

GCSE text2

GCSE text from Clear Creative Learning

The first is a complete GCSE text from Clear Creative Learning, don’t be put off by the 2007 date – this is still useful, note the link to download a free pdf. The text includes numerous set of questions for each topic by grade with solutions for all the examples.

The other is ‘Street Fighting Mathematics‘ by Sanjoy Mahajan, with the excellent sub-title ‘The Art of Educated Guessing and Opportunistic Problem Solving’ (note the link on the left to the free Creative Commons edition under Essential Info).

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).

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!)

I wrote recently on the treasure trove that is the National STEM Centre; the resources here include books, the search function described in that post includes the facility to search by type and one of the options is textbook. This search for example is the result of searching for texts on equations.

Storybird Sequences

Storybird – click the image to see the story on Storybird

You could even write your own! If publishing your own Kindle eBook feels a little too much right now – you could try something simpler!


STEM Learning

STEM LearningSTEM Learning hosts hundreds of Mathematics resources, (resister free here). Try exploring the extensive collection of Mathematics resources.

I’ll mention just a few here; these are resources I found of particular interest for my own teaching.

By Susan Wall, this collection of resources on Active A-Level Mathematics is excellent, I have used several of Susan’s activities very successfully in the classroom; I do like Thinking Questionsopen–ended questions which should certainly make your students do just that – really think. (Added to Rich Questions).

From MEI the MEI GCSE Mathematics Extension Materials are aimed at students who are working towards GCSE Mathematics and would benefit from exposure to mathematics beyond the GCSE specifications. There are many excellent ideas here which encourage students to explore concepts. In fact some of these activities would be a useful introduction for older students.

GAIM Investigation

GAIM Investigation 1

The Graded Assessment in Mathematics (GAIM) resources includes a wonderful collection of 80 activities for investigations and problem solving with  accompanying teachers notes.

The collection from the Royal Academy of Engineering includes high quality Mathematics for Engineering Exemplars, for example a look at Formula One Race Strategy. It strikes me that these materials would be useful for many students as they develop literacy as well as mathematics. Notes and solutions are provided.

cre8ate digital design

cre8ate digital design – working with photos

The cre8ate maths project features resources applying maths to key areas of the economy focussing on functional mathematics skills. Digital Design for example includes a ‘Working with Photos’ activity to help students understand enlargement.

The complete, superb collection of Improving Learning in Mathematics materials is hosted here. (See this page for associated resources for this collection).

The Durham Maths Mysteries are activities based on cards with statements about the area of mathematics being covered. Students then have to use reasoning to decide how to tackle the the task.

Now here’s a collection I am delighted to find, we used to use the New National Curriculum Mathematics from Nelson Thornes, how useful to have the set available electronically, there are some great problems amongst these pages! Now I can project them on the IWB. The set includes the A/A* book aimed at able students. I was always particularly fond of the problem solving exercise in Book 6! (See Number, Problem Solving, Exercise 1:1); Book 6 also has some rather good exercises on Equations in the Algebra section).

So much to explore, so many lovely collections! A couple more that caught my eye – Nuffield’s Making Sense of Data with its emphasis on analysis and interpretation and Decision Mathematics from the OR Society.

This post took a seriously long time to write as I came upon so many resources I know will be useful in my teaching! I have added a copy of the post to the resources section so it can easily be found again in future.