Mathematical Miscellany #53

Three updates, a puzzle, and the mind-blowing Mathematics of sunflowers!

My post, Reading has proved very popular.

The student version has been updated with a STEM book list from Imperial College, the list has many recommendations in several categories including Mathematics. Imperial College says that the list is aimed at A Level students but is suitable for anyone looking to develop their STEM knowledge and have a great read.

The CGP Headstart to A level Maths, Biology, Chemistry and Physics are all still free as is a GMAT Foundations of Math Practice book with 900+ problems.


The information on the Autograph web page has been updated and now includes an example file for reflection in y=mx+c and recordings of creating a page to illustrate reflection in a vertical line and creating a reflection in y=mx+c. These are early experiments with recordings, I’ll keep practising!


Published July 2021, we have an updated version of the document which provides details of the Statutory guidance for governing bodies, school leaders and school staff. I have checked and updated my post Linking Curriculum Learning to Careers. We are fortunate in Mathematics to have so many good resources to help us here.


It is the holidays so time for a topical puzzle from OCR, I really like the #OCRmathsPuzzles, look out for them.

You can also see a post on this puzzle from Don Steward, and try three levels of the puzzle on Transum Mathematics.

Transum Mathematics

It’s summertime so I’ll finish with the mind-blowing Mathematics of sunflowers; read Citizen scientists count sunflower spirals from +plus magazine and check the Scientific American video.

Photo by Skitterphoto on Pexels.com

Reading

A job for the summer break is always to think about the organisation of posts and pages of this blog.

The first project is a check on the reading series of pages; this series is devoted to various reading materials – many of which are free!

Looking at the Books (free) page, check that search on Mathematics books by price from lowest to highest on Amazon. If you search on all titles this gives all the free entries which seem to include lots of toddler books and samples. The most relevant results can be worth checking.

Currently, I see CGP’s Head Start to A Level Maths free on Kindle (Physics, Chemistry and Biology are also free), as is this Year 1 A level AQA book.

A post for students with the books listed individually is on Mathematics for students; note the GMAT Practice book with 900+ practice problems.

For puzzle fans perhaps try Henry Ernest Dudeney’s puzzle collection.

Mind Hurdles

Looking at the free offerings, these include 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.

And do make sure you have Colin Foster’s KS3 books in your collection.

Colin Foster - Instant Maths Ideas
Colin Foster – Instant Maths Ideas

Colin Foster’s KS3 Instant Maths Ideas (3 books) are now 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.

Summer Maths

Reading the latest newsletter, I see that Nrich will be publishing a challenge a day throughout the UK summer break, every weekday from 19 July to 31 August, a new game or puzzle will appear on this Primary page and this Secondary page. Once students have tried the day’s challenge they will be able to compare their approach to previously published students’ solutions.

Also from Nrich remember there are many interactive games and puzzles.


Wayne Chadburn – Summer boost calendars

For calendars with a GCSE question a day from 19th July to 5th September have a look at Wayne Chadburn’s Summer boost resources, one for Higher and one for Foundation. He writes these calendars to provide regular, varied practice. In the next academic year he will produce calendars for year 11 students each month from September to April; the calendars for September 2021 are already available. Note the three versions including crossover questions, Foundation, Foundation plus and Higher.


Transum – Newspaper Type Puzzles

On Transum, a whole collection of school holiday Maths activities to do at home is available. To quote from Transum Mathematics:

Here are some suggestions for activities that will keep children thinking mathematically while having fun and learning new skills.

These are really clearly categorised and we have a lovely mixture of learning and puzzles and games to make you think. There is a great deal of choice here. See also the full list of all fun maths activities.


Try these brilliant GeoGebra puzzles from Daniel Mentrard, also his 64 geometric puzzles.

Puzzles – Daniel Mentrard

Perhaps try Tangram on Mathigon.
How many of the different shapes can you make?

rich also have a Tangram activity for students age 7 – 11 or for 5-14 years olds try Tangram Pictures.

Nrich Tangram Browser


End of term…

For those in school for another week, some end of term activities…

There are numerous suggestions on this page, End of term activities and have a look at these brilliant GeoGebra puzzles from Daniel Mentrard.

Puzzles – Daniel Mentrard

From Daniel Mentrard on GeoGebra, Puzzles.

And 64 geometric puzzles.

Autograph – Web Version

From The Complete Mathematics Conference, I really enjoyed Maths Conference #26, July 2021. The highlight for me (apart from very much enjoying my own session presenting with AQA on the New GCSE Maths tests from Exampro which been developed for the two-year AQA key stage 4 scheme of work) had to be the first session of the day I attended – a first look at the web version of Autograph.

I have also added this information to a new page in the Autograph section of my Use of Technology series.

A web version for Autograph is now available, a game-changer for this sophisticated object-based dynamic geometry system. It has a great deal of functionality already and will be developed even further. I am so pleased to have the option now of sharing pages easily with students. The interface is intuitive. Select the various options to see all the functionality available. Add some points or an equation and experiment! I really like all the style options in Autograph making it possible to create attractive resources. And look at all those colours! That certainly appeals to me with my interest in using colour in Mathematics to add clarity to explanations. Note the colours of the points I have used in my reflection example below. This is just my own first look, I will be learning much more.

Autograph – web version

I find Autograph very intuitive for illustrating transformations. It is very simple to enter a shape and transform it. The shape can be user-defined so it is very easy to set up illustrations. It is also very simple to add labels. With Autograph when you select objects you get a menu of appropriate choices; selecting an object and equation offers the option to reflect. I thought I would create a page to show reflection in x=a:

Autograph – web version

Select the image or this link to see the above page. Select the workspace if nothing appears and try changing the variable a by tapping along the line.

It is possible to embed a page as well as share it…

A web version for Autograph is available, it has a great deal of functionality and will be developed even further. The interface is intuitive. Select the various options to see all the functionality available. Add some points or an equation and experiment! I really like all the style options in Autograph making it possible to create attractive resources. And look at all those colours! That certainly appeals to me with my interest in using colour in Mathematics to add clarity to explanations. Note the colours of the points I have used in my reflection example below.

Autograph – web version

I thought I would create a page to show reflection in x=a:

Autograph – web version

Select the image or this link to see the above page.

It is possible to embed a page as well as share it… (select to see the embed and change variable a using the menu