From **Immersive Math** a Linear Algebra book with fully interactive figures. Have a look at the **Table of Contents **and you will see this is a very comprehensive coverage of Linear Algebra.

From **Immersive Math** a Linear Algebra book with fully interactive figures. Have a look at the **Table of Contents **and you will see this is a very comprehensive coverage of Linear Algebra.

STEP (Sixth Term Examination Paper) Mathematics is a well-established mathematics examination designed to test candidates on questions that are similar in style to undergraduate mathematics. For students studying for STEP papers try this **excellent portal **from stepmaths.co.uk which has (all free) access to STEP questions and solutions. Create an account, login and you have access to a complete library of resources.

The resources are very clearly presented. For each question you have access to a pdf with the question, Examiners’ Report and both an Official and thanks to Peter Mitchell a fully worked handwritten solution.

Note that you can also download a copy of **Stephen Siklos’ Advanced Problems in Mathematics and Core Mathematics**. *Advanced Problems in Mathematics* is excellent preparation for ANY undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 43 problems. Each problem has been given a title and a rough indication of the mathematical content which means you can pick out questions by topic.

See also, from Cambridge University, their **STEP Support Programme**.

And from Nrich, **Prepare for University**.

A project – note the new tab Demos – a place for some favourite demonstrations / simulations. Currently just two pages but note the numerous **PhET simulations** for a variety of subjects to explore.

The most recent addition is the PhET Projectiles Simulation.

Use this excellent **PhET simulation to explore the path of a projectile**. Try changing the angle to investigate the relationship between the angle of projection and the horizontal distance (range) travelled.

Have a look at these problems on Underground Maths to extend your thinking:

**Where did it land? **and** Maximum Angle Throw**. Note the questions given on these problems and things you might have noticed.

For amusement try projectiles of different types!

You will find some very useful **notes on Mechanics** on **Mr Barton’s website**.

There are **numerous PhET simulations** covering Physics, Biology, Chemistry, Earth Science and **Mathematics**. Note the growing collection of **HTML5 versions **which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

You can download an app for **iOS** also for **Android**.

**PhET Balancing Act** working nicely on my phone!

**UK Maths Challenges
**You can practice for the

You could generate a random quiz, using Mathster’s **UKMT Mathematics Challenge Online Quiz**. Choose Junior, Intermediate or Senior and one of three difficulty levels; you can also choose the number of questions, a time limit and the order the questions are presented in – random or in order of difficulty.

Note **Geoff Smith’s advice for young mathematicans** and as he says you will find thousands of questions are available at all levels on the **Art of Problem Solving** site.

Nrich have a **series of short problems** based on the UK Junior and Intermediate Challenges.

**Nrich** publish new problems every month. Why not try and get a solution published on their website? There is a **menu specifically for students. **You can **sign up** for an Nrich student newsletter if you want to be notified of new developments on the site.

If you have not tried Nrich problems before you may find their **recommended starter problems** good to try. You can **search for problems by topic** if you wish.

If you have not tried Nrich problems before you may find **their recommended starter problems** good to try. You can **search for problems by topic** if you wish

Signing up to** Brilliant** (including an easy option for sign in for Facebook users) will allow you to join an international community and try numerous.questions at **various levels**.

Have a look at the teddy bear – can you identify all the equations from **this list**?

This problem comes from the excellent **Underground Maths** site.

You can view the Teddy Bear on Desmos by selecting the image above.

Note that on Desmos you can choose to display or hide a graph.

As with all problems on the site you can see the question and a **very full solution** with all reasoning explained.

For further notes on the equation of a circle, check these **Helm Project notes and exercises on the circle**.

It struck me that it might be useful to think about my top recommendations for students. Using some categories again gives me the excuse to mention more than 10! All these resources are free to use.

For an online graph plotter try the excellent **Desmos graphing calculator**, it is very easy to use and allows you to save your graphs if you sign up. (Facebook is one option you can use to sign in to Desmos). You can see more examples of Desmos graphs **here **and there is a **helpful user manua**l you can download from Desmos. There are many creative users of Desmos, have a look at the selection of **art work**! Make sure you get **Desmos on your phone and/or tablet **too.

For checking your work **WolframAlpha** is so useful, it is free to use for checking answers for as many queries as you want (step by Step solutions require a subscription). **The set of slideshows here** show you the syntax for a variety of queries.

For more excellent calculators and tools for checking your work, try **this collection**.

There are many sites with useful notes and examples online for all ages, you will find several on the **Notes page, **this Evernote shared notebook,** Mathematics notes** includes many links, several universities have very helpful resources which they have made available to all students. You do not have to be an Evernote user (**though I’d recommend it highly**), just select ‘View’ to access the notebook.

For reference materials see the various resources on the **Reference page** which includes links to online dictionaries.

If you like to watch videos to help you learn then you may find some useful resources on the **Videos page. **Though of course you need to actually ** do** lots of questions!

* The best way to learn Mathematics is of course to do Mathematics* and there are some excellent sources of problems for students of all ages to try.

**Underground Mathematics** has an extensive collection of questions to get you really thinking about your Mathematics. Suggestions and full solutions are provided but as always make sure you really do everything you can first with the question.

There are several sites with questions and examples for students of all ages. See more posts with many more resources in the **Questions Category**.

For revision you can use questions and examples already mentioned, **Underground Mathematics** includes examination questions for students age 16+. Note the above question comes from an Oxford University Mathematics aptitude test; it is one of the many **Review Questions**.

The **Revision pages** include questions from UK 15-18 Mathematics Examinations. These all include very challenging questions as well as more routine practice.

For 17-18 Year olds, **MadAsMaths** includes some very challenging questions for those aiming at the top grades. My student who recommended the site went on to achieve an A* grade!

If your teacher is not using **Diagnostic Questions** shown here, you can **sign yourself up as a student**. Note the many **Collections** of Questions as well as questions by topic. (You need to be signed in for the link to work).

On the **Challenges page** you can see resources such as the UK Maths Challenges, Nrich, Underground Maths and Brilliant. Signing up to** Brilliant** (including an easy option for sign in for Facebook users) will allow you to join an international community and get free weekly, personalised problems. Questions at **various levels** are available. Follow **Brilliant on Facebook**.

We all like to play Games, many games are available to help you practise Mathematics, you can see a whole collection on **Mathematics Games**.

Try Bart Bonte’s logic game ‘**Think Outside the Flock**’. The game is on **Math Playground **which I know has many games students enjoy. For more logic games and puzzles try the **Logic page.**

Are you wandering what mathematicians do or are thinking about **a career in Mathematics**? Aimed at anyone from age 11 to adult the **Maths Careers **site will answer your questions.

The Maths Careers site offers you many articles to read, for further reading materials try **Plus Magazine** from The Millennium Mathematics Project – University of Cambridge or perhaps **Math in the News** from the Mathematical Association of America or **Mathematical Moments **from the American Mathematical Society.

**The 11 Commandments of Mathematics** is perhaps a good way to end this post – and note 10 on Learning Mathematics – think about * how* you learn not just what you learn. Have a look at these

For valuable resources to support the techniques described here see the excellent

Obviously all these sites are those that I think are particularly good, I do know that many of my students use a lot of the sites I have mentioned here. You will find more recommendations on the **Useful links pages**. Students do let me know your own particular favourites.

Remember these ~~ten~~ eleven commandments for mathematicians!

Direct Download of PowerPointfile: **11-commandments-revised**

Alternatively – a pdf file, the links can work faster from pdfs.

**11-commandments-revised **

Appropriate for New Year Resolution Time – a revised and checked 11 Commandments of Mathematics!

Also available as a poster: **11-commandments-mathematics**

The Top Tools for Learning 2016, inlcuding top tools for Education. This is what the educators think. Students what do you think? What are your favourite tools for learning?

Mathematics, Learning and Technology

Jane Hart is the Founder of the **Centre for Learning & Performance Technologies **and **2016 marks the 10 ^{th} year of her annual Top 100 Tools for Learning list**. Jane has put together all the

The 2016 slideset is shown here.

Note from **Jane’s overview** she has done a finer analysis for 2016 including the **Top 100 Tools For Education** (for use in primary and secondary (K12) schools, colleges, universities and adult education.)

Back in April, I wroye about **my own choices for 2016 **and I am always interested to see where my own choices are in Jane’s list.

CY 2016 votes |
Education |
Personal Learning & Productivity |
Place in Top 200 2016 |
Place in Top 100 Tools for Education 2016 |

Evernote | x | x | 17 | 27 |

WordPress | x | x | 9 |

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Students try an alternative to chocolate – mathematical Advent calendars up to Advanced Level, and note the Primary calendars from Nrich if you have little siblings!

Mathematics, Learning and Technology

It’s that time of year again…!

Nrich Advent Calendars

December means Advent Calendars and Nrich have published two Advent Calendars, one for **Primary** and one for **Secondary** each containing twenty-four problem-solving activities, one for each day in the run-up to Christmas. The primary Calendar tasks focus on encouraging mathematical habits of mind and the Secondary tasks have been chosen to encourage mathematical creativity.

You can in fact find a **whole collection of advent calendars on Nrich** and clearly the year doesn’t matter! Note the different themes available – a **Sudoku** for each day perhaps? Or a **tangram**? Maybe you want to **play a game? **

Advent Calendar by Alex Pett

Alex Pett created his advent calendar complete with history and problems for each day. Alex has provided a **pdf version **or use as a**Google document**. For an Activeinspire resource **this version **also has sound.

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For some excellent GCSE (UK age 15-16) revision resources explore this collection. Thank you so much to the teachers who create these resources and make them freely available.

Jonathan Hall has a bank of **GCSE questions. **on his site**; **note that you can show solutions for these questions. Also on this site – you can **create a practice paper** with your chosen topics and the number of questions you want. If you would like a random collection you could also try his **Revision Grid**.

From Steve Blades, have a look at his very helpful **9-1 GCSE Help Book**. Note that you can download the **book (52 pages) free**.

For more resources see Steve Blades’ site **www.m4ths.com**;on the **GCSE page **Steve has a section (near the end of the page) of eBooks, and one of those is on** GCSE Higher wordy questions**. See also Steve’s **Think like a problem solver and mathematician book**.

**Mr Carter Maths **– for lots of practice questions. Select Differentiated Topics to see the selection available. If you want to practise this new topic – Iteration; **this is the direct link.**

On Tanner Maths you will find **Flashcards **for the new specification – choose A4 or A5.

**Many of these resources** are also very useful. Check with your teacher the detailed content for your specification.