A little problem for the holidays….

My son sent me the following problem which I have since discovered has been doing the rounds on the Internet.
I cannot find the original source – thank you whoever originally posed the problem!

This problem can be solved by pre-school children in five to ten minutes, by programmers in an hour and by people in higher education ….well, check it yourself!

I’m pleased to say despite my various Maths degrees I solved the problem quickly!
I obviously have the mind of a pre-schooler!
You can find a hint then check the answer here.

I present the problem as posed everywhere – though it looks like a misuse of the = sign!

The problem reminded me of some fun sequences to try with your students!
Get them thinking outside that box!

Try these ….

2, 3, 3, 5, 10, 13, 39, 43, 172, 177, …

2, 12, 1112, 3112, 132112, 1113122112, ….

For the answers and several more puzzles see Puzzle Sequences from the Online Encyclopedia of Integer Sequences.
See also this post on Sequences for further resources.

More puzzles resources.


Whether you want to work out some simple calculations or compute the eigenvalues and eigenvectors of a matrix there is probably a free online calculator to do the job for you!

WolframAlpha is so powerful (and not only for Mathematics) it deserves pages of its own. There are several links available and also slideshows to help you learn to use WolframAlpha. (WolframAlpha is still entirely free to use and so useful for teachers and students, though a new Pro option is now also available).

Using WolframAlpha widgets makes it possible to set up widgets for repeated use, older students for example need to solve absolute value equations.

When I find a new online calculator I like I include it in another blog: Mathematics Calculators and Tools so that the collection is together.

To highlight a few of the calculators I have used recently. For students studying quadratic equations this calculator which shows the use of the quadratic formula from Math Warehouse is very useful as it shows full working on how to use the formula.

There are numerous other calculators available from Math Warehouse.

The graphing calculator I return to again and again is the Desmos graphing calculator, for example I was recently studying the modulus function with my sixth form students, looking at modulus equations and inequalities a picture speaks a thousand words! (Just type y=abs…)

When marking the Further Mathematicians’ Decision Mathematics paper I found Stefan Waner’s Simplex Tool very useful,

The tableaus are shown in full.


Sumdog – practise with those directed numbers….

….and other arithmetic skills.

Sumdog provides free numeracy games at 10 different levels. For a great way to practice adding and subtracting with negative numbers, play these games at level 10.  There is a complete list of topics at each level here. Students can choose from several games.

I like the way that the various skill levels can be restricted; the site is aimed at students aged 6 to 14 (having said that some of my Year 11 (age 15-16) students looked like they were rather enjoying themselves recently) so I want my secondary age students to practise the skills at the upper end of the age range and have currently restricted them all to levels 8, 9 and 10. It is possible to set up competitions which I have done very successfully with Year 10 as one of our many Enrichment Week activities. See the Teachers’ page, also the help section for teachers.

Sumdog are creating a library of videos to help teachers get the most out of Sumdog.

I have linked to information for students on the companion Mathematics blog for students.

You can choose to play as a guest or sign up (free) so you can save your scores and see how you improve over time. The games are all completely free to use as are several other features for teachers.

You can follow the Sumdog blog for all the latest features.

Revision and Mobile Phones…

The exam season approaches and I have been talking to many students about revision. We were chatting about the fact that they always have their phones with them…so an experiment.  Would it help to look at some basic facts on your phone on the bus / train on the way to school or wherever? I know this displays well on a Blackberry,a Windows phone on Android and an iPhone.

Common integrals (that are not in the formula book for my students).

(Integration – for a pdf file.)

Top 100 Tools 2012 – voting open

Update 2013 – we now have the Top 100 Tools 2013,

Jane Hart of the Centre for Learning and Performance Technologies has opened voting for the Top 100 Tools for Learning 2012. This list is based on contributions from learning professionals around the world. My own choices are as follows:

Evernote – an outstanding note-taking tool and something I use every day. I have a notebook for each of my classes to which I upload any resources I want for that class. It is also a good way to share for example a list of websites with students – using a shared notebook. (Blog post on Evernote).

Twitter – great for professional development – I have contacts in education all over the globe and have been led to many useful resources by my virtual colleagues! (Blog post on Twitter).

YouTube – there are numerous videos useful for Mathematics teachers – perhaps to show in class or for students to use at home, for example the Math Centre videos or those from Khan Academy. (Videos page with many sources of Maths Videos).

Google Docs – I have used Google docs to collaborate on documents such as presentations with other teachers. Using Google Forms provides an excellent  way to get feedback from a group of people, their responses are all returned to a single spreadsheet. A comprehensive manual can be downloaded here.
For an examples of  forms see this one used to collect student self-assessments of their PLTS skills development in Mathematics and this to collect student feedback on their Mathematics experience at the end of their first year with us.

WordPress – obviously – you are reading a WordPress blog right now! I have several other blogs, GamesStarters and Mathematics Tools for example. I find a blog such as this an excellent way to share information with colleagues and students. For students I have recently created a new blog and something I am very pleased with is a blog I use to give the details of homework for each of my classes. I created ‘What was that homework?’ as a result of a survey of students across several schools where many students said that they would like homework details online. No student can ever say to me that they didn’t know what their homework was! (The very first post on this WordPress blog – which includes some useful WordPress links).

Moodle – I have a Moodle course for each year group in school; each course has links to any websites that we use in class so students can investigate further themselves if they wish. VLEs are sometimes criticised for being no more than ‘filing cabinets’; I would argue what useful filing cabinets they are – containing resources chosen by teachers for their students all in one organised place. For example prior to a recent GCSE Mathematics module the relevant Moodle course received hundreds of hits as everything students needed was available, not only syllabus information and papers but worked examples that we had uploaded. It is also of course possible to use forums and quizzes on a VLE. (Digital Tools blog page on Moodle).

Slideshare – it is very easy to upload presentations to this (free) presentation sharing site. Any PowerPoints for students could be uploaded for example. There are several examples on this site, such as the WolframAlpha slideshows.

Diigo – I have saved many hundreds of bookmarks using this social bookmarking / annotation tool; I can even find them again! There are numerous examples of Diigo lists on this site – see this list on Statistics and Probability for example; note that the green link takes you direct to the site. (Digital Tools blog page on bookmarking).

Wikispaces– I have used wikis with Mathematics classes – for doing exercises together for a change, as journals for example where each student has a page; also for any collaborative projects as it is easy for a student or students to be responsible for a page of a project. (Digital Tools blog page on Wikis).

Screenr – when trying to type Mathematical text is too slow, a quick scribble on some kind of screencasting tool can be the answer (graphics tablet essential). (Blog post on Online Whiteboards – consistently one of the most popular posts here).

The 2011 Top Tools: