Happy Numbers and more…

Happy Numbers ResourcesContinuing my theme from last week I have added a new page to the Investigations series – one of my all time favourites – Happy Numbers.

I have also added further resources to the Investigations – Links and Resources page. From the National STEM Centre which is an incredible source of resources for STEM subjects we have

Investigations L Mottershead - National STEM CentreLorraine Mottershead’s book: Investigations a complete book by including solutions to the puzzles and investigations.

STEM Centre Investigations Kirby & PatillaAlso on the NMoational STEM Centre from David Kirby and Peter Patilla we have Maths Investigations – Pupils’ Workshop together with a comprehensive teachers’ guide.

Investigations and more …

Some updates this week and tidying up the pages.

Under Resources I have added a new series of pages – Investigations. This came about because I have been looking at a favourite investigation on Palindromes  this week with Year 7 (UK age 11-12) who were thoroughly enjoying themselves and determined to find any two digit palindrome requiring rather more steps with the reverse and add process than most two digit palindromes. I have favourite investigations I use each year, so time to document those, an ongoing project, I will add to the series in the coming weeks.

The UK Maths Challenges have been included on the Problems & Activities page for some time, but note the recent addition of Extended solutions for each of the challenges. (Thank you to my wonderful colleague Anja who pointed this out to me a couple of days ago).

jmcFrom UKMT, the UK Maths Challenges we have a wonderful library of problems; note the these past papers where you will find questions and full solutions. Check also the Individual Challenges pages where you will find details of the challenge and see sample materials. Checking the Junior Challenge for example you will see the following samples. Note the addition for 2015 of extended solutions. As well as a full solution which does not use the multiple choice answers further ideas are given for investigation.

UKMT Extended Solutions

Under Problems & Activities we also have Here’s the Diagram …. the idea here is that you show students a diagram and work out what the question might be. It can also work well to show students an algebraic expression for example and ask them what the question might be which I have added to that post. This forces them to use correct vocabulary – expand, factorise and so on as I am convinced there is a whole class of words which students simply translate as ‘do something with this’!
(See Exam Terminology included in this Reference post for students.)

What's the question?

What’s the question?

My Year 7 students has a test recently; in one student’s review she wrote that she got something right in her test because she had got it wrong in a mini-test.I remain convinced that this is a very valuable activity. Details on mini tests can be found in the Revision Activities series of pages; I have also added this information to Mathematics Starters for completeness.

Updating pages I find myself pondering the distinction between Rich Tasks / Rich Questions / Problems …; it seems that the definitions are blurred and there is a great deal of overlap and I have in fact mentioned some resources on more than one page.

I have been giving Problem Solving a great deal of thought recently – more on that in the coming weeks … and I am very much looking forward to seeing those coming to Jo Morgan’s Christmaths 2015


I thought I would create a page for apps I come across which I find useful; these are mostly available for  Android as well as iOS. Just a small number currently, but these are all free and work very well.

Apps - Mathematics

Apps – Mathematics

Writing Mathematics Online

I have written various posts on the available tools online for writing Mathematics and this is a topic which remains consistently popular. Time for yet another revisit and update as new possibilities are now available – all resources / links here have been checked. I have removed resources where blogs / twitter have not been updated for some considerable time as I think this is a cause for concern regarding the longevity of the resource.

Something I use a lot. I should explain my requirements – I want tools to communicate Mathematics online, for example I may wish to provide some model solutions or answer students’ questions. Writing mathematics can be a pain (and yes I know about LaTeX). Note that there are various possibilities – sometimes just a static picture is required, sometimes you may want to display how to solve a problem in stages, or perhaps you require a collaborative space. You will also need to consider if you want the examples to be permanent or whether you just want a collaborative space for discussion. A graphics tablet is essential.

My favourite method for illustrating Mathematics online (and in fact the one I use most often) when I just need a series of static displays is to turn an interactive whiteboard flipchart (or a PowerPoint) into a pdf file; the pdf file can then be sent to students or uploaded to whatever virtual learning environment or online storage your school uses. If you do not have access to interactive whiteboard software there are alternatives, one could use Windows Paint for example; there are also various free online tools available; see some of the resources below.

flipchart to pdf example

flipchart to pdf example

For sharing resources, it is possible to upload a PowerPoint or pdf file to Slideshare. There are many examples on this blog of my SlideShare slideshows – see this for example

I should mention that I find Slideshare excellent – I use the free version which offers me everything I need – it works every time – I use it a lot!
I created the PowerPoint for the slideshow above by writing on the interactive whiteboard software using my graphics tablet and taking a picture of each page using the Windows snipping tool (it’s in Accessories) – this takes seconds – the snipping tool is something I use every day! (Alternatively I could have saved the interactive whiteboard flipchart as a pdf).

There are as always several options:



If you wish to record a screencast of the moving pen / step by step solution variety and save your work, Screencast-o-matic is an excellent option. It is very easy to use to capture the screen and your recording can then be uploaded to YouTube if you wish.

Illustrating how to simplify an algebraic fraction : simplify-algebraic-fraction

Note, my previous favourite in this category was screenr, but this has been retired and trying Screencast-o-matic again I see it offers everything I want in this category. I found it very easy to use indeed and think this latest version is excellent – I was able to write very smoothly whilst recording.

Further resources offering various solutions for writing Mathematics online:



For a collaborative board, try twiddla which seems excellent for collaboration – voice as well if you want. Twiddla offers some very sophisticated features including the ability to use mathematical formulae and upload files and images. Use of the board with all it’s features is free but you cannot save any of your work (possible with a subscription). This would be good for working online with a group of students.



Doodle.ly offers a very easy way to have a quick scribble and then share your thoughts! See quadratic example (and note that I created that just to test Doode.ly four years ago – a good sign that it’s still there!) Select Doodle Now, doodle, then if you want to publish you will need to sign in. You can sign in with Twitter or Facebook. I like the different pen tools available, the full screen option and the ease of publishing. Apps are available for Android and iOS

Glencoe - virtual manipulative

Glencoe – virtual manipulative

Richard Byrne on his wonderful Free Technology for Teachers blog wrote a post, “Seven Free Online Whiteboard Tools for Teachers and Students”. Richard has also written more on Screencasting tools.

If you are looking for more online whiteboard applications then you could try the interactive whiteboard manipulative from Glencoe  (I came across this in a Google search). Note the various backgrounds and manipulatives available.

Bruno Reddy - Geometry Toolbox

Bruno Reddy – Geometry Toolbox

I can’t mention online whiteboard tools without mentioning Bruno Reddy’s lovely Geometry toolbox – this is great for demonstrating constructions and is on the teachers’ section of his excellent site.

If you want to draw some pictures and like the idea of more crayons and pens then you might enjoy these tools!

Have some fun with Crayola!

Have some fun with Crayola!

writing repeater
Finally – your students may find this amusing – the Writing Repeater – write something and play it back – now this is a lovely tool for little ones learning to write but I’m sure we can think of some uses!

Mathematics Resources – New GCSE

Details of GCSE new content are on this page and a summary of the resources only can be found here. Both are part of the series on UK Assessment.

I have been looking further at some of the resources from the examination boards. In this post we will look at some of OCR’s Teaching and Learning Resources.

OCR GCSE 9-1 Teaching Resources

OCR GCSE 9-1 Teaching Resources

OCR GCSE 9-1 Check in tests

OCR GCSE 9-1 Check in tests

From OCR, it strikes me that the Check in tests (select link and scroll down the page) will be very useful in KS3, consider the language of functions for example, the first questions could be used with students as young as Year 7. Full details of the Check in tests can be found in the Teachers’ Guide. Each test is of a similar format in that Questions 1-5 cover procedural calculations (AO1), questions 6-8 require the ability to reason and communicate mathematically (AO2) and questions 9-10 relate to problem solving tasks (AO3). There is also an extension task.

OCR PowerPoint - HCF & LCMStaying with OCR, note the Delivery Guides which include useful links to resources and a series of PowerPoints including questions with answers (always so useful for busy teachers!).

I used the questions from this presentation with Year 7 (age 11-12) when we were studying highest common factors and lowest common multiples.


OCR Guide - Problem Solving

OCR Guide – Problem Solving

OCR’s Skill Guides include this OCR Problem Solving Guide , an excellent discussion on problem solving strategies, including examples and answers.


OCR Twitter


You can follow OCR Maths on Twitter and note the hashtag #OCRMathsPuzzle for a continual supply of problems!

Colleen Young x 2 = #hcsmca: Maths and Health

By @ColleenYoung and @colleen_young

(@colleenyoung‘s post: Colleen Young x2 = #hcsmca: Maths and health)

Also published on HealthWorks Collective

@ColleenYoung: On Twitter a mere underscore differentiates our identities. Add an underscore to my Twitter handle @ColleenYoung and you will meet @colleen_young  an Online Community Strategist; Engagement Specialist; Speaker; Founder ; Board Advisor ; Director of Community , Stanford . Two such similar Twitter handles means I sometimes get some rather interesting tweets about health care which I enjoy reading; I also reroute the misdirected tweets to the other Colleen!

Being pulled into Colleen’s world of health, community and #hcsmca got me thinking about how our worlds intersect and we thought we really ought to join forces!

There’s more reason to unite Mathematics and health than to separate them. As Dean Schlicter wrote “Go down deep enough into anything and you will find Mathematics. ” Let it be so for Mathematics and health. A quick search discovers a set of 5 lessons using biomedical science to study math and extend the maths curriculum at the secondary level (ages 11-16). The lessons “show how maths underpins cutting edge biomedical research. They also introduce students to important ethical issues.” (1)
Since connecting with Colleen (of #hcsmca-fame) I have been keen to find further resources linking Maths and Health related subjects; many of the students at my school go on to study Medicine in Further Education. You will find some excellent resources at the end of this post.

@colleen_young: Understanding numeracy is integral to improving health literacy. As Russell Rothman et al. explain in their Perspective: The Role of Numeracy in Health Care, many people with adequate reading ability have poor numeracy skills.

Many health-related tasks, such as reading food labels, refilling prescriptions, measuring medications, interpreting blood sugars or other clinical data, and understanding health risks, rely on numeracy.These tasks often require patients to deduce which mathematical skills to use and then to use these in multi-step fashion. Patients who had difficulty learning math skills during their primary education may now be too intimidated or simply unable to call upon these skills. For patients with chronic illness that rely on self-management to safely and efficaciously self-administer treatments this is particularly relevant and may place patients who lack adequate numeracy skills at increased risk for poor health outcomes. Numeracy may be a unique explanatory factor for adverse outcomes beyond the explanations provided by overall literacy.” [2]

Since October is health literacy month and by extension health numeracy, we decided to increase the Colleen factor to the power of 2 on #hcsmca this week. Join us on October 21 at 1pm ET and 6pm BT for a discussion on health, numeracy and maths.

Twitter chatColleen Young x2

  • T1: What numeracy skills are increasingly being required of patients and family caregivers?  
  • T2a: What actions/projects/solutions have you seen in health and education to improve the public’s health numeracy level? Examples
    T2b: Can social media help improve health numeracy? How? 
  • T3: Who on Twitter has brought you into their world and led to thinking about your area of interest differently? How?


[1] Motivate, Millennium Mathematics Project, Cambridge University http://motivate.maths.org/content/MathsHealth/

[2] Rothman R, Montori V, Cherrington A, and Pignone M. Perspective: The Role of Numeracy in Health Care. Journal of Health Commun. 2008 Sep; 13(6): 583–595.

Resources & Reading

Motivate - Maths & Our Health, supported by The Wellcome Trust

Motivate – Maths & Our Health, supported by The Wellcome Trust

From Motivate – Maths and our Health, five resource packs based on topical issues in biomedical science which support and extend the maths curriculum at secondary level (11-16 year-olds).

Note the link from Motivate to Plus Magazine’s Do you know what’s good for you? which is a series of articles, podcasts and interviews aimed at older students, teachers and general readers for a project funded by the Wellcome Trust exploring the role of mathematics and statistics in the biomedical sciences.

Nrich - Vaccination Game

Nrich – Vaccination Game

From Nrich we have STEMNrich where you will find a variety of resources, you could investigate epidemics for example or study the Influenza Virus and how it spreads. There are more resources on Disease Dynamics here, looking at substitution into formulae with Year 7 (UK age 11-12) vaccination gameI used the formula given in the Vaccination Game resource, it worked really well to be able to talk to them about the real use of a formula.

Skills for Health Resources

Skills for Health Resources includes some questions testing basic numeracy which would be suitable for younger students. (Look under Using the tools).

From Hull University for nursing students – Maths for Healthcare Professionals

Cardiff University – Maths Support Service – Maths for Health Sciences

Maths in Health Sciences – recommended resources from The University of Brighton

Further Reading

5 a day…and finally – I cannot resist mentioning here the very aptly named 5-a-day from Mr Corbett which I have telling my students for some time now is very good for their Maths health!

These resources do include basic numeracy questions as well as more advanced Mathematics questions.

More on Good Teachers

equationThis time from the younger students.

Last academic Year I asked my then Year 9 (age 13-14) students about good Mathematics Teachers, their thoughtful and often sophisticated replies can be read here.


This year I thought I would begin by asking some of Year 7 (age 11-12) who joined the school in September. In their own words, here’s what they have to say….

A good teacher:

  • Knows what they are talking about
  • Must have a good understanding of everything!!!
  • Explains things clearly
  • They take time to explain
  • Will explain again if necessary
  • Explains things in a variety of ways
  • Changes their style of teaching for people who need help
  • Has to be wise and clever
  • Loves questions
  • Guides you through the steps
  • Makes sure every child understands
  • Always recaps
  • Recaps and revises previous topics
  • Makes it memorable
  • Encourages students to like the subject they teach – they share their enthusiasm
  • Asks us questions to see if we are listening and understanding the topic
  • Gives us even harder work to build our confidence and get better. Challenges us
  • Explains homework and classwork in full detail
  • Is a knowledgeable and helpful guide
  • Always encourages students to persevere and try their best
  • Gives advice
  • Gives you tips
  • Marks work fairly and correctly
  • Recommends helpful skills
  • Gives useful criticism in class
  • Gives useful comments in books
  • Gives targets and writes down areas of improvement
  • Listens to everyone
  • Lets all the students engage
  • Lets you work the way you feel it works
  • Lets you express yourself
  • Gives people a chance
  • Doesn’t talk for the whole lesson
  • Helps everybody who needs help
  • Finds helpful ways to assist each student
  • Helps with struggles
  • Someone who makes you feel that learning / studying is fun

Our disposition, how we come across is so important:

  • Is happy to teach
  • Smiles and cares about us
  • Believes in us
  • Speaks softly
  • Makes the group feel comfortable
  • Is cheerful
  • Is caring
  • Gets excited
  • Is always joyful
  • Is funny
  • Has a passionate and kind voice
  • Is calm
  • Is supportive and enthusiastic
  • Is fair and respectful
  • Is approachable
  • Is patient
  • Is nice but firm
  • Is strict when needed yet kind hearted
  • Is approachable but when you step over the line they are strict
  • Reminds students to listen to each other
  • Reminds students to respect each other
  • Has a laugh with the students
  • Must be organised

That comment about guiding through the steps reminds me of one of my Sixth Form many years ago who said:

“What are the baby steps Mrs Young?”

There is some repetition here, but so many students came up with similar themes it seemed worth repeating their statements. They remind me of the earlier Year 9 comments in that once again, it seems to me that their thoughts fit well with the key components of this extremely worthwhile read: What makes great teaching? Review of the underpinning research. Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major October 2014.

Like Year 9, their comments seem to fall into these categories:

  1. (Pedagogical) content knowledge (Strong evidence of impact on student outcomes)

“The most effective teachers have deep knowledge of the subjects they teach, and when teachers’ knowledge falls below a certain level it is a significant impediment to students’ learning. As well as a strong understanding of the material being taught, teachers must also understand the ways students think about the content, be able to evaluate the thinking behind students’ own methods, and identify students’ common misconceptions.”

  1. Quality of instruction (Strong evidence of impact on student outcomes)

“Includes elements such as effective questioning and use of assessment by teachers. Specific practices, like reviewing previous learning, providing model responses for students, giving adequate time for practice to embed skills securely 3 and progressively introducing new learning (scaffolding) are also elements of high quality instruction.”

  1. Classroom climate (Moderate evidence of impact on student outcomes)

“Covers quality of interactions between teachers and students, and teacher expectations: the need to create a classroom that is constantly demanding more, but still recognising students’ self-worth. It also involves attributing student success to effort rather than ability and valuing resilience to failure (grit).”

  1. Classroom management (Moderate evidence of impact on student outcomes)

“A teacher’s abilities to make efficient use of lesson time, to coordinate classroom resources and space, and to manage students’ behaviour with clear rules that are consistently enforced, are all relevant to maximising the learning that can take place. These environmental factors are necessary for good learning rather than its direct components.”

I’ll head for the other end of the school and ask the Sixth Form next!



Future Learn – Free Courses

For excellent and free professional development sign up to FutureLearnLooking at what is coming up for example, we have from The University of Leicester a course on Real World Calculus: How Maths Drives Formula One and Launches Angry Birds. The course starts on 9th November for three weeks and requires about 2 hours a week. The course is entirely free; certificates of participation are available to buy (£34 plus delivery for this course) if you would like proof of your training.

This particular course is one of the FutureLearn Choices series which offer a chance for students to see what studying a subject at university will be like. It strikes me that these could also provide professional development for teachers too and offer ideas for teaching in the Sixth Form (and lower down the school).

The Preparing for University course (started 28th September so you can join and have a look) includes a video on what lecturers value in their students; I’d say that is what teachers at school value in their students too and all through school, particularly in the Sixth Form we need to be conscious of preparing our students for university.

From The University of Reading, A Beginner’s Guide to Writing in English for University Study strikes me as a useful course for Sixth Form students many of whom take a Level 3 Extended Project qualification.

Looking at courses running and coming up I noticed Logical and Critical Thinking from The University of Aukland which has just started. It is simple to join FutureLearn, sign up with Facebook or create an account free. I joined the course very simply, had a look at the materials and tried a quiz – it seems I understand my obstacles well!

Once you have signed up to a course you can use it at any time, looking at my own profile I realised I had signed up to a course back in 2013 and happily all the materials are there for me to return to at any time I like.

Future Learn Course Categories

Future Learn Course Categories

There are many courses to choose from, take a look at all the course categories here. Checking Science, Maths and Technology, I see from The University of Bristol Cracking Mechanics: Further Maths for Engineers; I suspect there may well be some useful videos there to show my Year 13 Further Mathematicians when we study Mechanics.

And look at this – Assessment for Learning in STEM Teaching led by Dylan Wiliam and Christine Harrison, to help STEM teachers get to grips with Assessment for Learning.

Another interesting category for teachers and students is Teaching and Studying. I mentioned the Extended Project above, under this category I discovered a course on just that. Already under way, from The University of Southampton is Developing Your Research Project.

You can find out more about FutureLearn here. Looking at FutureLearn’s description of why their online courses work I discovered a reference to John Hattie and his work on Visible Learning. Certainly the structure of the courses is very clear.

I personally like the flexibility of online courses – I can access them for as long as I want whenever I want. I also like the fact that the courses include quizzes to check learning; something I believe is very helpful in supporting our students’ learning.

Writing this blog post I have signed up to rather a lot of courses!

(Student version of this post to highlight some courses).

Supermoon Lunar Eclipse September 27th / September 28th

NASA activity tableThe rare Supermoon Lunar Eclipse on September 27th / September 28th reminds me of the extensive Mathematics resources available from NASA. The eclipse might inspire you to do a little Lunar Math!

The total eclipse will last one hour and 12 minutes, and will be visible to North and South America, Europe, Africa, and parts of West Asia and the eastern Pacific.

The moon will start going into partial eclipse at 12.07am in the UK. The eclipse will then become total from 1.11am until 2.23am. The eclipse will end entirely at 4.27am.

Space.com – photographs of the Supermoon eclipse

Top Tools for Learning 2015

Jane Hart has now published her Top 100 Tools for Learning 2015 list, appropriately using Slideshare, one of my own favourites (these presentations are all uploaded to Slideshare) and I see is number 20 in the list of top tools:

I wrote about my own selection recently, it was very hard to choose 10. I thought it would be interesting to see where they came in the list.

Tool   (CY votes) Place in Top 100 2015
Evernote  10
WordPress  8
Google (search)  3
Twitter  1
Slideshare  20
PowerPoint  5
Excel  56
Diigo  42
WolframAlpha  –
Desmos  –

So I am not alone in my choices for most of my favourites; I did not really expect WolframAlpha or Desmos to appear in this particular list but they still get my vote! WolframAlpha is useful for so many subjects – not just Mathematics.

I found it interesting looking at the list, seeing Screencast-O-Matic back in the list at number 27 reminded me to try it again; I downloaded the recorder and it certainly works very easily – now this is not the most exciting video in the world – just a test, but it took just a very short time to record and upload to YouTube:

Other reminders for me in this list:

Wallwisher - quadrilaterals


Padlet (29), formerly Wallwisher is such a good idea and I have not used this for a while; Wordle and the other various word cloud generators are another example. Tools to try with Year 7 I think.



Piktochart is a new entry in the list and provides an easy way to create infographics.

Scroll down Jane Hart’s page to see new entries and the big movers up the list.