Tidy UpMy tidying up seems to have caused confusion! Wanting to revamp a post on feedback I seem to have the dates in a muddle so apologies if you received an email leading to a page not found message! The updated post on Feedback is here.

So important to give great feedback and help students get good at feeding back to themselves – a subject I will return to in the new academic year.



In class this week ….

Year 7 (age 11-12)
…had an Independent homework this week and I was really pleased with the variety of choices made. Some chose to use online resources / their text to practise a topic tested recently, others worked further on some investigations we have looked at in class, some chose to do a Junior Maths Challenge. A couple of students used the Diagnostic Questions site to practice their chosen topic. One of the investigations we have looked at recently was on the number of winning lines in a noughts and crosses game – the 2 dimensional  game was fairly quickly sorted out – so moving to 3 dimensions is the natural extension.

Nought & Crosses

Some were fascinated by this and determined to find the number of winning lines in a game of 3D noughts and crosses – two students so keen that they made a model of their own to help them answer the question successfully! They made some counters as well!

I have read some great posts on feedback recently, see Alex Quigley’s Improving Written Feedback  and Verbal Feedback Given….. on Shaun Allison’s ‘Class Teaching’. Such a good idea, I couldn’t resist – so I bought myself the stamper and decided to try this with Year 7 – early days yet, but I love the idea so far..

Another student in the same Year 7 class mentioned above was determined to find the number of winning lines in a game of 3D noughts and crosses which she did successfully. She drew some clear sketches of the different groups of winning lines and after a discussion with me was the recipient of my first stamp! I was very enthusiastic about her written work on this as you can see from her response! I had explained to the class that if I discuss their work with them, then give them a stamp – they have to write down that feedback as Shaun suggests in his post. 

verbal feedback v3

Year 10 (age 14-15)
desmos-gradients1Year 10 and I have been looking at inequalities – using algebra and graphs. After a ‘self-check’ (somehow that sounds so much better than test and the emphasis is very much that it is useful to see what they can recall) in class, the feedback from the students was that most of the questions were fine but any problems seemed to be on working out the equation of a line when trying to describe a given region. The wonderful Desmos graphing calculator to the rescue – this page allows students to experiment with several variables. (Post for students here.)


,Update – since writing this post, along came Desmos

Desmos tweet
and created a superior version! This shows many of the awesome Desmos features. I really must explore these further – note that where a folder is used selecting the arrow shows or hides the contents. This is a brilliant feature for creating pages to share with students.

Gradient of a straight line by Desmos

I mentioned feedback from the students – a simple feedback idea – I asked this class as the first part of a homework to email me with any outstanding queries from the mini test, having looked at the worked solutions on our homework blog. I have been impressed by their understanding and articulation of what they initially found tricky.

Year 12 (age 16-17)

zweigmedia – numerical integration utility

In Year 12 we have been studying integration. Teaching the trapezium rule I remembered some applets I used last year which demonstrate this well. 

Graphs images - WolframAlpha

Graphs on WolframAlpha

The Year 12 Further Maths class are currently studying Decision Mathematics and a student asked what WolframAlpha can do?! Looking at the examples we can see that describing connections between nodes will generate images of a graph. I must explore further!


Normal Trainer – Mike Hadden

Year 13 (age 17-18)
Studying the Normal Distribution I showed students Mike Hadden’s excellent normal trainer which generates an endless supply of examples. I really like the step by step approach and the very clear page on the backwards problems.

With the Year 13 Further Mathematicians I was reminded of the huge variety of Tarsia puzzles around and that these are not just for younger classes. In Year 13 we use a Tarsia on De Moivre’s theorem.

Diagnostic Questions revisited

questionsIt was a couple of  weeks ago I wrote about Craig Barton’s and Simon Woodhead’s brilliant Diagnostic Questions site. At the beginning of November I wrote that there were in excess of 1300 questions, just a short time later there are over 1600 questions (September 2014 update – more than 2500) – brilliant! There are some fantastic new questions – do explore all the recent additions.

I have been using this in class, with Year 7 we used some algebra questions; this led to some excellent discussions, not only did we discuss the right answers but all the wrong ones as well. We even decided on some alternative responses that could have been used. I feel a homework coming on here – we’ll write our own questions. Watch this space!
Update: Diagnostic Questions by Year 7.

It is now possible to download a quiz you have created and easily create a PowerPoint slideshow for offline use. I have created a slideshow with instructions:

Diagnostic questions download and create PowerPoint slideshow from Colleen Young

Craig has created this video giving a tour and commentary on the site:

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!


Questions, Questions …

questionsOur lesson planning should include planning for some high quality questions; good questions help us know more about our students’ learning and help us to address misconceptions.


An outstanding new resource to help us do just that is Craig Barton’s and Simon Woodhead’s Diagnostic Questions site. The site has over 2500 multiple choice questions with carefully designed responses to address common misconceptions.
The questions are very clearly categorized, there are numerous sub-categories under the main headings of Number, Algebra, Shape, Space and Measure, Data and Statistics and Post 16 – Pure.
You can just use the site online but registering is highly recommended as you can then create your own quizzes and save them for later use. I found that using the Instant Quiz facility provides a very easy way to do do that as it is possible to add any question to the Instant Quiz. Suppose we wish to create a quiz on Diagnostic Questions - AlgebraAlgebra – Expanding Single Brackets; head for the questions and select Algebra – Expanding Single Brackets. The questions will then be displayed and you will see as you hover over any question you have the option to select + which will add that question to the Instant Quiz.
Once you have selected your questions select Quizzes and then the Instant Quiz, you will find that you can select all the questions and add them to a new quiz. Instant Quiz - rename v2

Once you are satisfied that your new quiz is saved you can delete all the questions in the Instant Quiz and you are ready to go for the next quiz you wish to create!

Instant Quiz - delete

Teachers everywhere – this is a chance to collaborate – it is easy to upload your own questions – so far I have found the PowerPoint route the easiest way to go – here’s one I created earlier! 

I think we all owe a huge thank you to Craig and Simon for making this happen – I really look forward to seeing how this develops.

Update – download your quizzes.

I am pleased to say that the Rich Questions post is one of the most popular on this blog – so the Diagnostic Questions site has been added there. There also seems to be a great deal of interest in the 5 Minute Lesson Plan which quite rightly includes planning for questions.

Last word to Einstein: “The important thing is not to stop questioning.”

See also: Diagnostic Questions Revisited and Diagnostic Questions by Year 7