Spot the Mistake

…and other updates.

Edexcel Model Answers example
Updating the page on Edexcel’s Teaching and Learning materials (part of the A Level (16+) Resources series) I have included their now complete set of GCSE to A Level Transition worksheets and also exemplar answers with examiner comments, a particularly valuable resource. These booklets look at questions from the AS and A level Sample Assessment Materials, which was used in the trial undertaken in summer 2017. Real student responses are shown together with commentary showing how the examining team apply the mark schemes. The commentary includes always useful notes on common errors. Noting that these could be used in class and students asked to find errors reminded me of some more excellent resources – time for an update of the Spot the Mistake collection.

Erica's Errors - A Lutwyche

Particularly excellent resources come from Andy Lutwyche, look at his excellent Erica’s Errors series for Spot the Mistake activities.

For more resources – see the Spot the Mistake collection.

MEI Making Sense of Information
Another updated page in the A Level series is on Statistics; this includes links to all the large data sets used by the examination boards as well as suggestions and resources for teaching. Note the September/October 2017 edition of MEI’s very helpful M4 magazine which has a focus on the teaching of Statistics and includes information and examples of updates on the large data sets for all the examination boards. The PowerPoint resource could also be used with younger students to get them thinking about the presentation and interpretation of data.

Other checked and updated posts include



Open Middle

Open Middle

I was happily distracted this morning by this lovely problem, Create a System of Two Equations by Daniel Luevanos on Open Middle, accessible for students yet such a great task for mathematical thinking. We could discuss inequalities here as well as simultaneous equations.

Noting the link to a Desmos page as a suggested answer I couldn’t resist creating a more general Desmos page.
Open Middle Problem

Graspable Math created a canvas for this problem, in class we could have this available as well as Desmos. Note the scrub feature.
Sim Eq Opn Middle Problem 1
Sim Eq Opn Middle Problem

Now we could systematically change one variable at a time and start talking about inequalities….

If you are not familiar with Open Middle do explore these excellent problems; you can read more about the type of problems you will find on the site on the About page.

Note you can search by grade using the drop-down menus and you will find a clear index on the right hand side of the home page.


Top Tools for Learning 2017

Jane Hart, of the Centre for Learning and Performance Technologies, has published her annual list of Top Tools for Learning. Like last year, she has three sub-lists including Top 100 Tools for Education. Note that you can easily see the rankings for each sub-list using these rankings. Jane Hart’s analysis includes details of the contributors as well as her commentary on trends.

Looking at the Top 100 Tools for Education I see my favourites WordPress (Blogging and website tool) and Evernote (Personal information system) in there, these are also popular in all the lists.

Continuing to look at the Top 100 Tools for Education Excel is quite rightly highly placed. I regularly use Excel resources; just a few examples of some favourites:

Normal Trainer

Excel Files – Mike Hadden


STEM Centre – Descriptive Statistics

See STEM Learning, part of the A Level (16+) Resources series.

A few more for investigation …
KahootKahoot (Classroom response tool) is very easy to use and free for teachers and students. In a few minutes I created a quiz on Directed Numbers … (not very exciting – just a test, very easy to create.) Kahoot qn

Another popular quizzing tool I know some of my colleague’s use is Quizlet.

Seeing Padlet (online discussion board) on the list reminded me of this very easy to use tool. I shall try this with Year 7!
Padlet equations

Unsplash – beautiful free photos to do anything you like with! Perhaps not surprising that this has moved rapidly up the lists!

Photo by Marivi Pazos on Unsplash

Apart from illustrating Unsplash, I can have pictures of flowers to illustrate a mathematical connection! From Science News reading Fibonacci’s Missing Flowers we discover that the most common number of petals is five and whilst there are many flowers with the number of petals a Fibonacci number there are also flowers with four, six, seven or nine petals!

GrammaryI added a comma in a couple of places in this post thanks to Grammarly which has jumped up the Top 100 Tools list by 70 places. Very easy to use, Grammarly lets you check for 250 types of grammatical, spelling, and punctuation mistakes.




Formulae: A Level Mathematics

Looking at the Subject content for A Level Mathematics we see that Appendix A, pages 16-22 describes the mathematical notation for AS and A level qualifications in mathematics and further mathematics. Appendix B, pages 23-26 is on mathematical formulae and identities.
Checking individual examination board specifications shows us the formulae which will be provided in the examination; each looks very similar.

OCR (MEI) Formulae

OCR (MEI) Formulae

I think it is useful for students to be aware as they study the course which formulae they must know and which will be provided; though they should be very familiar with any provided formulae.

MEI Technology

MEI – Use of Technology

Teaching Calculus from the new specifications I see that the formula for Differentiation from first principles is provided which seems fair. Looking at MEI’s very helpful advice on Integrating Technology into your scheme of work we see some suggested resources for teaching differentiation, including this GeoGebra resource on First Principes. I like the way one can choose between numeric and algebraic.
GeoGebra first principles

MEI – Use of Technology, Differentiation

Staying with Calculus and technology, note that Desmos allows you to very easily see a function and its gradient function; note the requirement of the subject content that students should be able to sketch the gradient function for a given curve.
Desmos gradient function
A resource I found very useful for the matching a functions with their gradient functions comes from Underground Maths. I included Gradient Match which can be used interactively online in this post on introducing gradients at GCSE. Note that you can simplify the task by giving students the set of six functions and the six gradient functions separately.






Underground Mathematics – Gradient Match




MEI Ritangle Competition (& Technology!)

From MEI comes Ritangle, a competition for teams of students of A level Mathematics, Scottish Highers or the International Baccalaureate. This year’s Ritangle competition  launches Monday 2 October!

For the main competition, one question will be released daily for 21 consecutive weekdays, the first question will be released on 9th November 2017. I am looking forward to seeing the problems which I am sure will be of interest to many Mathematics students even if they are studying for alternative qualifications and cannot enter the competition.

Something which caught my eye is that Technology can help with some Ritangle questions which led me to some excellent Excel resources, which you can use whether or not you are participating in the competition.

Excel is a favourite for me – I use it in both my Mathematics teaching and in my Deputy Head role. Note from Nrich, we have many uses of Excel for Mathematical Investigation. I like this very clear illustration showing fraction multiplication.

Nrich Fractions multiplication

Excel Interactive Resource – Fraction Multiplication

For teaching sequences, Interactive Number patterns will be useful.

Quadratic Sequences

Nrich – Interactive Number Patterns 2

…and one of my favourites – Happy Numbers! (For the Excel spreadsheet – Nrich investigation)
Happy Numbers

Talking of technology, the Excel fractions resources here reminded me to try fractions with Graspable Math. Having tried Graspable Math on the Interactive whiteboard recently I can confirm it works perfectly.
Add Fractions

And finally, talking of Graspable Math, this led me recently to Dave Taylor’s excellent Increasingly Difficult Questions, a wonderful collection – and with an eye on the copying budget too!
Change the subject DT

Looking at the Graspable Math Teacher Resources, I see some of the Increasing Difficult Questions have been added to a canvas. Graspable Math lets you save your work so you can come back to it later or share it with others. Saving requires a google account. To share a file, use the share menu to get a link that gives others read access to a file. I decided I liked the idea of having a canvas ready for Simplifying Expressions, starting with IDQ-Simplifying Expressions 1, I opened it on my own canvas and adapted it slightly. I do like to keep all steps of the working displayed, so I have put the exercises on the left, creating a good space on the right.
Simplify Expressions IDQ