A previous post on Functions features resources aimed at older students; I thought it would be useful to look at resources for teaching younger students.

For an excellent introduction the PhET Simulation, Function Builder provides a very visually appealing resource. Using the pattern option even very young students could explore important concepts. This is very intuitive to use, the slides in the following slideshow demonstrate examples of its use. Note that teachers can register with PhET and gain access to supporting documentation.

Desmos can be used very simply to illustrate function notation and note the use of Desmos as a calculator to evaluate the value of a function for a given input.

Functions - Desmos. Select image for graph page

Functions – Desmos. Select image for graph page

As always CIMT is worth a search; we find:

CIMT Interactive Materials - Functions

CIMT Interactive Materials – Functions

In the interactive materials for year 7: Unit 16 Section 2: Function Machines and there is also a section in the associated text (16.2). All CIMT resources are free to access, a small number of documents such as text answers are password protected, you can obtain the CIMT password. These exercises could be used as an introduction and students also shown function notation. They could write the functions described by the function machines using f(x) notation.

On Transum, try this online exercise on function notation, inverse functions and composite functions.

Functions - Transum

Transum – Functions

On Maths Genie, under Grade 7, we have Inverse and Composite Functions. You will find some revision examples and also exam questions with solutions.

Maths Genie Functions

Maths Genie – Inverse and Composite Functions

From Don Steward, try these lovely questions on Compound Functions.
Don Steward Functions

TES Functions

TES Resources – Functions

On TES, this Crossnumber from cbarthur is an ideal resource for becoming familiar with function notation. Also on TES from Owen134866 we have a set PowerPoint resources including an introduction to f(x) notation for GCSE students.

AQA Bridging the Gap

AQA Bridging the Gap

The AQA Bridging the Gap resources includes a resource on introducing function notation; these resources are ideal for students who have completed the previous KS3 programmes of study but will be studying the new GCSE courses.

OCR GCSE 9-1 Check in tests

OCR GCSE 9-1 Check in tests

From OCR, it strikes me that the Check in tests will be very useful in KS3, consider the language of functions for example, the first questions could be used for students as young as Year 7 (age 11-12).




On Exam Solutions you will find an introduction to f(x) notation.

For further information on new content at GCSE see this page.

Plenary Tweets

Discovering a novel idea for a plenary via Twitter recently, a UKEdChat resource by @grahamandre I thought I would try the idea with my very able Year 9 class (the same wonderful class I mentioned some time ago who gave their views on Good Maths Teachers).

I should mention that “Somewhere over the 2a” is part of some lyrics by one of my colleagues sung to the tune of “Somewhere Over the Rainbow!”

In the first part of this lesson I used one of my mini-tests to review the key points for solving quadratic equations. When we reviewed the solutions I also used Desmos to illustrate some of the answers and for these students, the first year who will tackle the new GCSE course made sure I used function notation! This time I told them that I was using the mini test to review the material we have been studying and that they should try and create a useful revision resource by noting the questions carefully and annotating their answers clearly, adding to them where necessary when we reviewed the material. They know I will be looking at their books early this coming week.

I was of course particularly pleased at some of those hash tags!
#enlightened with the mini-test

and of course  #winning    and #maths is fun

You can find a resource on TES, Twitter Plenary from MrGator which provides includes PowerPoint slide and tweet slips.

Mathematics Conversations

There are many useful conversations on Mathematics on Twitter. Now just in case you hate Twitter or have no interest in it – you can still follow useful conversations and follow links to resources without even signing up to Twitter. I find Twitter a little like a lucky dip – usually in just a few minutes I find useful resources or the latest educational news.

For Mathematics teachers I would recommend the following:

Q3 Resources#slowmathchat  where different questions are posed for discussion; you can read more about the origin of #slowmathchat and how it works on Michael Fenton’s Reason and Wonder. A complete archive of all the questions and answers is available too.

#mathsTLP for lesson planning, a Sunday night chat but you can of course view at any time and many teachers share useful resources / ideas that work in the classroom.

Select image for resource on TES

Select image for resource on TES

Each weekly chat is very clearly archived on Ed Southall’s Solve My Maths.
Talking of Solve My Maths, I do love Ed’s Mr Men!

Mr Men Ed Southall

Mr Men – Ed Southall

All the links above to Twitter list the tweets in time order (Live); note that you can choose Top or Live;

Top & Live

Further useful Twitter people and hashtags to follow:

Craig Barton TESMaths

Diagnostic Questions

#mathschat for UK education and #mathchat for US education

#MTBoS for converstaions from the Math Twitter blogosphere

#maths and #math for general UK & US tweets on Mathematics

@Desmos for the latest on the fabulous graphing calculator

@Wolfram_Alpha and @WolframFunFacts


MAA – Mathematical Association of America 

Association of Teachers of Mathematics

If you are interested in learning more about Twitter see the very clear Twitter Lingo guide from Mashable and Russell Stannard’s training videos. And for a nice simple explanation try ‘Mom This is How Twitter Works’.

This page has been reproduced and added to the Reading series of pages, further updates will be published there.

Thoughts this week …

A compilation this week …


Normal Trainer – Mike Hadden

….is my favourite Microsoft program both for its use in Mathematics teaching and for data analysis. In 2013 at the TSM Conference I was very fortunate to meet and be trained by Mike Hadden. I had already discovered and often used Mike’s Excel files for my teaching; in 2013 thanks to Mike I discovered the joys of Excel macros which save me a serious number of hours in my job!

Mike now has a blog where you can find out more about his Excel files for teaching (scroll down) and also learn more about macros – have a look at the Macro Recorder Demo.

GCSE New Content

I have created a new page for GCSE resources for the new content which I will add to as we discover more! Note the addition of some resources at the end of the list under Further Resources. A list of changes is available on a separate page.

Further Resources – GCSE new content

  • AQA Bridging the Gap for students who have studied the current (2007) Key Stage 3 Programme of Study and are preparing for the new  Mathematics GCSE (8300 specification).
  • Transition Units – Cambridge
  • OCR Check in tests scroll down to Teaching and Learning Resources
  • Resourceaholic from Jo Morgan – links to support the teaching of new topics in GCSE Mathematics.

For problem solving, Brilliant…is just that, brilliant – I’ll return to this in another post but do have a look.

Select image to try problem

Select image to try problem

Circle Theorem

Circle Theorems – Tim Devereux

Circle Theorems 

For some excellent resources for Circle theorems try these including Tim Devereux’s updated excellent Circle theorems web pages.

…and finally

Rereading my post on the TSM conference reminded me of this wonderful entertainment – ‘Katie’s bad science’. I love this!
Original and re-edited version of Katie Melua’s song nine million bicycles proposed by Simon Singh and presented on Ted talks by Michael Shermer.