# Functions

Looking at some favourite resource websites, some recommended resources for teaching functions …

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.

From White Rose Maths, we have Year 7 work on algebraic thinking, including function machines, and in Year 11, Functions.

Dr Austin Maths on Functions

As always CIMT is worth a search; we find:

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.

The AQA Bridging the Gap resources includes a resource on introducing function notation; These resources were originally designed to support teaching and learning for students who studied the 2007 Key Stage 3 Programme of Study and were preparing for the then new Mathematics GCSE. The resources are still very useful.

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

There are also many more activities on functions on Transum.

For a challenging problem on Function Notation, try this from Open Middle.

From Andy Lutwyche, a resource I have always liked is one of his excellent Building Blocks series on Function Notation. We can also search his site on functions. (I am so pleased to see Andy’s resources on his own site, andylutwyche.com.)

Or we could help Clumsy Clive with his homework on Function Notation.

From CorbettMaths try the Practice Questions.

On DrFrostMaths, try the Functions Key Skills.

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

From MathsHKO see Function Machines, and also Functions.

We could simplify expressions on Graspable Math

On Starting Points Maths, a search on Functions returns several tasks, including work on Graphs and Transformations.

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

For a compilation of GCSE questions, William Neill’s GCSE Maths Questions site is so useful. Under Algebra, we see A7 Function Machines and A65-68 (H) Functions.

On MathsBot we could use GCSE Exam Style Questions for higher questions on Composite functions.

Or use a GCSE Revision Grid.

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.

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

See also these very clear notes with exercises from Plymouth University including Functions..

# Mathematical Miscellany #79

Looking ahead to summer examinations, this year there will not be advance infomation as there was last year, but in GCSE Mathenatics students will again have formaule sheets; the exam boards have now published these. This page, Examinations 2023, includes links to infomation and the formulae sheets for each exam board. The page also includes the series of revision pages with many ideas and resources for revision.

Formulae sheets 2023

OCR additionally have formulae sheets top tips, and GCSE formulae tests.

I often use Jonathan Hall’s wonderful Completion Tables so was delighted to see that these are all in one place on MathsBot, a personal favorite is his Directed Number.

(See Fill in the Blanks for many such exercises, and Negative Numbers for more resources on Negative Numbers.)

Regular readers will be aware a favourite website of mine is Transum, two recent additions are Algebraic HCF with Algebraic HCF and LCM exercises over 5 levels and Gradients now with a new level 2 which features straight lines drawn on axes where the vertical scale is different from the horizontal scale, soe labels are obscured for an additional challenge.

From Chris McGrane on Starting Points Maths, have a look at this lovely task on Integration which provides much needed practice on deciding on the integration required to determine the areas shown. Students are required only to write down the integrals with limits.

It struck me that the questions could be checked and illustrated on WolframAlpha.

Both MathsBot and Transum featured in my Enduring Websites collection, websites started between 1997 and 2013, and still there! MathsBot and Transum are regularly producing such excellent resources after many years. I believe Starting Points Maths will be included in the next Enduring websites collection!

These slides are from a session I presented at last year’s MA Conference.

# Mathematics Revision

Seeing that my earlier posts on revision resources including papers for the 2022 GCSE examinations are still popular I have created a page to include the resources from those collections, whilst some of these are based on the advance information for the June and November 2022 exam series they still provide very useful revision. We are fortunate in Maths that the subject content is the same for all the UK exam boards. The collection of pages brings together many varied revision resources.

The page, GCSE Revision 2022 is one of the Revision series of pages:

# Looking back…and looking forward

Looking back at 2022, last week I looked at some posts popular in 2022. Continuing the theme of looking back, from the Office for National Statistics, The Year in Numbers in which the National Statistician, Professor Sir Ian Diamond looks back on a year of notable statistics, and from Quanta Magazine, The Year in Math including notes on a bumper year for number theorists from a high school student throught to more experienced mathematicins.

I was interested to see the Top 10 OpenLearn courses of 2022, OpenLearn is the The Open University’s free learning site. The Top 10 includes Everyday Maths and also MSE’s Academy of Money, a course where The Open University joined forces with MoneySavingExpert to produce a course to help people master their finances.

For 2023, a very happy new year to all, I have created the annual look at number properties for the new year and links to NCTM’s year game to play with your students in January. I will keep this page updated with any new resources and ideas.

Looking ahead to some new resources, recently created we can use for the year ahead, see the following:

I have often mentioned Wayne Chadburn’s monthly calendars. He writes these calendars to provide regular, varied practice – a little bit of maths each day. Three versions of each monthly calendar are available, Higher, Foundation Plus, and Foundation; answers are provided. Calendars for January through to May are now available.

For another source of calendars, including the option to create your own, use Matt Woodfine’s resources on Maths White Board.

Fawn Nguyen has provided all her wonderful resources in one place, see Fawn Nguyen, for her new resources page which she plans to add to as time permits. The Collections include a selection for Elementary, chosen from her brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who have used visual patterns in their classrooms.

Jack Brown has recently completed his teaching video collection for A Level Further Maths, Mechanics a / Minor.

You can see the OCR B MEI specification for each section, with much in common between the boards, these are useful resources for other boards also; the differences between the exam boards are identified in the resources.

For Further Resources on Dimensional Analysis see this page in the Further Maths series:

Mechanics – Dimensional Analysis

For A Level Mechanics – see this post: Mechanics.

Staying with A Level, Mark Willis has updated his A-level Year 2 resources. Each topic now has the question with gaps for students to fill in whilst either trying the questions or watching the videos.

Note that IGCSE resources are also available on Mark’s site – included in the IGCSE resource collection.

The Doctor Frost Maths Key Skill Team remain busy, still on a Mechanics theme, here’s a recent addition to the Key Skills for Mechanics, K428c – equilibrium on an inclined plane, with an inclined force.

The Dr Frost Maths – Key Skills for Mechanics were included in this post highlighting resources for A Level Mechanics.

Checking Amanda Austin’s wonderful Dr Austin Maths – New, we see recent additions on Functions.

Peps McCrea is launching a weekly 5-min email for teachers who are keen to keep up-to-date with thinking and research around effective teaching. For ‘Evidence Snacks’, you can subscribe here.

I will finish with Jake Gordon’s Christmas present for all teachers! It will be really interesting to see developments on his resource – an infinite canvas to use as a whiteboard in 2023. See Jake’s YouTube Channel, Mr Gordon’s maths universe which includes an Introduction; the interface is very simple and intuitive to use.

I have mentioned Eric Curts before, for example see his introduction to Mathigon, a Control Alt Archive Workshop where he interviews Mathigon’s head of content David Poras.

His recent EdTech Links of the Week 1-2-23 features Jake Gordon’s Infinity Whiteboard.