Technology in Mathematics

An update has been made to the Use of Technology page.

In particular note the GeoGebra resources from Edexcel (and also OCR).

From Edexcel you can use A Guide to using GeoGebra when teaching AS and A Level Mathematics which links to numerous GeoGebra files clearly mapped to the specification content. You can also access an excellent collection relating to the Pearson books (see table below). Whilst linked to the books many of these GeoGebra resources do stand alone, for example check this equations and inequalities example from the Pearson Maths A Level Pure 1 collection.
Edexcel Geogebra Equations and Inequalities

Pearson Maths A Level Year 1
Pearson Maths A Level Year 2
Pearson Maths Statistics and Mechanics Year 1
Pearson Maths Statistics and Mechanics Year 2
Further Mathematics
Pearson Maths A level Core Pure 1
Pearson Maths A level Core Pure 2
Pearson Maths A level Further Pure 2
Pearson Maths A Level Further Mechanics 1
Pearson Maths A Level Further Mechanics 2
Pearson Maths A Level Decision 1
Pearson Maths A Level  Decision 2
Pearson Maths A Level Further Statistics 1
Pearson Maths A Level Further Statistics 2

It is good to see all the GeoGebra resources for Further Mathematics, for example, check Explore toppling and sliding using GeoGebra.

Pearson Maths A Level Further Mechanics 2 Toppling and Sliding

For exploring the Large Data, on AQA’s All About Maths see AQA Large Data Set – Guidance and Worksheets including a tool to help support teaching the statistics content of the specification. This is an amended version of the large data set spreadsheet, the first three sheets are as on the AQA large data set but there are many additional sheets which allow students to explore the large data set. The tools are all provided for students, they do not need knowledge of Excel, meaning time can be spent on interpreting the data rather than learning about Excel. The worksheet on Exploring the Large Data Set could I think be usefully used lower down the school to get students used to working with more data.

A separate page is available on Statistics.

Venn Diagrams


The DfE document describing the GCSE Mathematics subject content is an excellent starting point for checking new content, all exam boards must include this content.

Note that only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content. See page 4 of the DfE document.

There are many excellent resources for teaching Venn Diagrams; investigate this collection.

Diagnostic Questions

On Diagnostic Questions – Probability with Venn Diagrams.

Diagnostic questions now has over 21000 questions on Mathematics including wonderful collections of examination questions. The site is completely free (and promises to remain so). Plenty of help is available to help you learn how to use the site.

CIMT Venn Diagrams

CIMT is one of my Top >10 websites for a very good reason – when I want additional examples for any topic at any level I can always find them on CIMT! Venn Diagrams are no exception to this, you can find Sets and Venn DiagramsSet Notation and Logic and Venn Diagrams in the student interactive resources and the text chapter on Logic from the Year 7 text here; in sections 1.3, 1.4 and 1.5 of the text you will find examples and exercises on Set Notation and Venn diagrams. See also the additional Teacher resources for this unit (Unit 1, Logic) such as Additional exercises are also available as are Aural Tests. Other teacher resources include slides and Revision Tests (you will need the CIMT password for the Revision Tests).

Problem from section 1.4 CIMT Venn Diagrams


AQA – Bridging the Gap

From AQA’s excellent Bridging the Gap resources, Sets and Venn Diagrams is superb, also see the OCR resources, from OCR’s Check In tests, see Combined events and probability diagrams. For further information on the changes to Probability at GCSE see this post.

Transum – Venn Totals

From Transum try Venn Totals 4 different levels of exercises which can be checked are available. Level 1 – Reading information from a Venn diagram containing two intersecting sets. Level 2 – Reading information from a Venn diagram containing three intersecting sets. Level 3 – Adding information to a Venn diagram containing three intersecting sets. Level 4 – Adding information to a Venn diagram containing three intersecting sets with some problem solving required. There are also exam style questions, to see the worked solutions a subscription is required.

On TES the GCSE topic specific resources include Probability resources. Included in this collection are several (all free) resources on Venn Diagrams.

Nrich too can always be relied on to provide resources – a search on ‘venn’ returns these resources.

Nrich Venn Diagrams

From Sums Mathematics come two very useful activities to illustrate Venn Diagrams. From the Index choose Sorting & dbases under Data Handling where you will find Venn Diagram activities for two sets and three sets.

Venn Diagrams

teachitmaths Venn diagrams

From teachitMaths, try Venn diagram dominoes (pdf versions of all the resources on this site are free).


However, note that some of these questions refer to ‘difference’, examination specifications should be checked for notation, for example AQA’s helpful teaching guidance includes notation such as this illustration.

AQA Teaching Guidance

AQA Teaching Guidance

vivaxFor a useful way of displaying these regions on Venn Diagrams you could use the demonstration from the Venn Diagrams tutorial on Vivax Solutions. Geogebra or WolframAlpha can also be very easily used as shown near the end of this post.

Or returning to Transum, try Venn Paint.

Level 2 has 3 set Venn Diagrams. Exam Questions are included also (solutions are provided for subscribers).

Included in Jonny Griffiths wonderful RISPS – see RISP 10.

fmsp-gcse-extension-tasksOn a similar theme – from the Further Maths network have a look at the excellent GCSE extension tasks, see NA1 for example.

From Craig Barton – see this whole collection of rich tasks with Venn diagrams.

Underground Mathematics

To really challenge your students combine Venn Diagrams and Algebra and try this review question from Underground Mathematics. (From a 1969 MEI O Level Additional Mathematics paper.

A search finds more problems – all resources on Underground Mathematics include complete documentation including suggestions, a full solution, printable materials and more.

Perhaps try Can we find how many boys study French, Latin and German? or Quadratic Solving Sorter – not a traditional Venn diagram problem but certainly a diagram as in the possible solution presented is a very good idea.

washing-upFrom Census at School combine Statistics and Venn diagrams, and check this task on Washing Up!

These three interactives from Shodor are a good introduction to Venn diagrams:
Venn Diagrams, Shape Sorter and Triple Venn Diagram Shape Sorter 

With the Triple Venn Diagram Shape Sorter you can either set the rules or guess the rules by selecting the appropriate botton:

Some excellent activities are available from the Illuminations site.

The Shape Sorter allows exploration of geometric properties of shapes.

Select Instructions and Exploration for clear information on how to use the resource.

WolframAlpha can be used to illustrate Venn Diagrams.
The slideshow here shows several examples.

Alternatively – try GeoGebra or this UCLA  applet.

On a lighter note – a Twitter conversation on a fun idea!
Twitter Venn

Here’s some more on MailOnline

If you want to create your own there are plenty of tools to use – there is a good summary here on Cometdocs.

New Scientist Gallery - Venn Diagrams

…and to take Venn Diagrams to their extremes have a look at these wonderful images from New Scientist!

Colourful Chi Squared!

Updating a presentation, Colour in Mathematics or pdf version, Colour in Mathematics led to a happy find…

Chi Squared examplw

When teaching the Chi Squared test I have often found that students are not always clear on their interpretation of the contributions to the test statistic. A worked example with a little colour to help where we look at the observed data. the expected probabilities and the chi squared contributions seems to work well . This exercise made me realise that a chi squared calculator I had previously recommended did not seem to be working, so fortunately I found a better one!

From Social Science Statistics this Chi Squared Calculator is for a contingency table with up to 5 rows and columns. It is very simple to use, enter the group and category names, then the data, choose the significance level and calculate.
Chi Squared Calculator 1
Chi Squared Calculator 2

A clear conclusion is then given:
The chi-square statistic is 10.2061. The p-value is .037096.
The result is significant at p < .05.

The calculator is included on the Statistics 16+ page of Calculators & Tools.

Note the many other calculators  for statistical tests  available on Social Science Statistics.

A Level – Draft Specifications & a Statistics Qualification

The A Level Draft Specifications have now been published, including specimen papers.
Use this Twitter List to see updates from all the exam boards. As you can see @Ofqual are making announcements about accredited specifications.

For the specifications use the following links.

Further resources:
AQA Resources including a very useful Specification Summary. AQA have several very clear resources, see: Planning  Teaching and Assessment which includes the Specimen Papers and mark schemes.

Edexcel Specification & Sample Assessment Materials note the inclusion of a data set for AS and A Level.

Edexcel – Assessment support including mapping documents.

From OCR, specifications, specimen papers and other resources can all be downloaded here.
Note the option to download a zip file with the specifications and sample assessment materials.

OCR have individual subject pages with further resources:

MEI have helpfully compared Further Mathematics Specifications so you can compare the content and structure from each board.

OCR have also linked to some new sample MEI resources. These include some very nice “problem shorts” and also the use of technology to analyse large data sets.
MEI Sample Resources

OCR A Level Check In Test

OCR A Level Check In Test

I do like OCR’s check in tests for GCSE and I see a small number check in tests and lesson elements on the A Level subject pages; I assume this collection will grow.

From MEI, see this short video presentation on the new specification including the new work on large data sets.

For further reference documents and some suggested resources see A Level Reform.

For easy access to announcements regarding Maths from the examination boards, use this twitter list. (You do not have to use Twitter to access the list).

Royal Statistical Society Problem SolvingEduqas will not be offering AS / A Level Mathematics specifications, but note their Level 3 Statistical Problem Solving Using Software. See also  the International Centre for Statistical Education (ICSE) with Plymouth University and you can follow @IntCSE on Twitter. It may be that some of the resources here will be useful for our teaching of Statistics.

Educas state: “The objective of this qualification is to assist the understanding of the problem-solving cycle of planning, collecting, processing and discussing in meaningful contexts and to use statistical software to process real data sets. It has been specifically designed to be taught in schools and colleges to equip learners aged 16-19 with a broad range of skills empowering them to successfully negotiate statistical problems in Higher Education or the world of work.”

This discovery led me to a treasure trove of resources from Educas for Mathematics at all levels, including GCSE – this definitely needs further exploration!

Mathematical Miscellany #3

Exam PowerPoint @westiesworkshop

Mr Westwater – TES Resources

With revision still in mind, for some excellent PowerPoint resources with A Level questions and mark schemes by topic try Mr Westwater’s resources on TES. (Twitter @westiesworkshop). 

Diagnostic Questions

Diagnostic Questions

Craig Barton’s and Simon Woodhead’s Diagnostic questions site includes some excellent question collections for revision; as well as GCSE questions, there are quizzes for AQA’s excellent Level 2 Further Mathematics specification and for Core 1 at Advanced Level. Questions from the Oxford University Mathematics Admissions Test are also available.

GCSE Problem Solving: Steve Blades’ site has many excellent resources; on the GCSE page Steve has a section (near the end of the page) of eBooks.

Visual Patterns

Visual Patterns – Fawn Nguyen

From Fawn Nguyen comes the brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who’ve used visual patterns in their classrooms.