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.

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.

I have several references in various places on this blog to some great visualizations.
Time to put them all together!

Jeffrey Ventrella’s Composite Number Tree

From Jeffrey Ventrella this wonderful Composite Number Tree – I have used this successfully with many students. It makes a great starter. Students can work out themselves how the tree is being formed and comment on any patterns they notice.

Stephen Von Worley

Brent Yorgey

Another excellent visualization, animated factorization diagrams comes from Data Pointed. And here is Stephen Von Worley’s blog post, Dance, Factors, Dancewhich tells the tale of the animation. Noting his reference to Brent Yorgey’s factorization diagrams led me to Brent’s own later post, More factorisation Diagrams. I love Brent’s use of colour here. If you want even more on these great diagrams he has more information and links on this page on his blog, The Math Less Traveled.

The DfE document describing the GCSE Mathematics subject content is an excellent starting point for checking new content, allexam 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 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 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 Diagrams, Set NotationandLogic and Venn Diagramsin the student interactive resourcesand 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).

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.

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.

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

For 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.

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.

The Shape Sorter allows exploration of geometric properties of shapes.
Select Instructions and Exploration for clear information on how to use the resource.

A clear diagram can be so helpful in understanding a problem, look what one of my Year 7 students did when asked for the nth term of a sequence having been given a diagram:

Mobile Puzzles

For more Algebra with diagrams try Mobile Puzzles a collection of problems varying in difficulty for simple for young students to rather more complex.

For a very easy to use activity, try Jonathan Hall’s Algebra Tiles on his wonderful Mathsbot.com site.

And From Fawn Nguyencomes the brilliant Visual patterns, note the menu; the Galleryincludesblog posts from teachers and students who’ve used visual patterns in their classrooms.