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



Numbers – Visualizations

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

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

Brent Yorgey

Another excellent visualization, animated factorization diagrams comes from Data Pointed. And here is Stephen Von Worley’s blog post, Dance, Factors, Dance which 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.

Visual Patterns

Fawn Nguyen – Visual patterns

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.

On the subject of Diagrams generally I have several posts on the subject.

Diagrams in Mathematics

Brilliant - Balances Warmup

Brilliant – Balances Warmup

Seeing this problem on Brilliant recently reminded me how useful diagrams can be in the study of Algebra. I solved the problem using Algebra (with a little colour for clarity!) as follows:

Brilliant Balances solution

select for larger image

Sybilla Beckmann’s paper, Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4–6 Texts Used in Singapore is an interesting read on the subject of the use of diagrams.

Sybilla Beckmann paper

Sybilla Beckmann paper

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:

Master Level

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.

Algebra Tiles Factorisation

NCTM Illuminations – Algebra Tiles

Algebra Tiles are such a good way to demonstrate algebraic manipulation, see the online demonstration on

Write x2+6x+11 in the form (x+a)2+b

Complete the square

Complete the square – use algebra tiles

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

And 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.

Visual Patterns

See also:
Here’s the diagram, what’s the question?

Here's the diagram, what's the question?

Here’s the diagram, what’s the question?

…and for some lovely visualisations have a look at this post.


Stephen Von Worley