With all A Level courses now linear, Retrieval Practice is essential. From crashMaths these AS Maths Key Skills Check worksheets will be very valuable for Year 13 in the second year of their A Level course. The Skills Checks are all on Pure Mathematics.

Further recent updates to Advanced Level resources include:

This guide has been added to The Use of Technology Page, also to the latest update of this file on technology resources mapped to content which can be found on The Use of Technology Page. The file includes links to instructions for the Casio ClassWhiz calculator.

Updates to the Further Mathematics content include this link to a post on Maclaurin Series for students which includes Desmos pages. The post also links to some useful notes and examples for students.

For Further Maths, this post on the new topic of Differential Equations may be useful. Again, notes and examples are linked to, also instructions on using WolframAlpha to check work on Differential Equations. WolframAlpha is also useful for checking work on Matrices.

The teaching of Polar Coordinates offers an ideal opportunity to use Technology.

Dr Frost Maths: Full Coverage – Algebraic Proofs involving Integers

On Dr Frost’s site, it is possible to browse all his excellent resources by topic so if, for example, we search on KS2/3/4 then Algebra, we see Algebraic Proofs. Under Proof the Year 9 file PowerPoint file is excellent for high ability students, you will also see a very useful worksheet on counter-examples. I do like Dr Frost’ Full Coverage resources which are compilations of GCSE questions (GCSE – UK qualification taken at age 15-16). Answers are provided at the end of the document. Explore this outstanding site full of very high-quality resources, all Dr Frost’s clear indexing make the resources simple to find.

MathsBot – GCSE Questions

MathsBot is another superb site and very easy to find questions by topic, the GCSE Exam Style Questions are a good example. Select any filters and note the many question topics.

Maths4Everyone – Algebraic Proof Workbook

This search of TES resources returns several highly rated free resources on proof.
Try Algebraic Proof – Expressions and Proofs from James Clegg, the worksheet “teases out expressions to show certain situations (e.g. the sum of 2 consecutive odd numbers) and features options on an “answer grid” at the bottom of the page.” There are also some questions to try. From the excellent Maths4Everyone this Algebraic Proof (Workbook with Solutions) has numerous problems to try as well as very clear examples. Answers are provided – highly recommended (as are all the resources on Maths4Everyone by David Morse).

Also from Nrich, try this Interactive Proof Sorter example which works on my phone as well as on my laptop. This would make a good starter – if you want to give out paper copies for students to work on as they come in, you can easily fit 4 copies to an A4 page!

Teachit Maths, though a subscription site offers an extensive collection of activities as free pdf files. A search on Proof returns some great resources. I do like this Worksheet on Proof which has 20 varied tasks aimed at older students 16-18, though some would be accessible to younger students. Full teachers notes on solutions are provided. In the task illustrated here, a full proof is given and students asked to explain each step.

(This post is an update of my post from 2013 and now includes the more recent, excellent resource Goal Free Problems from Peter Mattock.)

Using diagrams as prompts like this is excellent for Retrieval Practice.

Seeing this well-received resource, GCSE Question Prompts on TES reminded me that I have successfully used this idea myself before. For example for GCSE revision I have given students a selection of various triangle diagramsand asked them what the question might have been. This proved to be a useful way of revising several topics – some of which students sometimes mix up! For several of these triangles there are many possibilities and students can be asked which lengths and / or angles they could work out.

Further excellent examples come from Mark Greenaway – GCSE Visual Prompts for both Higher and Foundation. Mark’s resources (Prompts 1) show the diagram first and then also include the complete question. Prompts 2 provides 25 starter prompts for students to produce their own questions and answers using the given information.

Peter Mattock has created Goal Free Problems, a site he set up, in his own words “to allow teachers to access and share goal free problems created by myself and others. Goal free problems have been proven to support pupils in improving their knowledge and understanding by removing the cognitive load of the goal and therefore not prompting means-end analysis of a problem.”

Here you will find hundreds of questions categorised by topic; there are also mixed questions available. A wonderful resource.

On the subject of diagrams, I really like Tom Sherrington’s post “Empowering students to own their learning solves maths problems“; a great idea to start with a diagram with no labels at all as a way into a problem. I tried this with Year 10 (very able students), presenting them with only Tom’s diagram and was very pleased indeed with the outcome. I didn’t even give them the question – just the diagram (a small copy each) and we started by deciding what the question might be. We quickly got onto areas as a possibility so then answered Tom’s original question ‘what fraction of the shape is shaded?’. The class happily discussed how to solve the problem and a student asked ‘can we write on the diagram?’ which of course was perfect – absolutely they could write on it. We solved the problem, revising some basics and had the discussion about what to do when you don’t know what to do! I will certainly use diagrams with no labels again.

This idea could be used for a starter on just about any topic – provide students with an image or perhaps just an expression and ask them to write a question to go with the image.

MEI have an excellent free collection of GCSE starters. Designed for the start of a GCSE lesson, the diagrams and questions are very clear and will display well on the IWB. There are several starters under the following headings: Mathematical Reasoning, Number, Algebra, Geometry and Measures and Statistics and Probability. Files with the answers and teachers notes are also provided. Many of the diagrams here could be used for students to write their own questions. It is not always possible to have the IWB up and running, particularly if you are coming from a different room and I do like to get students working straight away. Experimenting, I found that I could take a screenshot (I do like the Windows snipping tool) and fit eight to a page! I used a Word document with very small top and bottom margins and a two column layout.

Staying with MEI, Bernard Murphy has some great ideas here on using pictures in A Level trigonometry. Look at this diagram – all the trigonometric ratios!

How creative can you be? I wonder what they would make of something like this…

For A Level Teaching, Dr Jamie Frost has as always been very busy! These high-quality resources (slides/worksheets) provide complete coverage for the new specification.

Dr Frost has also provided very clear instructions for using the Casio FX99-1EX Classwiz calculator which you will find on his site. To really challenge your students Dr Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This document is 156 pages of categorised questions (brief answers are given). Also available is a pdf file of just the STEP questions.

Emma McCrea alerted us to The 5×8 Card generated by a SERP Team. You can read more information on the background to this resource here.

Not having come across the SERP website before I investigated further and found more delights. I particularly like AlgebraByExample which is a set of Algebra 1 assignments that incorporate worked examples and prompt students to analyze and explain. These look like good resources for discussing common misconceptions.

SERP – Algebra by Example

Note the tabs at the top of the home page, from the Materials tab you can access all the resources. Note the free downloads at the SERP download centre where you can download individual resources, or very simply, use the menu on the left to download the complete workbook; answers are also available as are introductory guides for teachers and students.

With UK A Level results having recently been published, the Results 2018 page has been updated and checked. Links to grade boundaries and results statistics are provided and note the useful resources from Ofqual. GCSE Links will be checked on Thursday 23rd August.

It is still Summer holiday time for some of us, so I’ll end with this lovely puzzle I had not come across before. See plus magazine – Finding the nine. (There is a link to a very clear solution in the video). The