Transition Time

Edexcel’s transition to A Level Maths videos and worked examples are a very comprehensive set of free resources designed to help the transition from GCSE to A level Maths. The content focus is on the overlap between GCSE Maths and the first year of the A Level Maths course making the resources useful not only for initial transition but also for the first year of the course.

From Sparx Maths, have a look at their Transition Booklets, one for Year 6 to 7 and one for GCSE to A Level; these booklets are free whether you have Sparx Maths or not. The Year 6 to 7 booklet with over 130 questions is based on the Year 6 DFE/NCETM ‘ready to progress’ guidance from June 2020. The GCSE to A Level booklet uses over 120 questions taken from 11 key topics on Sparx Maths. Answers can be obtained by completing a form with your school details.

OCR Transition Algebra Fractions
OCR- Bridging the Gap – A Student Guide

For students going on to A Level then a really useful publication is use OCR’s brilliant guide for students Bridging the gap between GCSE and AS/A Level Mathematics – A Student Guide. With sections on Algebra, Trigonometry and graphs including examples, question practice on key topics and suggested reading before starting the A Level this is so valuable for students.
pdf format: bridging-the-gap-between-gcse-and-as-a-level-mathematics-a-student-guide

Hegarty Maths

Free lessons from Colin Hegarty recorded on YouTube are available to help GCSE students prepare for A Level Maths.

From TL Maths GCSE to A-Level Maths Bridging the Gap is a series of videos looking at some of the basics of GCSE Maths Higher Tier that students should be proficient in before they start A-Level Maths.

You could also look at Step Up to A Level Maths from The Centre of Innovation in Mathematics Teaching which helpfully lists skills you should be confident with and provides resources to support your study of these skills.

AMSP – Transition To A Level Mathematics – Essential Skills

From AMSP – check Transition to A Level Mathematics – Essential Skills.

These Transition Takeaways from Mohammed Ladak have been specifically chosen to help with A Level Maths preparation.

Transition Resources

The many useful resources from OCR have already been mentioned; also available from OCR are transition guides. See for example this Equations Transition Guide which is very clear on the differences in the demand and approach at the different key stages. Each transition guide includes the relevant checkpoint tasks, in the Equations transition guide these activities focus on solving equations in one variable including those that require some rearrangement.

OCR Transition Guide

For the transition from KS2 to KS3 see MEI’s transition resources including an excellent series of webinars. The webinars explore curriculum and pedagogical continuity across the KS2 to 3 transition and look at the Primary Maths Guidance Document. The guidance for Year 6 is a valuable document for looking at the transition from Year 6 to Year 7 and includes example assessment questions for each of the ready-to-progress criteria.

Primary Guidance – Year 6

NCETM has produced an extensive library of resources offering support with the Primary Guidance documents. This includes 79 PowerPoints, these focus on the ready-to-progress criteria in the DfE maths guidance for KS1 and KS2. These can usefully be viewed by topic or by year.

You can find NCETM guidance videos on YouTube.

NCETM – Checkpoint sample

NCETM’s Checkpoints are diagnostic activities designed to help teachers assess the understanding students have on leaving primary school. You can see three examples of Checkpoints activities and teachers of Year 7 can download the first Checkpoints activities using their school or organisation name and email address. There will be further Checkpoint activities published, enough for three Checkpoints a week across the school year. 

Engaging Explanations

I was delighted to present a session at #MathsConfOnline from Complete Mathematics, August 22. The resources discussed in the session are all provided here with some relevant additional content.

‘When presenting content and ideas to students we need ‘engaging explanations that are just right for the students: neither too short nor too long; neither too complex nor too simple.’

Coe, R., Rauch, C.J., Kime, S., & Singleton, D. (2020). Great Teaching Toolkit: Evidence Review. Evidence Based Education.

Great Teaching toolkit: Evidence review – complete report, note the individual elements on page 6, including 4 Activating hard thinking.

Rosenshine’s Principles of Instruction – Research-Based Strategies That all Teachers Should Know.
(Further commentary and resources can be found in my post, Rosenshine’s Principles in the Mathematics Classroom).

White Rose Maths – Small Steps-Functions

White Rose Secondary Resources including Complete Secondary Small Steps

AQA – 90 maths problem solving questions

AQA’s 90 maths problem solving questions supports the problem solving requirement (AO3) of GCSE Mathematics. Very useful summary lists link questions to process skills and to content areas. Answers are provided for all the problems and very helpful full commentaries are given on 30 of the problems.

AQA GCSE Examination Questions

AQA GCSE Assessment Resources, AQA legacy GCSE question papers


There is also a good deal of evidence that the use of worked examples can
be helpful in introducing new ideas (Booth et al., 2017; Sweller et al., 2019).
Particularly effective are ‘completion problems’ where students are given
partial solutions and required to complete them
. These can help students to
focus on the examples but also manage the difficulty level while retaining
authentic tasks

For a collection of such problems, see Fill in the blanks…

Open Middle problems in GeoGebra

Distributive Property: Open Middle Theme

Building Blocks – Andy Lutwyche

Andy Lutwyche-Building Blocks

Spot the mistake resources including Erica’s Errors and Clumsy Clive from Andy Lutwyche
Show that… and What was the question? from Andy Lutwyche

PhET Interactive Simulations, University of Colorado Boulder,

Use of Technology including PhET Simulations

Colour in Mathematics

Colour in Mathematics – the use of colour to add clarity

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

Colin Foster – including Mathematical Etudes

Transum Mathematics

Transum – Venn Paint Transum – Topic Index
Transum  Maths Map (Students)

AQA – Bridging the gap

AQA – Bridging the gap

This set of AQA resources was originally designed to support teaching and learning for the cohorts of students who studied the 2007 Key Stage 3 Programme of Study and were preparing for the then new Mathematics GCSE (8300). The resources are still very useful for students in KS3-KS4.
KS3-4 Bridging the gap.

This series of termly tests covers Years 7, 8 and 9 and can be used to check understanding as well as showing younger students what GCSE papers look and feel like. Extension tests are included and analysers are available for all tests.
AQA Key Stage 3 tests for Years 7, 8 and 9.

AQA Key stage 3 tests

AQA KS3 Tests

Maths on Holiday

We have seen many great pictures on Twitter recently tagged #mathsonholiday.

Looking back over some previous posts, I thought I would check and update some holiday-themed posts.

An Italian holiday included a visit to the wonderful National Cinema Museum in Turin – see the Mathematics in the Movies post.

National Cinema Museum, Turin- Photograph by David Young
This image has an empty alt attribute; its file name is milan-cathedral.jpg
Milan Cathedral – photo by Sophie Young

Visiting Milan and wandering around the lovely Cathedral (one of the largest in Europe) I was struck by the geometry all around!

Some interesting sites on Mathematics and architecture:

From Maths Careers, see Interesting Buildings Based on Mathematics and from Tripbase, 9 Most Mathematically Interesting Buildings in the World.

The Tripbase article includes the cathedral in Barcelona Designed by Antoni Gaudi. 

Barcelona - Cathedral
Barcelona – Cathedral – photo by David Young

For some further reading Plus Magazine has an article on Perfect buildings: the maths of modern architecture by Marianne Freiberger.


A great resource on TES for when we get back to school is Laura Wilson’s Plans and Elevations, a PowerPoint of images showing plans and elevations of some famous buildings.

Holiday Pictures

All photographs by David Young, taken in the attic space of the Casa Milà Barcelona a building designed by Antoni Gaudí, constructed between 1906 and 1910.

cosh x Desmos image

Imaginary Exhibition


I do like to keep my eye open for mathematical pictures hence: (see Tetrahedral Numbers on Mathisfun)

Neuwied Schloss cannons Photograph by David Young
Neuwied Schloss Cannons –  Photograph by David Young
Bottle sequence
Barrel holding equivalent of 200,000 bottles


The Mercier champagne barrel which contained 200,000 bottles of Mercier Champagne, Mercier Champagne House, Epernay France

Algebra Resources

Back in March, I wrote, Number Resources, still very much a beginning and a work in progress, I have been reorganising pages. Making things easy to find is a never-ending task! Having written this blog since 2009, many older posts are still very useful – I want to make those easier to find.

Hence some new pages, the first created was Number under GCSE (14-16). This shows GCSE content and links to some favourite posts, also to sites that are particularly easy to search by topic. Further posts and resources and sites will be added, this is quite a project, but watch this space!

I have now added Algebra which brings some posts together such as:

Algebraic Notation

Factorisation of Quadratic Expressions

Lyszkowski’s method

Simultaneous Equations

White Rose Maths – Exemplar Questions


Transum Mathematics – Iteration


Activities to help learn reasoning and proof

Links to sites that are particularly easy to search by topic for Algebra are included, including some brilliant Underground Mathematics questions to challenge your GCSE students.

Underground Mathematics Algebra Review Questions (old O/AO level).
Some favourite tasks to challenge your GCSE students:

Resource typeTitle
Review questionTwo values of x that differ by 5 satisfy x2 −12x + k = 0, what is k?
Review questionHow small can this triangle be?
Fluency exerciseQuadratic solving sorter
Review questionCan we solve these simultaneous equations of degree 1 and 2?
Review questionCan we simplify these algebraic fractions?
Review questionIf we know two values satisfying a quadratic, can we find the quadratic?
Rich exampleQuadratic grids
Building blocksWhich quadratic?
Review questionCan we find the three inequalities that define this region?
Review questionCan we solve these simultaneous equations that involve reciprocals?
Package of problemsName that graph
Building blocksGradient match
Fluency exerciseMultiple manipulations
Review questionWhen are these quadratic inequalities true together?
Building blocksA tangent is …
Review questionWhen are the coefficients of a quadratic equal to its roots?
Many ways problemTwo-way algebra
PhET Interactive Simulations, University of Colorado Boulder,

If you like the old exemplification examples – there are still some great questions, these have been added to the following pages:

Algebra Exemplification Examples

Algebra – Exemplification Examples

Watch this space for further additions to all these pages.