Good Mathematicians Can Go Backwards!

There is so much opportunity for thinking backwards when we teach – a great learning opportunity and also a problem-solving strategy.

I was delighted to present a session at IOE, UCL’s Faculty of Education and Society on Saturday 18th June and later in July for the NANAMIC Summer Conference 2022. We looked at lots of ideas and activities to get our students thinking backwards as well as forwards. The Slides from the session are available at the end of this post in PowerPoint or pdf format. The resources used are listed below.

Nrich Articles and Resources



Questions such as this can make a great starter for a lesson and provide the chance to discuss number operations and the relationships between them. Manipulating numbers like this can also help with algebraic manipulation.

Looking for some more examples of this type, I came across a really useful resource on TES, “If I know this then I also know …” by Piers Butler. This would make an ideal lesson starter. As it is an Excel spreadsheet, I thought it would be simple to add another worksheet with the answers and created the Excel file CY If_I_know_this_then_I_also_know_ which is a copy of the original, but just adds another worksheet with the answers.

Number Operations


Resource Collections

From AQA comes an outstanding resource, GCSE Mathematics: 90 maths problem solving questions. Strategies discussed include work back familiar and work back unfamiliar. Problems are indexed both by strategy and also by content.


Transum – Arithmagons

This post on Arithmagons includes the resources discussed and many more.

See also Digitisers from Jonny Griffiths.

Maths White Board

Standards Unit

A2 Creating and Solving Equations

This is an outstanding resource – many excellent activities here for the secondary classroom. Start by reading Improving Learning in Mathematics – Malcolm Swan

The resources are hosted by Nottingham University, including all the pdf files very clearly indexed. Note that this site includes the complete set of resources including the software; however, this software no longer works on modern browsers and mobile devices, but see note on my Standards Unit page for HTML5 versions.

Open Middle

Distributive Property, Open Middle

Mathsbot – Jonathan Hall
Variation Grids

Fill in the blanks

Nathan Day – Factor Trees

There are many suggestions for fill in the blanks resources in this post.

Coordinate Geometry Table, Transum, Adapted with permission from a learning resource created by Rob Southern @mrsouthernmaths.

The answer is – what was the question?

Andy Lutwyche – TES resources

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

Presentation Slides – PowerPoint, followed by pdf

GCSE Mathematics Paper 3

On Third Space Learning note their complete collection of free GCSE revision resources. See the GCSE Maths Checklist 2022 page which provides a GCSE maths checklist for all GCSE advance information (2022) topics listed by the exam boards Edexcel, OCR and AQA. Filters enable you to pick your exam board from AQA, Edexcel or OCR and your chosen paper.

Third Space Learning GCSE Checklist

A reminder of other useful resources for Paper 3 final revision we have:

From White Rose Maths (scroll down the page) their excellent pre-exam workshops for GCSE paper 3 for Edexcel, AQA and OCR exams boards. These workshops are suitable for foundation and higher students; the workshops are slideshows with answers included – ideal for final revision.

White Rose Maths

Corbett Maths

See GCSE 2022 on Corbett Maths, John Corbett has released lots of high-quality support material for Edexcel, AQA, OCR, and CCEA for both Foundation and Higher. You will find papers, revision checklists (hyperlinked to videos), also YouTube playlists, content is still being added. The papers are in the style of John Corbett’s “A Bit of Everything” papers – a resource I have always liked.

Mathsbox Skills Checks

On Mathsbox, we have some really useful skills checks – one or two-page documents with answer sheets aligned to the AQA, Edexcel and OCR advance information.

Craig Barton – Diagnostic Questions

Craig Barton has provided links for quizzes on Diagnostics Questions mapped to Edexcel’s and AQA’s Higher and Foundation advance information.

For Edexcel schools, a very useful read from Christine Norledge is GCSE Maths Paper 2 2022: Summary Of Topics, Questions & Planning For Paper 3. In this post, we have a very careful analysis of the papers and suggestions for selected revision topics for Edexcel’s GCSE Paper 3. You can find Practice Papers for AQA, Edexcel and OCR from Third Space Learning here.

PixiMaths – Edexcel Higher 2 & 3
Maths Genie

On Maths Genie, you will find videos, exam questions and solutions for AQA, Edexcel and OCR.

From PixiMaths, Best Guess Papers and Mark Schemes for Edexcel Paper 3.

Jess Prior Breakfast Warm-Up, Edexcel

Edexcel Breakfast Warm Ups from Jess Prior. Jess has provided warm-ups with four different levels of difficulty – two Higher, and two Foundation for Edexcel paper 3.

From Prime Maths, Foundation and Higher Edexcel GCSE revision papers, Paper 3.

If you are looking for a set of short questions, remember Wayne Chadburn’s little bit of Maths each day calendars, see May (paper 3). These calendars have been written to focus on each of the papers and the topic lists announced by Edexcel. Solutions are provided.

Wayne Chadburn

From 1st Class Maths A full set of prediction papers for AQA GCSE Maths including video solutions is available free.

See also – A Level Summer 2022 and Examinations – Mathematics Summer 2022.

Mathematical Miscellany #66

Still in the examination season – I have updated GCSE Revision Papers 2 & 3.

Jess Prior Breakfast Warm-Up, Edexcel

See also A Level Summer 2022.

Parallel from Simon Singh is written to challenge your student mathematicians; all materials and resources are completely free and teachers will have access to all the student scores from the Parallelograms which are automatically marked.

Some exciting news currently:

Complete Maths CPD

From Complete Maths, try some Bitesize CPD, CPD Shorts.

Free for students who are intending to study Mathematics at university, an online event from the Institute of Mathematics and its applications, ‘What it’s like to study Mathematics at University?’ Conference 2022. Find out what it’s like to study Mathematics at University, hear from some current students and guest speakers on topics such as university applications, interviews, tips for entering the field of mathematics at an early career stage, and postgraduate research. Full details are available on the IMA site.

From MEI, it’s nearly Calculator Crunch time! Have a look at these excellent free resources from previous Calculator Crunch competitions.

Calculator Crunch 2021