Identities – Equating Coefficients

Looking at the GCSE content, we see that A6 is on equations and identities and using algebra to show expressions are equal and to construct arguments and proofs.

The AQA teaching guidance is as follows, note the inclusion of “use identities to equate coefficients”.

Resources are not always easy to find for this topic and depending on the GCSE specification students have followed then the first time they meet this important technique may well be at A Level.

So – a resource collection to practice this skill…

To begin, we must be sure students understand what an identity is, we could use this self-checking exercise from Transum Mathematics, Identity, Equation or Formula.

The following resources all provide practice in equating coefficients all resources include answers.

Identities (Equating Coefficients) Foundation – Mr Thompson10 questions. 3 of which have two unknowns.

Identities, one of a set of Algebra Skill Review Sheets from Miss B’s Resources.
6 questions on identifying equations and identities and 5 on equating coefficients.

Equating Coefficients (supporting materials – Answers)
from Dave Taylor, Increasingly Difficult Questions

Corbett Maths, 17 varied Practice questions and video.

Nathan Day – Identities, PowerPoint and pdf

Equating Coefficients in Identities – Jo Morgan

Two versions are available – an easier version (8 questions) and 10 questions on the original version.

Something I frequently do is use colour for emphasis and certainly this is a topic where colour can make worked examples clear.

Mathematical Miscellany #89

A Mathematics resources compilation:

From the brilliant 1st Class Maths, 114 Edexcel Foundation Exam Questions covering the full specification with video solutions to all questions.

Christine Norledge has created a searchable database of all Edexcel GCSE maths past paper questions from June 2017. Christine intends to gradually add shadow questions for each paper and topic and will update the database with these links once the resources are available.

Remember that you can search for questions on Mr Neill’s brilliant resource for Edexcel, AQA and OCR, or use ExamQ from Mr Watts:

From Mr Neill, a brilliant resource, all Edexcel, AQA and OCR GCSE maths questions categorised by topic with answers from June 2017 to Nov 2021 (9-1), available all on pdf, PowerPoint or Promethean. And to add Mr Neill’s latest update: “WEBSITE UPDATE – JUNE 2022 ADDED. Thanks for all the support, over 70,000 visits. Added a few extra surprises under miscellaneous. Take a look at the QR coded past papers. A real favourite with my students.”

On ExamQ from Mr Watts you can quickly search for Edexcel Maths GCSE and A-Level exam questions. You can choose from GCSE Foundation or Higher, AS or A level, you can also select by exam series, paper, area and topic.

The interface is very clear indeed, easily display the questions or mark schemes.

A September update from the legend that is John Corbett.

September Update

• 1015 new practice questions created
• 50+ hours of video solutions
• 27 new practice question booklets
• 84 practice question booklets updated

The quick video goes through some of the work that John has been working on recently and his aim to finish updating the Practice Questions and the video solutions this academic year.

I was delighted to see in the comments that one of John Corbett’s next projects is A Level.

Remember that GCSE Level 2 Further Maths is also available on Corbett Maths.

King’s Maths School publish a weekly maths challenge designed to intrigue students aged 13-16 who are interested in mathematics.

From Emily Rae, a lovely resource – Video of the week for A Level students, available on Emily’s padlet – KS5 Maths – Enrichment and Extras; two Word documents are available, one with two years’ worth of video links each with a short description to introduce each clip and a second document with the links only.

Mathematical Miscellany #88 – back to school

You can see full details in the Eedi Newsletter.
Craig’s instructions:
To access these materials:
1. Log-in / register at https://eedi.com (you can use your DQ login)
3. Click View the collection
4. Find a topic you are teaching soon
5. Click on the Eedi link!

Note the tabs on the spreadsheet, All quizzes, White Rose (for Years 7, 8 and 9), and Maths Mastery (for Years 7, 8 and 9)

For every topic you will find:
1. A 5-question DQ quiz
2. Worked example videos
3. Fluency Practice
4. Intelligent practice
5. Problem-solving

A reminder of the resource collections for

Each of these pages includes a description of the GCSE content and links to resources, there is a link at the top of each page for sites easily searchable by topic; the old but still useful National Strategies Exemplication Examples are also included.

Information and resources for IGCSE Mathematics is available from the top menu tab, GCSE/IGCSE/L2 Further Maths (14-16)

Also available from the top menu tab are resources for AQA Level 2 Further Mathematics

Many excellent resources for A Level teaching can be found on this page, A Level (16+) Resources. I have included the A Level baseline test and resources from Pixi Maths. This very useful set of resources includes solutions as well as the baseline test, a question-level analysis and also an intervention booklet and solutions.

We also have on Webmaths, new for A Level Maths, “3 a day” for Year 12 Maths; these resources look excellent; you can also find Year 13 3 a day. The starters are included in the Advanced Level Starters collection.

Staying with the Transition from GCSE to A Level, this post, GCSE to A Level Transition includes a resource collection for students starting A Level Maths, and supporting their Year 12 work.

Information and resources on University Admissions tests can be found here.

Mathematical Miscellany #86 published in July includes the following resources:

Some updates to this popular collection…

All resources are included in the Knowledge Organisers collection which includes resources for KS3, KS4 and KS5 (ages 11 – 18).

My post on Knowledge Organisers begins with some comments on an organiser from William Emeny, realising the original link to that organiser is broken as sadly, Great Maths Teaching ideas is no longer available, I have uploaded the file I discussed to the post.

Last week I noted that Mrs D Maths has been writing Knowledge Organisers for A Level Maths, ( free on TES Resources). She is still busy, we now have a knowledge organiser on Binomial Expansions.

For a collection of Cornell notes linked to topics found in the Maths curriculum see Mr Hawes Maths.

On the subject of notes, a reminder of the brilliant series of Helm Notes for older students.

Mathematical Miscellany #87

Mrs D Maths has been writing Knowledge Organisers for A Level Maths, ( free on TES Resources). These are included in the Knowledge Organisers collection which includes resources for KS3, KS4 and KS5 (ages 11 – 18). Very recently, she has written an organiser for Year 2 Functions and Graphs.

These organisers are included in the Knowledge Organisers collection which includes resources for KS3, KS4 and KS5 (ages 11 – 18).

Looking ahead to return to school for UK schools, from Pixi Maths see the A Level baseline assessment. This very useful set of resources includes solutions as well as the baseline test, a question-level analysis and also an intervention booklet and solutions.

Staying with the Transition from GCSE to A Level, this post, GCSE to A Level Transition includes a resource collection for students starting A Level Maths, and supporting their Year 12 work.

I was very interested to see this article from NCETM on Three calculations to encourage and support fluency. Note the acknowledgement; the examples are from Gwen Ineson and Sunita Babbar, from Brunel University. See a related chapter, part of a wider publication, by Gwen Ineson and Sunita Babbar in Mental maths: just about what we do in our heads?

From the GeoGrebra resource team, a resource to interpret meanings of different rates of change across a graph that represents the water level in a hot tub.

For some more watery demonstrations, see Pouring and Filling.

See the page Exam Results 2023 for results statistics and grade boundaries from the UK exam boards.

FFT Education Datalab, check their blog for the latest information. See A-Level and other level 3 results 2023: The main trends in grades and entries.

Graham Cumming on Twitter has been crunching the numbers since the A Level results were published.