If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include very clear worked examples. Whilst the workbooks cover the basic engineering mathematics and statistics teaching for first and second year students in a typical UK undergraduate engineering degree many of the workbooks include content appropriate for A Level Mathematics and particularly, Further Mathematics. For easy access to these resources, the HELM Project Workbooks are hosted by Loughborough University’s Mathematics Learning Support Centre. Alternatively, the complete set is hosted by the Open University. To access the Open University resources you will need to create an account (easy and free), this will also give you access to the numerous free online courses.
You will see from Loughborough’s description that each workbook varies in length from 25 pages to 75 pages (average 50 pages), and includes Mathematics (and Statistics) for engineering simply explained, worked examples, tasks and exercises with answers provided. Note the last workbooks in the series, Workbook 49 is a Student’s Guide and Workbook 50 a Tutor’s Guide.
The Student guide includes a description of the format of the workbooks and a comprehensive list of contents.
For exploring the Large Data, on AQA’s All About Maths see AQA Large Data Set –Guidance and Worksheetsincluding a tool to help support teaching the statistics content of the specification. This is an amended version of the large data set spreadsheet, the first three sheets are as on the AQA large data set but there are many additional sheets which allow students to explore the large data set. The tools are all provided for students, they do not need knowledge of Excel, meaning time can be spent on interpreting the data rather than learning about Excel. The worksheet on Exploring the Large Data Set could I think be usefully used lower down the school to get students used to working with more data.
For UK Examination Boards AQA, OCR A, OCR B MEI Further Mathematics.
This posts gives details of the specifications and teaching resources for Dimensional Analysis.
First a look at the specifications and we see a similarity between all three specifications. For AQA see the first image below. OCR A and B (MEI) additionally mention the relationship between the units of a quantity and its dimensions, with OCR B MEI adding ‘be able to change the units in which a quantity is given’.
Specifications AQA: Optional application 1 – mechanics Assessed at AS and A Level
AQA have a very helpful Teaching Guidance document for Mechanics, explaining how AQA have interpreted the content of the specification, the guide provides examples of how the content of the specification may be assessed.
The guidance is available on AQA’s free Maths portal for teachers, All about Maths. The resources are for teachers who offer, or are considering offering AQA maths qualifications. See this page for how to register.
OCR A Mechanics (Optional paper Y543) Assessed at AS and A Level
AQA Specimen questions paper and mark scheme. The only question on Dimensional Analysis is question 2, a multiple choice question on dimensional consistency. AS Practice Papers and A Level are available on All About Maths
For some Legacy questions and mark schemes see the paragraph on MathedUp below.
The Legacy Mechanics 3 papers which included Dimensional Analysis are available on All About Maths.
From amsp this brilliant collection of short videos produced by the legacy Further Mathematics Support Program supports the Further Maths Specification. I have used many of these successfully in class and recommended them to students to support their studies. Look at any of the examination boards to see the coverage for the course. Check the list for your examination board and you can find the videos on Dimensional Analysis for AQA, OCR A and OCR B MEI.
OCR Section Check In Tests and Delivery Guides OCR have very useful check in tests on Dimensional Analysis with fully worked solutions for OCR A and OCR B MEI. These both seem to use the same questions.
Each check in has 10 questions, the first four questions are are routine procedural questions which primarily assess ‘Use and apply standard techniques (AO1)’ The remaining questions primarily assess ‘Reason, interpret and communicate mathematically (AO2)’ and ‘Solve problems within maths and in other contexts (AO3)’
At least half of the questions are appropriate for the AS course.
These Delivery Guides discuss general approaches to the delivery of the topic, common difficulties and common misconceptions. A good approach, whenever a formula is taught, a dimensional analysis can be performed to check the validity. Both guides have the same suggested list of Further Resources including some good Nrich resources such as this article. The Springer notes are helpful, with clearly explained examples. The University of Guelph resource seems to have an unwanted full stop at the end of the address – the resource is here.
For a very comprehensive set of notes with many fully worked examples and exercises, have a look at Section 47 of the HELM Project which was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include very clear worked examples. For easy access to these resources, the HELM Project Workbooks are hosted by Loughborough University’s Mathematics Learning Support Centre. Alternatively, the complete set is hosted by the Open University. To access the Open University resources you will need to create an account (easy and free), this will also give you access to the numerous free online courses.
MEI’s fun and free summer challenge is back again this year.
To quote MEI
MEI’s fun and free summer challenge is back for 2020!
Our Calculator Crunch is a fun way to continue to engage Year 6s with maths whilst also developing their confidence with calculators, ready for maths at secondary school. The activities in the challenge provide extra practice for Year 6s and 7s in key areas of the maths curriculum.
Parents and carers can use the challenge activities with their children at home, and teachers can incorporate them into work they are setting for pupils either in school or remotely.
On each weekday from 15-25 June @MEIMaths will tweet a question for children to work on. Each question will involve using a calculator (basic or scientific) to solve an interesting problem. The problems are designed to deepen children’s mathematical thinking skills.
Teachers check the MEI website article for some great additional resources.
Jack Brown has created thousands of videos covering the complete A Level specification; the easiest way to navigate the videos is through his website, TLMaths.com.
Jack also has Further Maths teaching videos and exam paper walkthroughs. I see many useful videos on Proof, including the use of Induction for proofs of divisibility. This collection is growing and currently there are also videos available on many Complex Numbers and Matrices topics.
From amsp this brilliant collection of short videos produced by the legacy Further Mathematics Support Program supports the Further Maths Specification. I have used many of these successfully in class and recommended them to students to support their studies. Look at any of the examination boards to see the coverage for the course.
Joe Berwick has written a complete set of notes for Further Statistics 1, these are for the Edexcel and AQA specifications and include many very clear worked examples.
Sebastian Bicen (@BicenMaths) has created this really useful hyperlinked PowerPoint and pdf which provides Further Mathematics exam questions by topic. The exam papers included are as follows:
AS and A2 SAMs
AS and A2 Specimen
A2 Mock Paper
Jonny Griffiths investigative activities for the pure A Level Mathematics classroom are well known (details are included in the A Level resources pages, see RISPS. He has now published Further Risps, forty rich tasks for the pure Further Mathematics classroom.
The pdf not only provides the forty problems but also full teachers notes for each. The notes for each task begin with the topic or topics covered, identify the type of task, for example, introductory and state any preliminary knowledge required. This is a valuable resource for teaching Further Mathematics.
Investigating the first Risp on Matrices at the session this certainly would help students with fluency in finding the determinant of a matrix. Rich tasks like this can provide students with a greater understanding than just a traditional exercise and will hopefully stick for longer!