Mathematical Miscellany #25

dates as operations 2019Have a look at the latest newsletter from Simon Job’s MathsLinks, Don’t just write the date this year – write it as a number sentence using the digits of the date in order.

dynamic calculusA brilliant resource shared on MathsLinks here – Dynamic Calculus, a collection of interactive learning objects for teaching calculus. This is an HTML version, there is no reliance on the Java version of GeoGebra and no use of Flash.

Or try Errors in Measurement, a very clear GeoGebra resource.
errors in measurement

Subscribe to the newsletter and/or follow @mathslinks on Twitter or Facebook for regular updates – highly recommended.

I do like the ClassWiz calculator and have been collecting some useful videos from the excellent Calculator Guide on this page, many of which I have shown students in class. Checking some ClassWiz resources from the Calculator Guide, a happy discovery, Learning Mathematics with Classwiz, a free ebook by Barry Kissane; all you ever wanted to know about the calculator with exercises, activities and notes for teachers.


stem jobs
MEI (thank you) alerted me to this poster – 100 jobs in STEM! This poster and many other careers resources are available from Tomorrow’s Engineers. Looking at the UK Statutory Careers Guidance we see that schools should link curriculum learning to careers. We have the brilliant Maths Careers site to help us here.
careers 4

Look at all the events available through The Advanced Mathematics Support Programme (AMSP); the events include free online courses for teachers in state-funded schools and colleges in England.

amsp courses

AMSP On Demand Professional Development

Use the Event format dropdown menu for event types, one type is On Demand Professional Development; teachers can access the materials at any time over a period of up to one year. I have signed up to ‘Preparing your students for the MAT and the TMUA’ course myself; the materials I have looked at to date are excellent. In each unit short videos guide teachers through the ideas of the topic along with practice materials, triggers for reflection and suggestions for further study. Forums are provided for teachers to interact and collaborate with others studying the same material and all the forums are monitored by an expert tutor who will respond to queries.


A reminder that the AMSP Problem Solving Competition closes 1st February and is for any students in Years 7 to 11. Can your students solve a vexing vexillology problem? Full details are available on the AMSP competition page.


Multiple Choice Questions

Multiple Choice Example
I have been updating posts on Multiple Choice Questions to make sure all links are working correctly and any outdated resources removed.

The posts Multiple Choice Questions and Multiple Choice for older students can be found on this new page, Multiple Choice Questions under Problems and Activities.

There are many excellent sources of questions in these posts, Don Steward for example, who has so many outstanding resources on his Median blog, includes some multiple choice quizzes.

Don Steward Multiple Choice

Don Steward – Rearrangement Steps

See this on rearrangement for example. Note that Don has a collection of practice and quiz questions which includes multiple choice quizzes.

amcA recent happy discovery is the excellent multiple choice questions from the American Mathematics Competitions (AMC). There are several competitions which increase in difficulty by student age. Detailed Problems and solutions are available, I do like this problem, a good one to use when teaching Systematic Listing Strategies perhaps.

multiple choice phil bruce

Phil Bruce – Multiple Choice Starter Questions

On TES resources, author pbrucemaths has a brilliant collection of clearly indexed multiple choice starter questionsPhil Bruce has aimed to cover every objective on the GCSE syllabus.

multiple choice

Colin Billet – GCSE Multiple Choice Questions

Also on TES, Colin Billet has created multiple choice questions from old GCSE papers, one set is for the higher tier and another for foundation.


Mathematics for Science

gcse science mathematical skills

GCSE and A Level Science includes much mathematical content, it strikes me that is important for Mathematics Departments to be aware of the mathematical requirements for these qualifications and where appropriate use resources which will support Science as well as Mathematics. The GCSE subject content for science clearly shows the GCSE requirements in Appendix 3, page 49; if we are teaching Algebra, changing the subject of a formula, for example, we might as well make sure we include formulae required for GCSE Chemistry and Physics or teaching Histograms, we can be aware that it is also a requirement for GCSE Science.

AQA Teacher Training Pack – Maths in Science

From AQA one of their excellent Teacher Training packs includes Maths in Science. Included in the Activities booklet you will find examples for discussion, AQA suggest:

For each of the examples on pages 6–10 of the Activities booklet, discuss:

  • approaches you could use to help students to be able to access these types of questions
  • how this approach might be different in maths lessons
  • whether there any other differences between the two departments.

AQA Teacher Training – Maths in Science

We also have, on pages 18-21 of the Activites booklet a very comprehensive table of Misconceptions and common errors.


Guide to Maths for Scientists – Pearson

There is plenty of material available for supporting the teaching of Mathematical Skills for Science, try the following:

On Just Maths, note this Guest Post, Maths in Science, which includes PowerPoints and worksheets from an INSET session for Mathematics and Science teachers. Also, note the Guide to Maths for Scientists from Pearson.

The excellent Teachit Maths site has been recommended before on this blog, Teachit resources are also available for other subjects including Science. The generous subscription model options, like that for Mathematics includes free membership with access to all the pdf resources. Note the Maths Skills in Science resources.

tes resources

TES Resources

From TES Resources, a Maths in Science Scheme of Learning is available; this resource looks very helpful, Maths skills are shown in scientific contexts. Written as a transition unit before beginning GCSE work. The aim of the scheme was to increase the confidence of the students in the areas of maths that were common to all three sciences. The author wrote the scheme after consultation with the maths department to guide as to when and how these areas were taught in their school.

The scheme covers standard form, orders of magnitude, significant figures, shape (areas and volumes), ratios and interpreting graphs.

The GCE A Level subject content for science, clearly states the mathematical requirements in Appendix 6, pages 24-40. The assessment of quantitative skills will include at least 10% level 2 or above mathematical skills for biology and psychology, 20% for chemistry and 40% for physics, these skills will be applied in the context of the relevant science A level.

The examination boards have helpful teaching resources for each subject, looking at AQA for example:

Teaching Resources
Biology Teaching Guide for Statistics in Biology

Looking at the Chemistry website resource list, we see that The Royal Society of Chemistry provides many resources for schools; a search on Maths returns a large collection of Maths resources for Chemistry.

aqa biology transition guide

AQA Biology Transition Guide

physics transition guide

AQA Physics Transition Guide

The teaching resources include a transition guide for Biology (Biology answers), Chemistry (Chemistry answers) and Physics (Physics answers) These guides include mathematical activities for students to complete.

Maths Skills Briefings for A Level Science
AQA worked with a group of schools from Camden in London to create maths skills briefings to help with teaching the specific maths skills. Each episode is intended to fill about 15-30 minutes of a lesson and includes a PowerPoint presentation, Lesson plan and Worksheet for each skill.

Similarly, OCR has very helpful teacher guides and resources. Use this search page to search for teaching resources. Choose your qualification and resources type to explore the resources, look at the handbooks for each science, several mathematical skills handbooks are available.

pearson biology student maths support

Biology – Student Maths Support – Pearson

Pearson too has excellent guides for both students and teachers, see their Maths Guides for Biology, Chemistry and Physics.

On STEM Learning, we have Biology Resources for Home Learning which includes, for 16-19 years olds, Maths Skills for Biologists. For the resource in a convenient form with clear worked examples, download the pdf file.

Maths Skills for Biologists

Maths Skills for Biologists – STEM Learning