Mathematical Miscellany #23

Equality Explorer 2 - PhET SIMS

Equality Explorer – PhET Simulations

Firstly in this resource collection, a reminder of the many excellent PhET Simulations.


Try Graphing Slope-Intercept which allows you to easily demonstrate the equation of a straight line.
PhET slope intercept

Note the Competitions page, there are just a few more days available to submit an entry for The Royal Statistical Society’s Statistic of the Year 2018? Complete a simple nomination form by 25th November; full details are available on the site. Last year’s winners are fascinating, do you know the percentage of the United Kingdom land area that is densely built upon?

Learn Videos

Graspable Math – Tutorial Videos

A reminder of the excellent Graspable Maths; have you tried scrubbing numbers? This canvas on fractions illustrates the feature; select scrub from the top menu and see the feature in action. Thank you to the original author, it is very easy to copy a canvas and adapt to suit your class.

Here, Graspable Math took one of Dave Taylor’s wonderful Increasingly Difficult Question sets and created a canvas of the problems.
IDQ Changing the Subject



Edexcel Codebreaker

Edexcel Worksheets

Looking back at previous posts in this series, Mathematical Miscellany #16 on the many excellent teaching resources from the examination boards is very popular, this collection has been given its own page in the Problems and Activities series.

Another reminder, this time of the great resources on crashMaths.

With all A Level courses now linear, Retrieval Practice is essential. From crashMaths these AS Maths Key Skills Check worksheets are very valuable for Year 13 in the second year of their A Level course. The Skills Checks are all on Pure Mathematics. My Year 13 students have now completed several of these as starters and appreciate them very much. I have found I can snip the questions and get 4 copies on an A4 sheet – so very economical too!

crashMaths Skills Check

GeoGebra Resources – Nrich and MEI

Nrich GeoGebra AppletsHave a look at the excellent resource collection on the Nrich GeoGebra page. Look at the area of a parallelogram or perhaps explore Addition of Complex Numbers with Further Mathematics Students. Using applets such as these can help students pose questions to investigate and lead to greater insights into the problem.Isoceles Triangles

Searching for the same title on Nrich returns the problem. Searching on Nrich Isosceles Triangles, for example, takes us to a problem where we need to find isosceles triangles with a given vertex which have an area of 9. As always on Nrich we can look at Teachers’ resources and a solution. Looking at the Teacher’s Resources for Isosceles Triangles, for example, we see a commentary from Paul Andrews on why he likes the problem. This problem is included in the lovely Nrich poster collection. Nrich has really useful links to related resources, here we have a proof question for age 11-14 or a collection of resources where students must find all solutions.

Alternatively, search Nrich for problems which can be explored with GeoGebra.

Another collection of resources which can be explored with GeoGebra comes from MEI. For applets available to use, check the GCSE resources available here.
MEI Geogebra Quadratic Inequalities
If you want to learn more about GeoGebra and also look at some great tasks for thinking and understanding then these GCSE and A Level tasks provide clear instructions for constructing objects in GeoGebra and pose questions to help students explore many areas of Mathematics. MEI has designed the tasks so they can be accessed using the computer-based version of GeoGebra or the tablet/smartphone app. Each task instruction sheet is reproducible on a single piece of paper and they are designed to be an activity for a single lesson or a single homework task (approximately).

As MEI state:

These tasks are designed to help students in understanding mathematical relationships better through exploring dynamic constructions.   


These tasks for Further Pure Mathematics provide an excellent way for exploring several topics in the Pure content for Further Mathematics.
MEI Further Maths Pure Tasks

My file with the subject of content for Maths and Further Maths with links to resources using technology has been updated with the resources in this post. This can be found on my Use of Technology page.
Further Maths Resources

These resources have been added to the GeoGebra Series of pages.

No Calculators Allowed…

Working with a student recently taking her university admission test for Medicine, I have been looking at some BMAT questions. The practice papers with explained answers provide a good understanding of the test format, different question types and skills assessed by the BMAT examination.

There is no doubt that, given the time pressure, students need to be skilled at performing calculations by hand. The fact that questions are in multiple-choice format is helpful, skills in estimation will clearly be an important strategy in answering questions requiring any calculations.

Even though students have to do one GCSE paper without a calculator, calculators are allowed in all A Level Mathematics and Science exams; looking at these BMAT questions made me wonder if we put the calculators aside enough.

This has prompted me to look again at good resources for practising these important skills of estimation and doing calculations by hand.

Estimation - TES ResourceEstimation by rounding by cparkinson3 is is a complete lesson providing a great variety of problems from basic skills to more challenging ones where learners have to apply their understanding of estimation to solve real-world problems. All resources needed are provided.

On Transum Mathematics you will find many estimation resources including Rough Answers illustrated here. Note the different levels available.

Transum estimation
Transum Mathematics

Mathsbot Revision Grid

Mathsbot resources give us the opportunity to select non-calculator questions. A revision grid, with such questions, is a good example.

A starter is often a good opportunity to look at strategies for quick calculation, I have used several from Mudd Math Fun Facts which is a site well worth exploring if you are not familiar with it.   Mudd Math Fun Facts


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.

Thank you Piers! I have added this to the Number resources page

If I know this..

UKMT dignostic questions

UK Maths Challenge questions provide an opportunity for working without a calculator. Maths Challenge questions are an excellent resource at any time – not just for preparation for the competitions, particularly with the increased requirement for problem solving skills at all levels. On the outstanding Diagnostic Questions site, you can choose Junior Maths Challenge questions by topic by choosing the Themed Quizzes option. These quizzes consist of sets of four or five questions grouped by topic. (Log in to Diagnostic Questions to use the link.)

Further Resources
Wikipedia mental calculation

Mental Arithmetic Training site

For schools with Sixth Form Students taking this test, I feel it is important that the Mathematics Department has a good understanding of the mathematical skills required. These further resources are useful for understanding the requirements of the test.

Section 1 of the examination is a one-hour test of Aptitude and Skills which includes sections on Problem Solving, Understanding Argument and Data Analysis and Inference. Talking to students it is this section that they find the most demanding. With 35 multiple-choice questions to be answered in 60 minutes without a calculator, students need to work accurately and efficiently.

Section 2 on Scientific Knowledge and Applications includes Mathematics questions, the questions are restricted to material typically included in non-specialist school Science and Mathematics courses. The Mathematics content is covered at GCSE as you can see from the last pages of the BMAT specification. Students will, however, require a level of understanding appropriate for the able target group taking this examination. Questions are in multiple-choice format and calculators may not be used.