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 ResourceReviewing some resources recently as a member of the TES Maths Panel, I came across this excellent resource, Estimation by rounding by cparkinson3. This 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 collection on Mathematics Starters where you will find other ideas for Number starters.

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
I will return to this search in my quest to improve students skills at estimation!

Wikipedia mental calculation

Fantastic Maths Tricks

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 the able target group taking this examination. Questions are in multiple-choice format and calculators may not be used.


Mathematical Miscellany #22

Underground Maths R9452

Oxford MAT 2007, Q1d

On Mathematics for Students earlier this week, see the annual update on University Admissions tests. Many resources are available to help students prepare for the tests. Such resources are excellent for students aiming for high grades, not just those taking tests.

For a new Competitions page – note the link on the right-hand side. Check, for example, the poster competition from the excellent maths careers site and from MEI, Ritangle.

MEI & Maths Careers

ParallelNot a conventional competition, but to challenge your able mathematicians, try Parallel from Simon Singh. All materials and resources are completely free and teachers will have access to all the student scores from the Parallelograms which are automatically marked.

Students do earn points depending on their percentage score on each Parallelogram, which in turn earns mathematical badges. There will be prizes for schools and students linked to the badges in future. Keep an eye on Parallel for the latest news.

Maths GenieReturning to Mathematics for Students, I have updated the GCSE Revision Resources page. My students do like Maths Genie, which is excellent for both GCSE and Advanced level.

In case you have not seen my recent post on Advanced Level – Worked Examples, do check these superb resources from Hodder and from Maths Genie.

Hodder examples

Hodder – Solutions for My Revision Notes (Pure)

Advanced Level – Worked Examples

Hodder examples

Hodder – Solutions for My Revision Notes (Pure)

Looking at some A Level texts From Hodder, we see My Revision Notes for Pure Mathematics (MEI). Noting the link (on the left) to Answers and Full Worked Solutions, I was curious to see this document. Access to this resource requires registration (free) which I would highly recommend as this free resource is simply excellent. In 146 pages, the questions and fully worked solutions for each section are provided, the categories are ‘Target your revision’, ‘Exam-style’ and ‘Review’ questions. Whilst the document refers to the book, it is complete in itself. I do have and like this book, it is clear, attractively presented and written by very experienced authors. The companion Applied book, similarly has fully worked solutions.

Hodder texts

Hodder MEI A Level Texts

Note the five pages to scroll through to see the various texts; on page 2 you will find the AS Revision notes; again a pdf of full worked answers is available and also a complete set of Test yourself questions for each chapter in the book.

Hodder Test Yourself example

Hodder – Test Yourself example

The correct answer with reasoning is provided and also explanations as to why the other responses are incorrect.

Thank you to Hodder for providing such excellent and useful resources.

Maths Genie

Maths Genie

From Maths Genie, as well as all the excellent GCSE resources, we also have A Level worked examples. There are two AS Sample papers with worked solutions, Pure Mathematics and Statistics and Mechanics; also available are videos and examination questions by topic for both AS and A Level.

These resources have been added to the 16+ Resources series of pages.

Mathematics Competitions

List of Mathematics Competitions – Wikipedia

Why not 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,

From MEI – Ritangle, aimed at older students. Ritangle is a maths competition for teams of A level Mathematics, Scottish Highers or International Baccalaureate students attending the same school/college anywhere in the world.  Rules.
MEI Ritangle

MEI Ritangle 2

Maths Careers Creative Poster Competition. For UK students age 11-19.
Maths Careers

The closing date is Friday 11th January 2019.

ParallelNot a conventional competition, but to challenge your able mathematicians, try Parallel from Simon Singh. All materials and resources are completely free and teachers will have access to all the student scores from the Parallelograms which are automatically marked.

Students do earn points depending on their percentage score on each Parallelogram, which in turn earns mathematical badges. There will be prizes for schools and students linked to the badges in future. Keep an eye on Parallel for the latest news.

UK Maths Challenge

WorldMathsDay 2018World Maths Day is over! 7th March 2018 was the big day.

Follow World Education Games on Twitter and/or Facebook.

We can still practise our tables with these resources. There are many games available to help you practice your tables:

From Transum Software comes Flash tables which will present you with random questions from your chosen tables and then show the answer at the speed you select. Also from Transum, see this great Tables Collection which has several activities to try.


Try this Tables Test from which you can play at different levels.

BBC Skillswise though written for adults has some useful activities for students.

For a real challenge try a Find the Factors puzzle from Iva Sallay.