Functions – an update

function-builder

I have updated a post on functions with the excellent PhET simulation, Function Builder

The post includes several excellent resources for teaching functions. See also this further post aimed at older students.

PhET Simulations look excellent, I will be exploring more of these. I have used the Projectiles Simulation with Mechanics A Level students and have posted on this for students on Mathematics for Students. There are numerous PhET simulations covering Physics, Biology, Chemistry, Earth Science and Mathematics. Note the growing collection of HTML5 versions which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

You can download an app for iOS also for Android.

PhET Balancing Act working nicely on my phone!
balancing-act

 

Learning & Teaching GCSE Mathematics

Following my post, Learning Mathematicsthe following is the slide set used for the Learning & Teaching GCSE Mathematics session at the  excellent Somerset Professional Development Proramme February 2017.

Lots of pages, but if you are interested then the best way to view is via these files:
Learning & Teaching GCSE Mathematics PowerPoint and Learning & Teaching GCSE Mathematics for the pdf file. The pdf version seems much faster to operate if you wish to use all the embedded hyperlinks to the various resources. Note the table of contents which allows for navigation through the various pages.

On Slideshare – you can see the slides – hyperlinks will lead you to all the resources but for slide to slide navgation use the files above.

There have been several updates since this was first published, including:
content-gcse

  • Easier navigation via the Contents page
  • Additional resources, note the oustanding Diagnostic Questions with all its examination questions also the ability to assign your students to one of the streams so they will receive just two questions a day in the run up to the exams. The Insights provided are so valuable. Edexcel have like AQA provided some great Topic Tests.
  • A reminder of some of the many very useful revision resources including this post for students. (Something I will update further over shortly).
mathsbot-revision-grid

Mathsbot – Revision Grid

iteration-mr-carter-maths

For Valentine’s Day…Make Linked Möbius Hearts

The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  We even have 9 Maths skills you need to win the Great British Bake Off!

careers-heartsFor Valentine’s Day, have a look at this post from Maths Careers with instructions on how to make this wonderful pair of linked Möbius hearts.

If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked  as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….
valentine-mobius-hearts
use-to-create-mobius-heartsNote the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper. See Valentine’s Day for the Desmos details.

To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white spce at the end – the picture here has been made using strips 10 cells long.

Learning Mathematics

somerset-maths

I was delighted to be part of the excellent Somerset Professional Development Progamme February 2017.

I can confirm that Simon Singh was inspirational. His presentation slides are available for teachers to use – all that wonderful Mathematics in both The Simpsons and Futurama. In an earlier post here where Simon Singh spoke on Mathematics Teaching, you will find the link to his presentation.
slsingh

My own sessions were (1) on all the wonderful resources availabe for Mathematics but with an eye on the learning first and (2) on the new GCSE Mathematics Specifcation.

Firstly, Learning Mathematics – lots of pages, but if you are interested then the best way to view is via these files:
learning-mathematics PowerPoint and learning-mathematics-pdf. The pdf version seems much faster to operate if you wish to use all the embedded hyperlinks to the various resources. Note the table of contents which allows for navigation through the various pages.

My GCSE Mathematics presentation will follow in the next few days.

On Slideshare – you can see the slides – hyperlinks will lead you to all the resources but for slide to slide navgation use the files above.

Valentine’s Day …

It’s that time of year again – save your money and send your loved ones (or anybody!) a math-o-gram!

..and see also “Make Linked Möbius  Hearts“.

Click on the image and move that slider!

Click on the image and move that slider!

Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!
valentine-design

Valentine’s Day seems an appropriate time to express love for Desmos!
Geeky people you could even use the Desmos API …

Remining with the loving theme you can also express your feelings for WolframAlpha!

I Love YOU

valentine-relay

Valentine Relay – Chris Smith


For some Valentine class activities, try the Valentine Relay from Chris Smith and note all the other relays in this excellent set of resources. You can find more excellent resources from Chris on TES and follow him on Twitter here.

Transum Valentine Puzzle
and here’s a Valentine logic starter from Transum.


 

Mathematics – Have an Espresso!

cambridge-math
For really easy to digest research on Mathematics education from Cambridge Mathematics, see their Espresso page where in their words, “Each month we bring you an Espresso – a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind. Each Espresso considers one particular issue in mathematics education, and how the latest good-quality research can provide helpful guidance or further reading.”

Note the Research page which includes the link to this excellent site and more references whilst not specific to Mathematics I believe are important to teachers of any subject. Note the resources from Chris Moyse who understands that teachers are busy people!

espresso

Coordinate Geometry – Underground Maths

geometry-of-equationsExploring Algebra Review Questions from Underground Mathematics I came across some Coordinate Geometry questions I really like and yesterday spending a day with the very talented writing team and my fellow Underground Mathematics Champions we explored Straight Line Pairs, a question with much scope for exploration and possible methods of solution.
straight-line-pairs

The image above straight-line-pairs-1has been created from the Printable/supporting materials.

My Year 11s will be looking at Coordinate Geometry this week and I have some other questions I would like them to try. It is possible to create pdf files for a collection of questions, see Saving Favourite Resources, one of Underground Mathematics’ How To Videos. (See the tutorials page I have in the Underground Maths series of pages – a work in progress).

coordinate-geometry-resource-collection

You will find a whole collection of such questions if you look at Geometry of Equations. This includes many resources including Review questions. Note the Building Blocks resources. I think I’ll be using Underground Mathematics resources with ever younger students – Year 9 can try Lots of Lines! You will see from the the supporting materials that this has come from the brilliant Standards Unit (A10) collection. Students must sort the lines into six pairs, each pair matching one of the given descriptions.
lots-of-lines
Staying with the Building Blocks I do like Straight Lines where students must decide which of 17 equations are equations of a straight line.
Look at the list – a wonderful lesson in not jumping to conclusions here! Both my Year 9 and my Year 11 are going to be trying these this week!

ax^2+2hxy+by^2=0.

Straight Lines reminded me of Line Pairs, I feel an extension for Year 11 coming on!

 

Underground Mathematics Algebra Review Questions

Underground Mathematics provides such an outstanding collection of resources that I have begun to create a series of pages on the site. The resources are not only good for Advanced Level but for GCSE students too, particularly for students aiming at the very highest grades. This series of pages is very much a work in progress which I will be updating regularly.

I have used many of the Review questions for my able GCSE students. As you can see from the descriptions of  resorce types, the review questions are ideal for the new GCSE specifications as they have been selected to test students’ understanding of one or more topics and to exercise their problem-solving skills. The questions which have been chosen require non-routine thinking. You can browse all the Review questions or narrow your search by question type; note the O/AO-level questions which are questions from old papers. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.
underground-mathematics-review-questions

If you create an account you can easily save and organise your favourite resources. This list of favourites can be easily downloaded as a csv file. To further organise your favourites you can create subcollections.
subcollections

This too is a work in progress, I will create a collection of resources I believe are particularly useful for GCSE. I have several Algebra favourites so far. This Excel file has hyperlinks to all the resources shown here. algebra-gcse-9-1. Alternatively this pdf file also has the relevant hyperlinks. algebra-gcse-9-1
algebra-gcse-9-1

A Level Reform and Resources

As more news and documentation has become available for new specifications I have reorganized the A Level Reform series of pages.

comparison

Further Maths Supposrt Programme Summary of Changes

With any change of specification I have always found any documents on summaries of the changes and also mapping documents very useful indeed. Clearly much of the content is still on the new specifications and resources we already have can be used again.

Underground Mathematics
With a greater emphasis on modelling and problem solving in both AS and A Level specifications resources such as Underground Maths with its aim of “Enabling all students to explore the connections that underpin mathematics” will be very valuable. This page highlights useful resources.

The Specifications and Support page includes links to the specifications for all the examination boards, including specimen materials. Other supporting documentation and news updates including accredited specifications can be found on this page.

There is also a separate Edexcel page; I recommend signing up to the Mathematics Emporium. I suspect some of those old A Level papers might come in handy!

This is an ongoing project; pages will be regularly updated and new pages added.

Diagnostic Questions – Quizzes

venn-example

To use the links in this post you will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”

quiz-libraryI wrote earlier on the brilliant collections of Diagnostic examination questions available. As well as the various Collections, there is an extensive library of quizzes are available ready for you to use.

It is very simple to create a quiz of your own using the Instant Quiz Facility. The following slideshow shows how I created a quiz on logs and exponentials. To create a new quiz I make sure that the Instant Quiz has no questions currently in it so have got into the habit of clearing it out once I have created a new quiz. The instructions for doing so are included here.

To see the pdf version choose this file: Logs & Exponentials Diagnostic Questions and to view the quiz online then follow this link. I have created several quizzes, some simply to gather question types together; see for example the many questions on Probability and Venn Diagrams.included in this Venn Diagrams collection. I created a quiz of all these questions so I could download the pdf for reference. Included in the Further Resources section on Iterative Methods for Numerical Solution of Equations I have included the whole collection of Trial and Improvement and Iterative Methods diagnostic questions; the complete quiz is here.

Checking Insights for my Year 11 class I can see that students have completed many of the diagnostic examination questions. Two students in particular have been rather busy completing 253 and 484 questions, they both got 9s in their mock examinations! (We used AQA Practice Papers set 3).

There is also a mobile app which students can use to complete quizzes assigned to them by their teacher. Testing this recently it works on both my Android tablet and phone.

Extensive help on Diganostic Questions is available on the site. Clear step by step instructions are given.