A happy discovery on Twitter, a conversation with Christian Bokhove of Southampton University led me to another home for the Wisweb widgets. Try the Digital Mathematics Environmentfrom the Freudenthal Institute.

Explore Secondary Education (also the DME Widget list)

A guest login has restrictions but you will be able to explore and use resources, many of which make excellent demonstrations.

A site very well worth exploring to become familiar with what is available and one I’ll return to.
Some examples follow:

Choose Secondary Education, Algebra and also the Algebra Widgets to explore resources such as the following :

Algebra Arrows illustrated above is excellent for exploring functions. Form inputs, operations and output by dragging them onto the main workspace, connect them up and optionally connect to a graph. Click inside any of the elements to change the content.

The Digital Mathematics Environment has much more than the original Wisweb applets – a quick glance at Secondary Education shows we have resources to explore.

Choosing Secondary Education/Algebra/Exercises – Equations/Linear equations led me to another favourite. A whole series of these exercises is available. I like the way the steps and working are clearly shown

There are useful demonstrations that could work well in class:

Choosing Secondary Education – Geometry will give you the following choices:

I am very happy to see widgets such as Building Blocks again. This is useful for demonstrating plans and elevations. I discovered I could clear a block by selecting both left and right mouse buttons simultaneously.

Statistics and Probability widgets includes a widget illustrated here on the Normal Distribution; try experimenting with the various variables.

Probability Trees could be useful for creating diagrams as the basic diagram is very easy to set up – simply enter the number of branches you require.

These versions of the excellent Wisweb applets from the Freudenthal Institute do require Java which is a problem as most modern browsers are moving away from plugins and toward standard HTML5. There are certainly issues with Chrome and Java, Oracle say “If you have problems accessing Java applications using Chrome, Oracle recommends using Internet Explorer (Windows) or Safari (Mac OS X) instead.” This too is of limited value as Microsoft Edge does not support Java, though see further information. This includes the statement that “Internet Explorer 11 and Firefox will continue to run Java on Windows 10”.

If you still get Java error messages even though you have an up to date version of Java installed, check that Java is enabled in your browser. Additionally, it may be that you need to Configure Java (see your programs list) and under the Security tab add an exception site, eg: http://www.fi.uu.nl/wisweb/ I left my security setting as high and this did solve the problem.

Try Algebra Trees for example. Form inputs, operations and output by dragging them onto the main workspace, connect them up and optionally connect to a graph. Click inside any of the elements to change the content.

Once you have tried a few of these applets you will find them intuitive to use.

Algebra Arrows for example could be used to compare different orders of operations. Build a tree, make the input x and note the output generated:

How to use Algebra Arrows

(I used Screencastomatic to create the thrilling video! This is very easy to use.)

Try this applet which shows how a solid is formed from a net, just move the red slider from 0 to 100.

There are several applets which are excellent for showing plans and elevations. The applets work well on the interactive whiteboard for demonstrating to students, they are also ideal for students to explore themselves.

Cube housesshows several models with their elevations, select drawing then 3d-model to give a model you can rotate to generate different views.

Building Houses allows you to create buildings and see the plan, front and side elevations as you build. (If that link does not work – try this).
You can add (build) or remove (break down) bricks and control the size of the square base.

Building houses with side views challenges students to construct 3D models given the plans and elevations; the task is made more challenging by specifying that as few cubes as possible should be used.

Note that in order to achieve the minimum number of cubes, ‘floating’ cubes are needed.

Note that these resources have been added to the ‘explore‘ series of pages on the companion blog for students. Update – these resources worked well with my students – they particularly enjoyed the challenge of trying to build models using the minimum number of cubes!

Readers interested in the Improving Learning in Mathematics materials note the other resources including Interactive Whiteboard resources Malcolm Swan’s excellent Improving Learning in Mathematics – Challenges and Strategies.

Iterative Techniques – this has proved to be very popular; updated again with Mr Carter’s really useful questions on iteration.
This site has a great collection of topics.

Happy Birthday Nrich!To celebrate Nrich’s 20th Birthday they have been digging in the archives and freshening up some old problems. This is still one of the best websites around and one I have been using for a long time! See also their Hidden Treasures.and theTeacher Birthday Feature.

Note the Poster Competition closing in January 2017 for UK students age 11 to 18. The entries will be judges in three categories Years 7 and 8, Years 9, 10 and 11 and Years 12 and 13.

To achieve the highest grades at GCSE (taken in the UK by students age 15-16) students will need to be good problem solvers which include being able to make and use connections between different parts of Mathematics. There are many suggested resources in the Problem Solving Presentation.

These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

Checking the Review Question type in this category we see that O/AO-level questionsare included.

I see several questions here that will provide appropriate challenge for my GCSE students.
For example:

Can we fully factorise x^{4}+4y^{4}? Starts with a Show that….
And then we factorise and will need to recall the difference of two squares.
We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.

Can we simplify these algebraic fractions? Review algebraic fractions, simplifcation including the difference of two squares and quadratic equations. We could of course also talk about functions (including domain and range as these students are also studyling AQA’s Level 2 Further Mathematics)

Can we simplify these simultaneous equations of degree 1 and 2? Solve simultaneous equations, we’ll need simplification of algebraic fractions again and we can talk about the graphical solution of equations. We will also need to factorise a quadratic, 3y^{2}−y−80 with a coefficient which is not 1 for the square term. We have all decided we are fans of the Box Method!

You can also search on the Line and the Station to narrow your search; you can also save and categorise your favourites by creating a (free) account.

Mr Barton Maths
Craig Barton has been working hard redesigning his wesite, Mr Barton Maths. You will find a treasure trove here for teachers and students. Note in particular Craig’s Maths Topic Index Page.

For each topic, you will find information on all the GCSE specifications, a whole variety of resources, questions and more. The pages are very easy to navigate. Note the inclusion of Diagnostic Questions for each topic, a resource which is going from strength to strength this now has over 20,000 Multiple Choice Questions. Multiple Choice Questions when well written like this can be an excellent way of addressing student misconceptions.

Suppose you are interested in Quadratics and want to stretch your students – you’ll find an extensive collection here, As always, for each resource, you will find so much more than just the question and solutions but for example all the printable materials you need and suggestions for teaching with the resource. … If you create an account you can easily save and organise your favourite resources. This list of favourites can be downloaded as a csv file.
For some of my recent favourites see this Excel filecy-ugmaths-favouritesor as a pdf: cy-ugmaths-favourites Note the handy Excel =hyperlink(cell) command for turning the text to a hyperlink).

The favourites facility is sophisticated – you can create sub collections also.

I regularly feature favourite resources; here’s a great way to look at circles! The teddy bear! As with all the resources on Underground mathematics much more than just the problem is available; note the printable/ supporting materials for the teddy bear problem.

One of my resolutions for Maths teachers, one I think applies to teachers of any subject is a reminder about talking to the students about learning and study strategies. Read The Learning Scientists blog for more information and note the excellent downloadable materialson study strategies. Since I wrote that post more slides to use in class with your students are now available, including on Retrieval Practice, a subject I have long been interested in and something I have seen as important all through my teaching career. See my own Low Stakes Testing in the Mathematics Classroom.

Continuing on the theme of retrieval practice, a reminder of a favourite resource, something I have used in my first lessons this week with various classes, Corbett Maths 5-a-day. If you scroll down the GCSE 9-1 collection you will see that Mr Corbett is working on the answers too.

Students appreciate the idea of regular reviews throughout the course.

A reminder of just how useful Twitter can be!

As a member of the TES Maths Panel I have often come across the excellent resources from @Pixi_17. In fact writing the original post on Iterative Techniques (and note the June 16 update with a Further Resources / Questions section) I was able to include a resource of hers on the subject. An extensive collection of quality resources on piximaths.co.uk.