Review Questions – Underground Mathematics

Underground Mathematics - QuadraticsI wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications  I believe this site will provide us with rich resources for these new specifications.

Each section includes Review Questions, look at Thinking about Algebra for example; scroll down the different resource types for the Review questions for this station.

Alternatively you can browse all the Review questions.

Review Questions - types
An excellent feature of Underground Mathematics is the excellent search facility; we could look at the Review questions by type. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.
Review Questions - search

See the example question below, for each review question you will find the question, a suggestion, the solution and sometimes suggestions for taking it further with for example GeoGebra resources.

Note the star by the title – if you choose to log on to the site (you don’t have to but it’s a very good idea!) you can save any favourite resources to your collection.

Review Question - Gemetry

I can never resist a quick illustration on Desmos! I think I’ll start an Underground Maths Desmos collection! Note the use of the hyperlink on Desmos to link to the question.
Select the image for the Desmos page.
Desmos illustration

I think we have a wonderful supply of excellent questions here to challenge our students and help them see connections between the various areas of the subject. These are ideal to use with A Level students; some are also useful for higher level GCSE students aiming at those top grades or Level 2 Further Maths students. Any student who wants to study Mathematics at university should certainly be using this site.

Mathematics Conversations

There are many useful conversations on Mathematics on Twitter. Now just in case you hate Twitter or have no interest in it – you can still follow useful conversations and follow links to resources without even signing up to Twitter. I find Twitter a little like a lucky dip – usually in just a few minutes I find useful resources or the latest educational news.

For Mathematics teachers I would recommend the following:

Q3 Resources#slowmathchat  where different questions are posed for discussion; you can read more about the origin of #slowmathchat and how it works on Michael Fenton’s Reason and Wonder. A complete archive of all the questions and answers is available too.

#mathsTLP for lesson planning, a Sunday night chat but you can of course view at any time and many teachers share useful resources / ideas that work in the classroom.

Select image for resource on TES

Select image for resource on TES

Each weekly chat is very clearly archived on Ed Southall’s Solve My Maths.
Talking of Solve My Maths, I do love Ed’s Mr Men!

Mr Men Ed Southall

Mr Men – Ed Southall

All the links above to Twitter list the tweets in time order (Live); note that you can choose Top or Live;

Top & Live

Further useful Twitter people and hashtags to follow:

Craig Barton TESMaths

Diagnostic Questions

#mathschat for UK education and #mathchat for US education

#MTBoS for converstaions from the Math Twitter blogosphere

#maths and #math for general UK & US tweets on Mathematics

@Desmos for the latest on the fabulous graphing calculator

@Wolfram_Alpha and @WolframFunFacts
WolframFunFacts

MathsCareers

MAA – Mathematical Association of America 

Association of Teachers of Mathematics

If you are interested in learning more about Twitter see the very clear Twitter Lingo guide from Mashable and Russell Stannard’s training videos. And for a nice simple explanation try ‘Mom This is How Twitter Works’.

This page has been reproduced and added to the Reading series of pages, further updates will be published there.

Resources for Students

Resources

One of my personal resolutions for the coming year is to carry on with my practice of using resources that students can then refer to or use at home if they wish. Mathematics notes and calculators are a good example of such resources.

To consider an example, early this term with the Further Mathematicians I will be studying matrices and I will let them know the sources of any resources I use in lessons. I use a blog to provide the details of my students’ homework so I can simply add the links to their homework page. Sometimes where there are several useful resources I think maybe of interest to a wider audience I also add a post to Mathematics for Students, see for example, Polar Coordinates. In fact I think I will do that more this year.

To return to matrices, some useful resources include the following:

On the AQA website the Teaching and learning resources page for A Level Further Maths includes three online textbooks under the Resources for students heading. For example if I want a worked example of finding the inverse of a 3×3 matrix then we can look at  Chapter 5 of AQA’s Further Pure 4 text. This also has an exercise with the answers at the back if they want additional examples.

The Math Centre

The Math Centre

More sources of notes and examples include Chapter 9 on Matrices and Transformations from the CIMT Further Pure Mathematics A Level material, Just the Mathsthe Math Centre and The HELM Project. If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include clear worked examples. You can see on the list that a very small number of titles (that you are unlikely to want A Level) are ‘not ready yet’; for the sake of completeness I discovered the complete set hosted by the Open University. To access the Open University resources you will need to create an account (easy and free), this will also give you access to the numerous free online courses.

Obviously we need to keep an eye on the specification when looking at alternative sources of examples but surely that can only be a good thing, particularly for our students who will be off to university in the near future.

Matrices is an example of a topic where it can be very useful to check work with WolframAlpha; I have created a new slideshow of Matrix Examples to add to the WolframAlpha slideshow series so we can easily check any work.
The series is on Mathematics for Students also and a post including the matrices resources discussed here has been added also.

Mathcentre

A site I use frequently is mathcentre which was developed by a group from the Universities of Loughborough, Leeds and Coventry, the Maths Stats and OR Network and the Educational Broadcasting Services Trust. See this link for a list of topics. Reading about the news from mathcentre I see there are leaflets available mathcentre  and statstutor showing the range of resources available.

mathcentre - quotient rule

mathcentre – Maths Tutor

Looking at the second page of the mathcentre leaflet, I noticed mathtutor which provides mathcentre resources conveniently structured as a course.  I shall refer my students to that this week, I want them to look at the quotient rule in my absence (I’m very much looking forward to the annual TSM residential workshop at Keele University) and plan to point them in the direction of resources they can use – a flipped approach! (See ‘Prepare ahead‘ here). I’ll see what they have learned on my return.

The mathcentre site includes extensive resources. Many of my students like the quick reference leaflets which are available on numerous topics. There are also teach yourself booklets, revision booklets, videos and diagnostic tests. Resources are available for staff and students. This is a site well worth exploring and recommending to your students.

Words with WolframAlpha

WolframAlpha can be used for vocabulary, for example try typing ‘plus’ into WolframAlpha.

Note that WolframAlpha has assumed plus is a character but you can choose to refer to a mathematical definition or a word (or an internet architecture topic). Choosing word will not only give definitions but a wealth of other information that you would not find in a dictionary such as the first known use of the word, frequency of use, rhyming words and much more!

Other sites of interest for Mathematics vocabulary have been mentioned in this Mathematics Reference post. If you are interested in the first know use of mathematical words then try Jeff Miller’s ‘Earliest Known Uses of  Some of the Words of Mathematics‘.