Underground Mathematics – Save & Organise Favourite Resources

A new page in the series of pages on Underground Mathematics …

If you create an account (all free) on Underground Mathematics you can easily save and organise your favourite resources.

Register

Select User from the menu at the top right, then New User to create an account. Note that you also use the User menu to log in.

When you are logged in you can add any resource to your collection by selecting the star to the right of the title. And note this resource Pick a card, which I highly recommend, think about multiple representations for Quadratic Functions. This could be used with younger students too.
Save resource

See also: Tutorials – Saving favourite resources – a video from Underground Maths
To see your resource collection, select ‘Your resource collection from the User menu.
User Menu

You can also use subcollections to help organise your resources. Subcollection1

When you display your resource collection, note the options for each resource, the first of which is the ability to add the resource to a subcollection.

Subcollection2
Note the choice to add to one of your existing subcollections or the option to create a new one.
Subcollection3

Note that when you display your resource collection you can select a subcollection if you wish:
Subcollection4

See for example Building Blocks resources I personally like; I created a subcollection and downloaded as a csv file. The ability to add notes is really useful too.

For reference, this is one of a series of pages on Underground Mathematics. With so many outstanding resources on the site, this is a continuing work in progress.

Underground Maths: Prepare for the new A Level

This will be so helpful for our preparation for the new A Level, I particularly like the Resource suggestions.

For each content statement, Underground Maths have suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of Mathematical modelling have been highlighted.

These of course are suggestions. There are so many outstanding resources on Underground Maths. In our department, like many others I am sure we will be exploring the resources and bookmarking our own favourites.

I have a series of pages on Underground Mathematics. This is a work in progress and I will be adding more content over the coming weeks. Some of my many favourites are on these pages…

Follow Underground Mathematics on Twitter or Facebook.
Note there is also a closed Facebook Group for teachers. We’d love to hear which Underground Maths resources you’ve been using, share your thoughts, ask questions or show your students work for discussion.

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

Circles Station

circles-station

The home of the Teddy Bear and a whole lot more! The wonderful Underground Maths site has a whole new station – Circles.

Really challenge your students with the resources here.

I rather like this review question on circles:
Can we show that these four points lie on a circle?

4-points-on-circle
Good for A level mathematicians – also for my Year 11 Level 2 Further Maths Students.

And of course – Desmos to illustrate.

This diagram could make a rather nice starter…

4-points-circle-desmos

See all posts in Underground Mathematics.

Challenge Your Mathematics Students …

a03-problem-solving
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.

For older students (16+) I have included Underground Mathematics. I have also used Undeground Mathematics resources with my very able GCSE students; see for example Introducing Calculus. There are many Underground Mathematics Resource Types. One of the types I have written on before is the Review Questions which in the words of the Underground Maths Team:

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 questions are included.
underground-mathematics-review-questions

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

factorise

Can we fully factorise x4+4y4?
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, 3y2−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.

 

Mathematical Miscellany #7

Questions Questions..
questions

I have been busy checking and updating various pages on this blog, taking into account popular resources.
See:


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.
mr-barton-topics

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.


logoFor more on Underground Mathematics, an introductory post is here and you can view all posts in the category Underground Mathematics.

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 file cy-ugmaths-favourites or as a pdf: cy-ugmaths-favourites Note the handy Excel =hyperlink(cell) command for turning the text to a hyperlink).

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

scary-sum
Note Scary Sum – what a lovely problem!

Iteddy-bear 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.

I can never resist creating a Desmos page!

teddy-bear-desmos


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 resolution-study-strategieslearning and study strategies. Read The Learning Scientists blog for more information and note the excellent downloadable materials on 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.

Follow @AceThatTest on Twitter or on Facebook.

At ResearchEd 2016 I very much enjoyed Oliver Caviglioli’s session on Visual knowledge for better explanation and recall. Oliver is a trainer of Visual Strategies, he collaborated with The Learning Scientists to create the six posters on effective study strategies. Note his free resources for teachers coming soon, Cognitive Science HOW2s.


5-a-dayContinuing 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!
edexcel-sample-questions


Iteration TESAs 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.

 

Introducing Calculus

rates-of-change

New on the GCSE specification we have interpretation of the gradient at a point on a curve. I want to introduce this to my very able Year 11 (UK age 15-16) class this week. As this class is also studying for AQA’a Level 2 Further Mathematics Qualification I want to go beyond the GCSE specification. Talking of the Further Maths specification – a wonderful find – thank you Craig Barton  – so many wonderful resources for this specification. Thanks too, to Mark Greenaway, Thomas Whitham Sixth Form College and on YouTube, Raw Maths, Jerry Jam and Riley Maths.

Some resources – I plan on using:

Perhaps after initial explanations with reminders about what they already know about distance time graphs and emphasising that a gradient is a rate of change, a good starting activity, A tangent is … from Underground Mathematics which emphasises rather well that a tangent is a local property of a graph.

I want them to draw some tangents and see how accurate they can be, so I’ll give everyone a good size graph of f(x) = x2 and have them draw tangents at x=0, 1, 2, 3 and 4, something that has worked well with A Level students. We can use Desmos to check our work, Tangents to f(x)=x2 –  Desmos. (For even more @Desmos sophistication – see the end of this post).
gradient-on-a-curve-desmos

Back with Underground Maths again we will use Gradient Match to match functions with their gradient functions. This can be used interactively online. All the reources you need and a solution are provided.
gradient-match-underground-mathematics

Further Resources
AQA – Bridging the Gap – Pocket 3 is on Graphs and Real Life Contexts; this includes Distance Time Graphs and Velocity Time Graphs.

OCR’s Topic Check In 7.04 Interpreting Graphs     7.04

There are several resources for teaching this topic on AQA’s All About Maths including clear PowerPoints and suggested lesson activities.
(Free for AQA Centres, find out how to register).

Mathematical Miscellany #7

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 resolution-study-strategieslearning and study strategies. Read The Learning Scientists blog for more information and note the excellent downloadable materials on 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.

Follow @AceThatTest on Twitter or on Facebook.

At ResearchEd 2016 I very much enjoyed Oliver Caviglioli’s session on Visual knowledge for better explanation and recall. Oliver is a trainer of Visual Strategies, he collaborated with The Learning Scientists to create the six posters on effective study strategies. Note his free resources for teachers coming soon, Cognitive Science HOW2s.


5-a-dayContinuing 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.


#slowmathchat
#maths 
& #math come together here, @cbrownLmath (US) & myself @ColleenYoung (UK) decided we like the idea of a continuing anytime chat. The original idea from Michael Fenton,  see Twitter Chats vs Family Dinners….. (note #slowmathchat – math saves a charcter!)

This coming week we will focus on homework, appropriate for the beginning of the academic year as we establish routines. For some alternative homework ideas, see this page.


On the subject of Twitter, a reminder of just how useful it can be!
edexcel-sample-questions


Iteration TESAs 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. She has now organised her resources on her own website piximaths.co.uk.


Underground MathematicsCambridge University’s Underground Mathematics is an outstanding resource for teachers of students age 16-19 and I believe will be an important source of ideas for teaching the new Advanced Level specifications.

Iteddy-bear will be regularly featuring 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.

I can never resist creating a Desmos page!

Further posts on Underground Mathematics.

teddy-bear-desmos

Teddy Bear Problem – Underground Mathematics on Desmos

More posts in the Mathematical Miscellany category.

 

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.