Mathematical Posters

Math Gems

Math Gems

Carrying on with holiday Project tidy up; following a Twitter conversation where I saw a query on posters for displays reminded me to revisit and review a popular post on Mathematics Posters. This post includes several excellent sources of free posters to decorate your walls and get your students thinking too!

There are of course endless possibilities for putting things on walls! Student work obviously but also definitions and key facts to remember   particularly now in the days of no formula sheets! (See also Mathscard from Loughborough University) Or perhaps some exam terminology. Maybe put some mathematical puzzles on the wall for idle moments!

Put Desmos into projector mode and produce some posters of different graph types. And remind students to get the Desmos app free on their phones!
Desmos android2

Time to tidy up

Tidy UpIt’s holiday time so time for a bit of tidying up, just like last year – my
house and my blog!

I’ll be doing some tidying up and updating in the never ending quest to make useful things easy to find! I’ll post details of my weekly tidy ups!

Transum - Arithmagons

Transum – Arithmagons

 

One task is to revisit popular posts and update them as appropriate, one such post is that on Arithmagonswhich has been checked and updated – Craig Baton has written a whole set of resources on Arithmagons.

These can provide great starter activities and the ‘backwards’ versions really promote great thinking and understanding.

(See also Good Mathematicians Can Go Backwards!

 

End of term…

So school’s nearly out for the summer in the UK; time to mention those end of term activities again.

workers of zen

Workers of Zen

The selection of activities here reminded me how impressed I was when I first saw the Counting Chimp and how I loved my Spirograph as a child. I had also forgotten the excellent Workers of Zen problem.

I have added the UKMT team challenges, their crossnumber puzzles make a great end of term activity. The junior materials can be found here and senior here.

Some lovely end of tern ideas from Jo Morgan can be found here.

So it’s time to reflect, tidy up and plan for next year!

Wishing educators everywhere a wonderful and well deserved break – if you are already on holiday I hope you are relaxing – if the end of term is near then enjoy the last days of term and then have a great summer.

RAG 123

At Maths Conference 4 recently I attended a session on marking, Martin Noon’s “Marking for the Reluctant Marker”. you can find Martin’s resources from the session here.

The session was a reminder to me that I really wanted to try the RAG 123 idea, something I had already read about from Kev Lister.

I decided I wanted a very simple version without the word level anywhere and created my version as follows: Marking Guide (Word) Marking Guide (pdf). (We assess students on their “Engagement with Learning”, criteria they are familiar with.)
RAG 123 CY

I also created a version for students to stick in their books for reference.
Student version RAG 123 student books (Word) RAG 123 student books (pdf)
RAG 123 student

Having tried this with my Year 9 class this week I am convinced this is something I want to try next academic year. Talking to a student later she said she thought it would be useful in other subjects too.

I explained the idea at the beginning of the lesson and let them know that I would ask them for their assessments at the end of the lesson, stressing that a 3 for understanding was a note to me that they needed help

Having collected the set of books it took a very short time to go through the set and see their I believe very honest RAG 123 assessment on the work on Functions we have been studying. I signed my agreement of their assessment. Some students also made additional comments to clarify / justify the reasons for their assessment.

 

 

Functions

A previous post on Functions features resources aimed at older students; I thought it would be useful to look at resources for teaching younger students. Desmos can be used very simply to illustrate function notation and note the use of Desmos as a calculator to evaluate the value of a function for a given input.

Functions - Desmos. Select image for graph page

Functions – Desmos. Select image for graph page

As always CIMT is worth a search; we find:

CIMT Interactive Materials - Functions

CIMT Interactive Materials – Functions

In the interactive materials for year 7: Unit 16 Section 2: Function Machines and there is also a section on the associated text (16.2). All CIMT resources are free to access, a small number of documents such as text answers are password protected, you can obtain the CIMT password. These exercises could be used as an introduction and students also shown function notation. They could write the functions described by the function machines using f(x) notation.

TES Functions

TES Resources – Functions

On TES, this Crossnumber from cbarthur is an ideal resource for becoming familiar with function notation. Also on TES from Owen134866 we have a set PowerPoint resources including an introduction to f(x) notation for GCSE students.

AQA Bridging the Gap

AQA Bridging the Gap

The AQA Bridging the Gap resources includes a resource on introducing function notation; these resources are ideal for students who have completed the previous KS3 programmes of study but will be studying the new GCSE courses.

On Exam Solutions you will find an introduction to f(x) notation.

For further information on new content at GCSE see this page.

 

Plenary Tweets

Discovering a novel idea for a plenary via Twitter recently, a UKEdChat resource by @grahamandre I thought I would try the idea with my very able Year 9 class (the same wonderful class I mentioned some time ago who gave their views on Good Maths Teachers).

I should mention that “Somewhere over the 2a” is part of some lyrics by one of my colleagues sung to the tune of “Somewhere Over the Rainbow!”

In the first part of this lesson I used one of my mini-tests to review the key points for solving quadratic equations. When we reviewed the solutions I also used Desmos to illustrate some of the answers and for these students, the first year who will tackle the new GCSE course made sure I used function notation! This time I told them that I was using the mini test to review the material we have been studying and that they should try and create a useful revision resource by noting the questions carefully and annotating their answers clearly, adding to them where necessary when we reviewed the material. They know I will be looking at their books early this coming week.

I was of course particularly pleased at some of those hash tags!
#enlightened with the mini-test

and of course  #winning    and #maths is fun

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.

Thoughts this week …

A compilation this week …

normal2

Normal Trainer – Mike Hadden

Excel
….is my favourite Microsoft program both for its use in Mathematics teaching and for data analysis. In 2013 at the TSM Conference I was very fortunate to meet and be trained by Mike Hadden. I had already discovered and often used Mike’s Excel files for my teaching; in 2013 thanks to Mike I discovered the joys of Excel macros which save me a serious number of hours in my job!

Mike now has a blog where you can find out more about his Excel files for teaching (scroll down) and also learn more about macros – have a look at the Macro Recorder Demo.


GCSE New Content

I have created a new page for GCSE resources for the new content which I will add to as we discover more! Note the addition of some resources at the end of the list under Further Resources. A list of changes is available on a separate page.

Further Resources – GCSE new content

  • AQA Bridging the Gap for students who have studied the current (2007) Key Stage 3 Programme of Study and are preparing for the new  Mathematics GCSE (8300 specification).
  • Transition Units – Cambridge
  • OCR Check in tests scroll down to Teaching and Learning Resources
  • Resourceaholic from Jo Morgan – links to support the teaching of new topics in GCSE Mathematics.

For problem solving, Brilliant…is just that, brilliant – I’ll return to this in another post but do have a look.

Select image to try problem

Select image to try problem


Circle Theorem

Circle Theorems – Tim Devereux

Circle Theorems 

For some excellent resources for Circle theorems try these including Tim Devereux’s updated excellent Circle theorems web pages.


…and finally

Rereading my post on the TSM conference reminded me of this wonderful entertainment – ‘Katie’s bad science’. I love this!
Original and re-edited version of Katie Melua’s song nine million bicycles proposed by Simon Singh and presented on Ted talks by Michael Shermer.

 

Looking for Resources

Q3 Resources

Pondering a #slowmathchat question on Twitter I realised that I always have a few sites I rely on where I know I can always find something. So I thought I’d pick a random example to illustrate.

A3 Constructions
So – constructions, for demonstrations I always use John Page’s Math Open Reference, his demonstrations are so clear and can be shown step by step; students can also be given the website so they can access them themselves. I found this many years ago when I wanted some demonstrations for constructions – a Google search returned it as the first entry!

bisect angle Math Open Ref

Math Open Ref – Bisecting an Angle

So obviously we need some questions / activities. Where to look – our textbooks are fine – plenty of questions there, but what else is available?

On Nrich, try a search by topic facility to find all the resources for a particular topic; searching on constructions there are several resources returned.

Nrich constructions

Nrich - triangle construction

Nrich – triangle construction


CIMT – I don’t think CIMT have ever failed me! One can actually do a Google search such as CIMT constructions to very quickly find resources. It is worth being familiar with the site so you know what is where; I would always check the Year 7, 8 and 9 material and also the GCSE course. In this case, the Year 9 resources include Unit 12 on Constructions and loci. As well as the text we have all the supplementary teacher resources, extra exercises for example and extra activities.

I often find Nrich and CIMT more than sufficient and

I want to spend time planning my lesson and thinking about my students’ learning and how I’m going to help them understand and make it stick. And how will I know?

So of course quality resources are key but I don’t want to spend too much time looking for them if it stops me spending sufficient time on the above. I believe it is very worthwhile to have a few key sources so you can find something efficiently and quickly.

Having said that, since this post is on finding resources I’ll mention a few more!


The old Exemplification examples for Key Stage 3 have some very useful example. In this case use the Geometry and Measures document and do a search for constructions.


Teachit Maths though a subscription site offers its entire collection of activities as pdfs free. A search on constructions returns a small number of resources including a good card sort.

TeachIt Maths constructions


I’ll finish with Craig Barton’s and Simon Woodhead’s wonderful Diagnostic questions site. (Select this link for all posts on Diagnostic Questions, these include some instructions for use and other resources for rich questions.) Start typing construction into the search box and various choices will be returned.

Diagnostic Questions

GCSE New Content – Iterative Methods for Numerical Solution of Equations

Looking at the new content for UK GCSE Mathematics a completely new entry on the specification is “find approximate solutions to equations numerically using iteration”.

For some more information on this AQA have some very useful resources, including their Bridging the Gap resources which look very useful for students who have studied the 2007 Key Stage 3 Programme of Study and will be studying a new  Mathematics GCSE specification. The resources include examples on iterative methods for solving equations numerically. 

Iterative techniques 1

AQA Bridging the Gap resources

Students can be reminded to use the ANS key on their calculators; it seems to me that this will be a good opportunity to show students how useful Excel can be for such techniques and will enable teachers to quickly generate results with different starting values.
Excel - iterative solution of equations

From an AQA specimen paper, we see how this may be examined:

AQA Specimen Paper 2 Higher

AQA Specimen Paper 2 Higher

AQA specimen exam question a

AQA specimen exam question b

 

 

 

 

In case you are wondering about that flowchart, Newton-Raphson is the method being used.
Iteration NR
a little algebra and we see what AQA are up to in their flowchart.
Iteration NR 2

I do love my graphics tablet!
(See Writing Maths Online)