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)

 

Mobile Puzzles – Algebra

Mobile Puzzles

Mobile Puzzles

The Transition to Algebra (TTA) project, an initiative of the Learning and Teaching Division at Education Development Center, Inc. (EDC) includes a wonderful collection of Mobile Puzzles. Visit solveme.edc.org to play SolveMe Mobiles (also available for the iPad.)

Looking at the menu, you will see categories with different levels of difficulty available from very simple puzzles to rather more complex puzzles which promote good mathematical thinking.

Menu

Students must determine the weight of each object shown which makes a good introduction to the skills required to solve equations, linear and simultaneous.

Looking at some of the Master level puzzles, you will find rather more complex puzzles:
Master Level

Note the menu in the corner of each puzzle page:
Play Menu

Selecting ‘Information’ provides extensive help; note that various tools are available so you can annotate puzzles and / or add symbols and equations.

create equation
Note that you can then drag a heart to subtract a heart from both sides:
puzzle demo
Note that under settings you can choose to show numbers in the mobile as in the illustration. If the solution is correct, the mobile will balance.

On the other hand….
puzzle demo wrong answer

 

GCSE New Content

Note that GCSE New Content has now been given a dedicated page which will be regularly updated.

GCSE New Content is one of the UK Assessment series of pages.

Reading various documents on the new GCSE specifications I thought it would be useful to create a simple summary of new content. (This will be updated with additional information and resources in the coming weeks). Note that I have very recently updated (May 2015) the post on Venn Diagrams which includes several resources for teaching this new topic; currently I have added a link to Brilliant for combinatorics problems, Trigonometry demonstrations,  Nrich and TES resources for Frequency Trees and Desmos graph pages for inequalities including quadratic, circles and tangents to curves.
GCSE

Aural Test – Statistics

StatisticsMy post on using mental tests for revision seems to have interested many readers so I thought I would follow this up. Having looked back in time to GCSE many years ago when an aural test was actually part of the exam (10%) I shall in future refer to these as Aural Tests. It was these tests that started me using the idea of an aural test on anything any time! They can be short and make ideal starters or plenaries or in the case of revision aural tests can last a lesson with lots of associated questions and discussion.

Looking through some old resources I came across a cassette (!) recording of myself reading the questions for a GCSE aural test I recorded for a correspondence college. I intend to transcribe that and will write a post on these old style tests in the near future.

Having successfully given my Year 13 students two aural tests on the Pure Mathematics C3 and C4 modules (after the first they requested the second) my wonderful colleague who teaches the group with me joined in the venture and gave them a third aural test on their  Statistics module. We and our students feel we have done some really useful revision in their last lessons for all three modules on their Advanced Level course.

So this week I have my last lessons with Year 11 (UK age 15-16) who are preparing for their GCSE. I want to look at their Statistics unit with them and have decided that an aural test should work well. Looking at various papers I have extracted some diagrams and asked questions around those. These are topics that I feel my particular class needs; I want to review various statistical diagrams. In case this is of interest I have made all the resources available here. Students need the answer sheet only. The teacher reads the questions and they have to listen very carefully and answer the questions. They will need to write answers in their exercise books or on paper as well as using the answer sheet. With these longer revision aural tests it is sometimes appropriate to give feedback after each question as opposed to waiting till the end to mark all questions. I use both techniques.

Creating the solutions reminded me once again of how useful colour can be to make solutions clear.

I would be interested to hear from teachers who try aural tests with their students; I find them useful for all ages.