Arithmagons


What is an arithmagon?
Clearly, the numbers in the rectangles are the sum of the numbers in the adjacent circles. Of course, there is no need to use addition and no need to use triangular arithmagons!
These could be used with students of all ages. Young children could practice basic skills or students studying advanced Mathematics could look at Calculus or Complex Numbers for example.The challenge is, of course, to go backwards…(Going backwards in Mathematics really helps understanding).

Colin Foster has written a suggested lesson plan on Arithmagons with full commentary.

Nrich Irrational ArithmagonNrich has some very useful resources including this introduction to arithmagons which includes an interactive allowing numbers to be changed and would work well on an interactive whiteboard. See also these further Nrich resources – this on multiplication and for older students a rather more advanced multiplication arithmagon using complex numbers. Also on Nrich, Irrational Arithmagons.


Algebra1 Alan Hodson

Arithmagons by Alan Hodson on emaths

From Mark McCourt’s emaths, the Teacher Resources include Investigations, Rich Tasks and Puzzles; these include a small collection of Arithmagons by Alan Hodson covering Number and Algebra. The Algebra resources include simplification using like terms and solving linear equations. A PowerPoint file showing an investigative approach using number and algebra and notes are included as is a useful sheet of 15 blank Arithmagons for students to record answers.


Don Steward

Expressions Arithmagons – Don Steward

From Don Steward, try his Expressions Arithmagons. Note the very efficient use of space here! Also from Don Steward, have a look at Directed Number Arithmagons.


For ideas to use with older students see Jonny Griffiths RISPsRISP21 is on ‘Advanced Arithmagons’  (if you choose RISPs organised by topic,  you will see RISP21 Advanced Arithmagons under Basic Algebra).

Jonny Griffiths

RISPS – Jonny Griffiths

Jonny Griffiths RISPS have been mentioned before – see the Rich Tasks resources for Older Students. Another site included in the Rich Tasks resources is the New Zealand Maths problem solving site; a resource on that site uses arithmagons to form and solve linear and simple quadratic equations.


Arithmagons - TeacherLED
Noting this tweet from Spencer Riley (I really like his TeacherLED site which has free high-quality teaching and learning resources compatible with desktop and mobile devices.) I had a look at his Arithmagons resource and can verify it worked very well on my phone as well as on the desktop.

Spencer Riley - Arithmagons

Arithmagons – Spencer Riley on Teacher


Craig Barton - Index & Factorising Quadratics
Arithmagons Collection – Craig Barton

From Craig Barton, we have a complete collection, covering Number, Algebra and Shape and Space. Each resource includes a PowerPoint File with clear instructions and a selection of challenges to really make your students think.


One of the many free resources (do a search on ‘free’) on the excellent MathsPad is this interactive – Negative Arithmagons. (MathsPad is a subscription site, but very low cost and good value for schools – see details).

MathsPad

MathsPad – Negative Arithmagons


Transum - Arithmagons

Transum – Arithmagons

On Transum Mathematics (home of the excellent Starter a Day), the Arithmagon activity has options for forwards and backwards problems on Addition, Multiplication and Subtraction at various levels.

Have you seen…? #1

A new style short post, simply for some quick updates…

Have you seen…?

Minimally Different Problems from Jess, (@FortyNineCubed on Twitter)

Quadratic Minimally Different Problems

Using the Quadratic Formula – Minimally Different Problems

Note the menu on the right-hand side to help you find exercises.
As Jess says, text exercises can become too varied too quickly, so perhaps try some minimally different problems to explore what happens with these small changes.


MEI M4 Archive

MEI M4 Magazine Archive

MEI has been busy, their M4 Magazine is a source of excellent resources as well as articles to read. Now you can search the archive for GCSE problems categorised by topic.


I enjoyed many excellent sessions at the recent BCME9 conference; I particularly enjoyed the Nrich session. Nrich has so many accessible problems, it’s not just all about high ability students; try these problems on Factors, Multiples and Primes for example.

For the new specification – A Level proof, I’ll certainly be using this Interactive Proof Sorter example which works on my phone as well as on my laptop.

Nrich - Proof

Nrich – IFF – Interactive Proof Sorter


From the brilliant Maths Emporium, some very useful GCSE examination advice for your students. This particular guide to life made me laugh!

Edexcel Guide to life

Edexcel Maths Emporium Guide to Life – GCSE Maths

Very entertaining – and very true!


 

Retrieval Practice – Mathematics

Following the BCME 2018 Conference 2018 where I presented a session on Low Stakes Testing in the Mathematics Classroom, I have created a shorter version of the Slide set to concentrate on ideas and resources for using Retrieval Practice, something which can be a regular part of lessons. Retrieval Practice does not have to be about quizzes, it can be as simple as the right choice of task which will involve students reviewing previous learning. Slides have been annotated which I hope will add clarity.

A new page, Retrieval Practice has been added to the Lesson Planning series. That page includes further background and reading as well as links to all the resources mentioned.

Calculator Questions

Just a quick post this weekend…looking forward to the BCME Conference this week where I will be presenting two sessions, one on Low Stakes Testing in the Mathematics Classroom and one, co-presenting with Julian Gilbey on the brilliant Underground Maths resources. I will update this blog with details of both of these sessions.

A quick look at Twitter this morning and I noticed this tweet from the ADA Project, a free Mathematics Question Bank with no login required. The ADA Project is created by Sam Powell, a mathematics teacher from the UK, working in Australia. All questions have answers, some have a fuller solution and a video explanation. The site is a work in progress with questions added regularly. I rather like this calculator exercise which caught my eye today; students can check that they can key in all the calculations correctly by answering the questions and checking their answers.

ADA Calculator Questions

On the subject of recurring decimals, some older calculators have dedicated buttons, with others like the Casio Classwizz, for example, there is a way…
From the very helpful Calculator Guide:

Returning to the ADA Project, several categories of questions are available; look at Algebra for example and we see some nice use of colour in presenting a solution to a problem expanding double brackets. These examples could be helpful for students when revising.
ADA Project Algebra

On the subject of colour in Mathematics…

Easter Mathematics 2018

It’s Easter time again, so time for some Mathematical Easter treats!

Also a post for students – a puzzle from Mathisfun which is just an excuse to solve some simultaneous equations (and how to do it on Excel with the neat MINVERSE function!) The post also includes some notes and examples for students on simultaneous equations.

Chris Smith - Easter Relay

Easter Relay – Chris Smith

From Chris Smith, try his great Easter relay and note the whole set. I have used many of these very successfully – have fun whilst doing plenty of Maths!

Google - easter

WolframAlpha, of course, can show you some graphs of Easter eggs!

Darth Vader curve
Darth Vader on WolframAlpha – select image

I have noticed whilst using WolframAlpha random suggestions of queries popping up that somebody out there thought I might enjoy (very worrying how right they are!); this popped up – typing, for example, Darth Vader curve into WolframAlpha gives you just that! And my favourite Dilbert and associates are all there too!

On the subject of Easter eggs, I must return to this definition. An updated edition of…
WolframAlpha – a little fun! 

Easter Egg AutographFrom an Easter post some time ago, Douglas Butler created this Easter Egg in Autograph, just enter:
x²/4 + y²/4 + 5z²/36 = 1
and: r = z + 3.5
Autograph Easter Egg

Happy Easter to educators and their students everywhere! Why not give your students a calendar from Just Maths, so they can do a little bit of Maths each day…?

Calendar Just Maths

Just Maths – a little bit of Maths every day