Proportionality formulae conceptual card sort

To help pupils understand the main concepts in the topic of proportionality formulae I have created this conceptual card sort. Pupils have to sort the cards into eight groups based on the types of proportionality assessed at GCSE. Within each group there will be 4 cards that include: the proportionality expressed in words, the proportionality expression, the proportionality formula featuring the constant of proportionality and a graph showing the general shape. I hope you and your pupils enjoy using it!

Click here to download the proportionality formulae card sort

100 Things Awesome Teachers Do goes live in the Amazon Kindle Store

If you have been holding out on getting 100 Things Awesome Teachers Do when it goes live in the Amazon Kindle Store, wait no longer! Here are links to the book on Amazon in various countries:

US Kindle Store

UK Kindle Store

DE Kindle Store

FR Kindle Store

IT Kindle Store

ES Kindle Store

Thanks for your support and I hope you enjoy the book!

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MEDIAN- a stunning blog bursting with rich activities by Don Steward

MEDIAN is written by Don Steward and is quite simply one of the very best maths teaching blogs I have come across. It’s aim is to share maths resource and lesson ideas for teachers of 11-16 year olds. The activities featured on the site are often problem solving based and very engaging. Don describes his interest as ‘finding effective tasks for teaching 11-16 maths’. His suggestions remind me of NRich type activities where pupils are ‘using maths with a purpose’. Rather than solving 10 questions for the sake of it pupils are solving questions to help solve a problem and that makes the activities so much more engaging.

One example of some excellent resources produced by Don are the Practice Makes Perfect Series:

An example of one of Don Steward's Practice Makes Perfect resources

Rather than just provide pupils with 24 questions to help them with their revision, these resources give you lots of options as a teacher to do something more engaging. For example, using the grid of questions above you can turn it into a game of ‘4 in a line’ where pupils are split into two groups and compete against each other choosing questions and highlighting them in their team’s colour to win by getting 4 in a line.

Another brilliant resource is fibonacci sequences and equations which introduces concepts in algebra such as variables, sequences and equation solving but in a way that hooks pupils as they try to figure out the maths behind the magic happening around them.

MEDIAN is regularly updated and top read. Highly recommended.

100 Things Awesome Teachers Do goes to n.o. 1!

Top of the Education section in the Apple iBookstore!

100 Things Awesome Teachers Do has today gone to the n.o. 1 spot in the Education and the Professional & Technical sections of the Apple iBookstore! I am totally speechless and overwhelmed. This will be a day I shall remember for a very long time. Thank you so much for all your support in making this possible. The growth of Great Maths Teaching Ideas over the last year and now the ebook completely blows my mind. Thank you for taking this journey with me and I hope to continue sharing ideas, resources and things I learn with you for many years to come. Here’s to teaching and giving the next generation the best chance possible.

100 Things Awesome Teachers Do goes live in the Apple iBookstore!

My ebook 100 Things Awesome Teachers Do has just gone live in the Apple iBookstore! It has started receiving testimonials. Here is the first one:

“William Emeny’s 100 Things Awesome Teachers Do is a fantastic book, crammed full of wonderfully unique ideas to engage learners, improve learning and create that buzz about your classroom. The book is separated into 10 key topics, each with 10 innovative ideas. It is thoroughly enjoyable to read and can easily be dipped in and out of as required. As a trainee teacher on the GTP, I have found the ideas Emeny presents invaluable and his passion for teaching shines through in every idea. Every teacher wants to be an awesome teacher; how many of Emeny’s 100 things are you currently doing?”
– Paul Collins, Mathematics Teacher

Feel free to download a free sample from the Apple iBookstore by clicking here or visiting the iBookstore and searching for 100 Things Awesome Teachers Do. I hope you enjoy the book and that it gives you some great ideas to try out with your classes! Thanks for your support.

UPDATE 25/03/12

It’s gone straight in at n.o. 2! If you visit the iBookstore and got to the Top Charts section you’ll see it’s gone in at n.o. 2 in both the Professional & Technical and the Education sections of the store! Thanks so much for your amazing support!

100 Things Awesome Teachers Do in at n.o.2 in the Education Top Charts of the Apple iBookstore

Interesting reads from the blogs 23/03/12

My teaching benefits a great deal from me reading the dozens of maths teaching blogs I subscribe to. Most days I take a read of them and grab the best of the latest resources and lesson ideas. Reading them is made much easier by subscribing to their RSS feeds in Google Reader, a free product from Google that I can’t recommend highly enough.

I want to share the best blog articles that I find with you and so will be sharing them with you in interesting reads from the blogs posts. I can’t say I’ll commit to doing it once every week but I hope to do it regularly as time allows.

So, without further ado here are interesting reads from the blogs 23/03/12:

James Paul Gee on Learning with Video Games- Edutopia

Instant Graphs- Number Loving

101 Questions- A New Maths Questions Site From Dan Meyer- Free Technology For Teachers

Using Latex in GMail- Math and Multimedia

Paper Toys- Free Technology For Teachers

Jumping- MEDIAN

Does the “Flipped Classroom” increase student understanding and proficiency? [Flipped Data Part 3 – Math Analysis Unit O]- Flipping With Kirch

DVR Dilema- Yummy Math

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The Standards Unit including software

The Standards Unit are a collection of resources produced in response to the Smith Report by the Department for Education and Skills. They use ‘active learning’ strategies that were originally planned for use post-16 but have now been introduced into the secondary sector. The well known Dr Malcom Swann of Nottingham University played a big role in the development of the resources that span the whole secondary maths curriculum.

I personally use these resources a lot and consider them to promote high levels of mathematical thought and making connections between topics. In addition to the paper-based resources, the Standards Unit also features software applets. I have added as many of these that I can find to the list below, but there are more out there. If you find a link to a piece of software discussed in the Standards Unit and it isn’t included below could you please send me the link so I can make it available to everyone.

If you would like to purchase a hard copy of the Standards Unit you can from the NCETM website.


The Standards Unit Resources

Mostly Number

N1 Ordering fractions and decimals

N2 Evaluating statements about number operations

N3 Rounding numbers

N4 Estimating length, using standard form

N5 Understanding laws of arithmetic

N6 Developing proportional reasoning

N7 Using percentages to increase quantities

N8 Using directed numbers in context

N9 Evaluating directed number statements

N10 Developing an exam question: number

N11 Manipulating surds

N12 Using indices

N13 Analysing sequences

Mostly Algebra

A1 Interpreting algebraic expressions

A2 Creating and solving equations

A3 Creating and solving harder equations

A4 Evaluating algebraic expressions

A5 Interpreting distance-time graphs with a computer

A6 Interpreting distance-time graphs

A7 Interpreting functions, graphs and tables

A8 Developing an exam question: generalising patterns

A9 Performing number magic. Adding pairs applet. Calendar applet. Consecutive sums applet. Pyramid applet.  Routes applet

A10 Connecting perpendicular lines

A11 Factorising cubics

A12 Exploring trigonometrical graphs

A13 Simplifying logarithmic expressions

A14 Exploring equations in parametric form

Mostly Shape and Space

SS1 Classifying shapes

SS2 Understanding perimeter and area

SS3 Dissecting a square

SS4 Evaluating statements about length and area

SS5 Evaluating statements about enlargement

SS6 Representing 3D shapes. Link to software referred to on mathsnet site.

SS7 Transforming shapes

SS8 Developing an exam question: transformations

Mostly Statistics

S1 Ordering probabilities

S2 Evaluating probability statements

S3 Using probability computer games. Coin races applet. Dice races applet

S4 Understanding mean, median, mode and range. Stats 1 applet. Stats 2 applet.

S5 Interpreting bar charts, pie charts, box and whisker plots

S6 Interpreting frequency graphs, cumulative frequency graphs, box and whisker plots

S7 Developing an exam question: probability

S8 Using binomial probabilities

Mostly Calculus

C1 Linking the properties and forms of quadratic functions

C2 Exploring functions involving fractional and negative powers of x

C3 Matching functions and derivatives

C4 Differentiating and integrating fractional and negative powers

C5 Finding stationary points of cubic functions


O1 Moving from Eulerian graphs to route inspection (Chinese postman problem)

O2 Exploring equations of motion

O3 Solving problems using Newton’s Law

Professional Development

PD1 Getting started. Presentation

PD2 Learning for mistakes and misconceptions. Presentation

PD3 Looking at learning activities. Presentation

PD4 Managing discussion

PD5 Developing questioning. Presentation

PD6 Using formative assessment. Presentation


Awesome maths blogs

Craig Barton has made a short video giving you a tour of what he thinks are the best maths blogs currently on the net:

Web Whizz 21- Maths Blogs

Here are links to the blogs Craig mentioned:

Number Loving

Reflective Maths Teacher

Maths, Learning and Web 2.0

Great Maths Teaching Ideas

Douglas Butler’s Blog

Mr Collins’ Reflective Journal




NRich activity about square numbers- Cycling Squares

Cycling Squares is superb NRich Maths activity to get pupils familiar with the square numbers. The idea is that the pupils get the worksheet above and have to place the numbers into the spaces in the circle. Each adjacent pair of numbers must add up to a square number.

I have used this activity a lot myself and find that pupils often get all the way around the circle only to find the last two don’t add up to a square number! It is a challenging activity that takes a lot of persistence to solve. The nice thing is that this is a true rich activity; even the lower ability pupils can still get going relatively easily and benefit from it.

As ever, answers and teacher notes are available along with the activity on the NRich website.

Click here to view Cycling Squares on the NRich website

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Singapore’s 21st-Century Teaching Strategies

The following video was posted on the wonderful website. It explains the contemporary approaches and strategies Singapore is adopting in their education system.

As a teacher, I want to teach in an environment like this and if I were a student I’d want to go to a school like this. Undoubtedly we only see the best and glossy side of this system in the video, but it clearly is working. Singapore came 5th in the world (averaged across reading, maths and science) in the 2009 PISA tests. The UK came 25th.

I particularly admire the way the schools are embracing social networking technologies, reclaiming them for learning purposes. Also, the way in which the head teacher says he considers fun an important ingredient in school is very refreshing.

Singapore’s 21st Century Teaching Strategies

The following Fast Facts were taken directly from the Edutopia article which can be accessed here.

Singapore Fast Facts

  • When Singapore gained its independence in 1965, most of its population of two million people were unskilled and illiterate.
  • The government invested in education, and by the early 1970s, all children had access to lower secondary education.
  • In 2009, the first year Singapore participated in the Programme for International Student Assessment (PISA) tests, they placed near the top for all tested subjects: fifth for reading, second for mathematics, and fourth for science. See all 2009 PISA scores.
  • Teaching is a highly-respected and well-compensated profession in Singapore. All teachers are trained at the country’s National Institute of Education (NIE).
  • All new teachers are paired with experienced teachers for mentoring, and peer feedback is built into the schedule.
  • Teachers are entitled to 100 low or no-cost hours of professional development each year.
  • There are approximately 522,000 students attending about 350 schools in Singapore’s education system.
  • Class sizes are large, especially at the secondary level, averaging 36 students per class.


The Ultimate Maths Faculty- using social networking and collaborative working technologies for amazing free CPD

Allow me to introduce The Ultimate Maths Faculty. This is a project created by Dave Gale (@reflectivemaths). Dave is a maths AST and founder of the Reflective Maths Teacher’s Posterous blog. The idea is simple, but the impact could be a paradigm shift in the way we look at CPD. I believe getting involved with this project could be the best CPD you’ve ever had, and it’s totally free.

The Ultimate Maths Faculty is an attempt to share best practice by connecting brilliant teachers around the world using social networking. These teachers then work in their free time using collaborative-technologies to share ideas and produce guidance on high quality pedagogy for teaching specific topics.

The social network of choice is Twitter and the Ultimate Maths Faculty’s actions can be followed at this hashtag: #UMFac. Dave also posts progress updates through his blog.

The first project worked on by the Ultimate Maths Faculty was to produce best practice guidance on how to teach surds. A GoogleDoc document was made available that anyone could edit to contribute their own ideas of how to teach this topic. Click here to view the document. You will see a melting pot of ideas with teachers recommending their own suggestions then sharing their views on those of others. Dave is going to collate the ideas expressed in the GoogleDoc document and then produce a’ model lesson’ and teacher guidance from it.

The project is still new but other topics are now being explored such as:


Linear Equations


Please feel free to join the Ultimate Maths Faculty yourself by contributing to the GoogleDoc documents above. Share your suggestions on best practice for teaching these topics. Follow the Twitter group at #UMFac and also Dave’s blog. Make sure you add your name to the Ultimate Maths Faculty list as it will allow you to connect with brilliant maths teachers around the world.

I am personally very excited about this project as it blends the power of ICT to connect people, with the collective will of teachers to improve their own practice through sharing their expertise. Isn’t this project the pure essence of what CPD should be?


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Inspiring pupils into a STEM career- agile flying robots…

More TED I’m afraid…! This time it is a stunning talk given by Vijay Kumar about small autonomous robots that can fly and cooperate. This cutting edge research really shows how exciting a STEM career can be. I believe passionately that pupils need to see videos like this one to understand what amazing things you can do with maths, technology and science once you leave school. Truly inspirational stuff and I’d encourage you to share it with your own pupils:

TED Robots that fly and cooperate

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