I’d like to tell you a bit about a new project that I’m running with a top set year 7 class at the moment. The project is called Information Is Beautiful and is based around techniques for data representation and visualisation. We have done a few lessons on the basics such as how to draw comparative or multiple bar charts, frequency diagrams, pie charts etc and now the pupils are using these skills in the context of infographics.
If you don’t know what and infographic is, it is a poster that uses different graphs and charts to communicate a message, but in a visually attractive, beautiful way. Quite often traditional graphs or charts are adapted to make them more visually appealing and relevant for the topic. Good websites to find infographics are InformationIsBeautiful.net and Good.Is.
Pupils started off by looking at this fantastic infographic about who is likely to buy the iPad 3:
Pupils looked at how traditional graphs and charts had been changed. For example, notice how the pie chart that shows the proportion of different sizes of memory in iPads in circulation is also divided into 3G vs Wifi connectivity too. The authors are showing two types of data on one pie chart!
Pupils are researching infographics for homework this week with a focus on answering the question ‘how have they changed traditional maths graphs and charts to make them more relevant to the topic and gorgeous to look at?’ In future weeks pupils are going to start researching their own chosen topic and getting their own primary or secondary data for it. An excellent source of free public data is the Google Public Data Explorer website that features wonderful interactive charts for real world data from greenhouse gas emissions to the proportion of seats held by women in parliaments. Here is an example of one of the interactive charts:
The pupils seem to be very engaged in the project so far. I’ll make sure to update this post with their own infographic productions once they complete them!
Here is a superb plenary for a lesson about multiplying and dividing by 10, 100 and 1000. This resource consists of two files. The first is a PowerPoint presentation that runs a game of Who Wants To Be A Millionaire. The Second is an Excel Document that gives pupils a worksheet to record their successes and failures on. A nice alteration to the traditional format of the game is to not eliminate players once they get a question wrong. Instead, encourage pupils to use the worksheet to record the winnings they get from each question and then to total up their prize money at the end. A super resource and thanks to Ceri Reece for bringing this to my attention.
The Nuffield Foundation have released a series of resources to support teachers in the teaching of applying mathematical processes. The resources are divided between ‘investigations’ and ‘practical explorations’. These remind me of the well-known Bowland Maths resources in their style and scope. They are certainly worth checking out. I think my favourite idea from the practical explorations is ‘How far can I get from here in an hour?’ Giving pupils access to timetables, Google Maps etc, they can apply so many different maths concepts to find out the furthest they could get away in an hour. All resources come with pupil copies and teacher’s notes. These are lessons ready to go!
Paul Collins is the author of the TES Resource of the Week 19 that helps pupils understand the specific language of GCSE maths exams. Craig Barton has recorded a video explaining possible teaching approaches you could use with this resource here.
Paul Godding is a board game and puzzle inventor. He got in touch via Twitter and kindly sent me two samples of his creations. Paul designs educational puzzles that allow pupils to practice key maths ideas and concepts whilst also being engaged and logically challenged. There is a large selection of Paul’s puzzles on his website www.paulgodding.com that I would encourage you to visit. In addition to board based games and puzzles he is also now developing smartphone apps in the same vain.
The first sample Paul sent me was of a product called Fractiles. This is a magnetic tiling toy that contains 96 magnetic tiles that can be placed on the accompanying 8″ by 8″ magnetic board. There are 3 different shaped and coloured tiles. The packaging comes with numerous ideas of designs you can make using the tiles and also some examples of how you could use Fractiles to teach translational, reflective and rotational symmetry and tessellation. Here are some pictures that my four year old daughter produced.
My daughter really enjoyed the creative nature of Fractiles and I could see a lot of mathematics going on. The packaging even includes an explanation of why the shapes tessellate; with the interior angles of the tiles being multiples of 1/14ths of 360 degrees. A great resource.
Secondly, Paul sent me a sample copy of The 7 Puzzle. This consists of a mouse mat with a 7 by 7 grid where each cell contains a shape and number. Accompanying this are 14 leather shapes that you place on the grid to cover up certain cells. If you place all of these on the grid with no overlaps there are 7 cells left showing. The idea is the 7 remaining cells must contain a certain type of number, colour or shape, depending on what is required for the challenge. There are 40 challenges that include number, colour and shape criteria such as even numbers, multiples of 5, heptagons, factors of 48, prime numbers, red etc…
My wife's solution to the even numbers challenge
Both Fractiles and The 7 Puzzle would make great resources in the maths classroom and I’d personally thoroughly recommend them. If you are interested in these resources and other offerings from Paul Godding be sure to check out his website: www.paulgodding.com. You can also follow Paul on Twitter @7puzzle.
MathsNet have a wonderful collection of 3D shape resources at this webpage. There are a variety of interactive applets that cover 3D shape topics including nets and 2D views of 3D shapes.
My particular favourite is ‘Building Houses 2’ where pupils have to build the 3D shape by using the 2D views given. They score maximum points by using the minimum number of blocks possible. By clicking and dragging on the 3D view pupils can spin their construction around in real time to help them with the task.
Building Houses 2 Interactive Applet
NRich Maths have a superb and challenging activity based on 2D views of 3D shapes called The Perforated Cube. Pupils can use the Building Houses 2 applet to help them with the investigation which is based around a cube made from 125 smaller cubes in a 5x5x5 arrangement. The cube has ‘mini-cubes’ removed to cause perforations. Pupils are given 3 2D views of the shape and have to calculate what is the maximum and minimum number of mini-cubes required to give those views. Highly recommended.
The excellent Craig Barton of mrbartonmaths.com is selecting a ‘resource of the week’ each week from the enormous TES resource collection. From now on I shall link to each resource from this blog. So, let’s get started with this weeks’ resource of the week:
To help pupils see the bigger picture in topics I have decided to experiment with some conceptual card sorts. I worry sometimes that pupils just learn methods and can’t see the links between them. Teachers I know encourage their pupils to ‘build a map’ in their minds of topics and ideas so that when they are faced with a maths problem they can ‘navigate’ to the correct section of their mind map and start using the skills they know. I love this idea but do think it is a perhaps a bit too challenging to ask pupils to do this with no support. My aim in producing the conceptual card sorts it to help pupils in their categorisation and organisation of maths concepts in their minds.
I plan to create a series of conceptual card sorts that cover challenging topics in GCSE maths. How far I’ll go with this depends on the success it has with my and your pupils. The first conceptual card sort is ready and about quadratic equations:
The idea is that there are 20 statements to do with quadratic equations that pupils have to organise into 5 groups. The group themes are given. Once pupils have completed the card sort they could stick it in their books, or even stick it onto paper and add to it with worked examples. This could be an end-of-unit plenary activity or a great revision resource. If you do use it I’d love to hear how you get on. Feel free to get in touch (williamgeorgeemeny at gmail.com)
The idea is you laminate all the sheets first then cut out all the numbers on the second sheet. Pupils can place numbers on the template sheet which then tells them which direction to shift the digits and how far depending on what operation they would like to do. Attached is also a worksheet of questions (answers included) that pupils can solve using the number cards and template.
Already featuring the maths of crisps and donuts, and looking at the artistic genre of pointillism, The Mathematical Palette is certainly a blog you could encourage your students to subscribe to if they want to find interesting uses of maths in the real world.
How one man can maintain so many high-quality blogs I’ll never know, but Guillermo Bautista has potentially done it again with this one. Early signs are good. Certainly one to watch…
If you read this blog regularly you’ll know what a fan I am of TED.com. I can’t speak highly enough of this wonderful organisation that provide inspiring talks from leading thinkers totally for free.
Last week I discovered an outstanding talk on TED.com by Shawn Achor that totally questioned my understanding of how important happiness is in our lives and for learning in my classroom. Shawn speaks about how the formula for happiness in many institutions, and even society as a whole in the Western world, is that success will lead to happiness. He speaks about about how this is an incorrect notion and entirely backwards to how our brains work. Calling on extensive research he and his team have done, he argues that the way to maximise performance is to totally reverse the formula: happiness leads to success. It may sound cheesy but just listen to his talk. You’ll be totally amazed. It made me realise how important it is that pupils in my lessons are happy. They don’t learn at their potential if they’re not happy.
I’ve started reading his book: The Happiness Advantage and am thoroughly enjoying it.
Cary Huang has created a fantastic website that shows how relevant standard form is to our lives. You can start at the 10^0 m scale and zoom in or out seeing significant objects that vary in size from the width of the universe to a Plank Length. Very engaging and interactive. Highly recommended.
This week is an extremely exciting one for me as I have realised one of my life ambitions: to publish a book! Ladies and Gentlemen, I give you: 100 Things Awesome Teachers Do.
Think of the book as like a breaktime chat between teachers who are sharing ideas that they have found work well for them. It’s not full of academic research findings. Instead it’s full of great ideas learned from the University of Life and Experience. This isn’t a book about producing a one-off outstanding Ofsted lesson. It’s a book about getting high-quality learning going on in your classroom day-in-day-out.
100 Things Awesome Teachers Do is divided into 10 sections such as Lesson Planning, Learning Styles, Learning Environment, Marking and Feedback, Motivation and Engagement, Making the Learning Stick and more. Each section has 10 ideas that I’ve learned from awesome teachers. It’s a book you can dip into for ideas whenever you find yourself feeling like you need something new to try out.
Published by Smashwords, the book will be available to download from the Apple iBook Store, the Amazon Kindle Store, the Sony e-Reader Store, the Barnes & Noble Store, the Diesel ebook Store and the Kobo Store within a few weeks. You can currently buy the book directly from the Smashwords website.
As a thank you to all of Great Maths Teaching Ideas’ readers, I am giving a 25% discount in the Smashwords online store! Just type in this promotional code: FY98V as you are checking out. The promotion ends on 03/03/12.
I’d love to know what you think about the book. Please send your thoughts to firstname.lastname@example.org. If you’d be willing to write a testimonial about it that I could include in the description of the book in the online stores please do get in touch.
I hope you enjoy the book and that it gives you lots of new ideas!