A+ Click- rich puzzles for developing logical reasoning

A+ Click is a new website that provides a vast collection of puzzles and challenges to develop logical reasoning skills in your pupils. You can search by topic or year group, making finding puzzles at your class’ ability easy. Like NRich Maths in many ways, A+ Click also keeps a record of how many answers your pupils got right. Ideal for computer room lessons. Craig Barton has made one of his Webwizz videos that explains all the details:

A+ Click Video

I’ll certainly be using these regularly for starters with classes who I want to show some more initiative in solving problems.

Top notch.

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Blog recommendation: Flipping with Kirch

The Flipped Classroom model is getting a lot of press in education circles these days as a teaching and learning strategy that promotes independent, student-centred learning. This approach is generally relatively new and experimental in maths classrooms and adopting a Flipped approach in your own classroom may be a step into the unknown. As with anything new we try, we will make lots of mistakes and learn from them. The wisest of all people learn from other people’s mistakes so they don’t make the same ones themselves.

There’s no need to start blind with a Flipped Classroom model now as an American maths teacher, Crystal Kirch has journalled in detail her experiences of flipping her maths classroom for a year.

Flipping with Kirch is a must-read if you are interested in running a Flipped Classroom model. Detailed and honest about the difficulties as well as the benefits, Crystal’s blog gives a balanced account about her experiences of running a Flipped Classroom model. She’s has done her best to collect data to analyse the performance of her flipped class against previous classes taught traditionally. Whilst not academically rigorous, she is doing all she can and being a scientifically accurate as is possible in an education environment.

Anyone interested in running a Flipped Classroom no longer needs to walk this path blind and alone. Have a read of Flipping with Kirch to learn from her mistakes and obtain her advice on the pros, cons and practicalities.

Great work Crystal!

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Meetings.io amazing free video chat without the need to sign up!

There are so many great social networks and other web services out there to help us all connect but the really annoying thing is that not one of them has all your friends and family on. Many of my teaching friends are on Twitter and Google+ and school friends on Facebook. Some of my family are not on social networks at all.

If I want to have a video chat with them I need to see if they have a Skype account or a Google+ account, of if they have the video plugin installed in Facebook. If they have an Apple device then a FaceTime chat is a possibility.

Isn’t this so messy! What if all you had to do to have a video chat with someone was send them a web address and then a video chat opens up? What if it worked in every browser and without signing up for an account? What if it didn’t require the other person to install any software at their end, it just worked in the browser straight away?

That day has finally come. Ladies and gentlemen, I give you: meetings.io

Check out this amazing service that does everything mentioned above and more. The uses in education could be huge. Imagine how easy it would make video conferencing if all you had to do was send pupils a web link?

Currently up to 5 people can talk in the same online video chat and there are additional features such as a note-making section that automatically emails you any private notes you made during the meeting, and live text chat between participants. This is a new product but they are working on additional functionality such as compatibility with Android and iOS devices, the ability to share files and share parts of your screen during the video chat.

To be able to use such a high quality service without the need for yet another login and password in this day and age is so novel and I thoroughly suggest you check it out!

If you have any suggestions and ideas or would like to share any experiences of how you can use this in education then please do let us know in the comments section below.

Click here to visit meetings.io

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Derive the trigonometric graphs using spaghetti!

If you’re looking for an interesting way of teaching the trigonometric graphs sine and cosine then you must watch this superb video of an activity to derive them using spaghetti. Chris Smith @aap03102 created this activity and then made the cheesy video explaining how to produce the spaghetti trig graphs.

Trigonometric Graphs Spaghetti Video 

Chris publishes a weekly maths newsletter that is a great read. To subscribe to it send him a quick email to aap03102@gmail.com.

To follow up on the spaghetti activity, here is a great Geogebra applet that demonstrates the same ideas in an interactive way.

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Where does pi r squared come from? Beautiful demonstration

Area of Circles Geogebra applet designed by Anthony Or, Education Bureau, Hong Kong

Here is something a bit special. It’s an amazing Geogebra applet that shows where the formula for the area of a circle comes from. I’ve had pupils cutting circles into sectors before to perform the same proof, but this interactive applet it first class in showing the concept in a visually stunning way and quickly. Top stuff!

Click here to launch the Area of a Circle applet.

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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.

Enjoy!

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

Other

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

 

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:

Constructions

Linear Equations

Probability

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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TED-Ed Lessons Worth Sharing

Regular readers of Great Maths Teaching Ideas will know what a fan of TED.com I am. TED has changed the way that I look at the world on countless occasions. Their videos are never anything but inspiring and thought-provoking. They remind us of what the best and worst parts of the human condition are about.

TED-Ed have recently launched a new initiative to bring awesome educational videos to the world for free. Think Khan Academy, but with professional levels of production and teaching. I could say more but this video says just about everything you need to know:

TED-Ed Lessons Worth Sharing

I’m very excited to see what’s going to come out of this initiative. If you’d like to follow TED-Ed, you can subscribe to their YouTube page or visit their website. Watch this space!

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Khan Academy releases iPad App

The Khan Academy has just released a free app for the iPad. For people unfamiliar with the Khan Academy, it is a website featuring over 2500 free educational videos about a variety of topics including maths, science, art and much more. Salman Khan, the site’s author delivered a superb TED talk last year explaining his vision. Many people who are trying out a Flipped Classroom teaching style are using the Khan videos for homeworks.

The app is good. It is easy to navigate to any video in the Khan collection and logging in with your Khan account details allows you to save your progress. Overall the user interface is well designed and intuitive.

Click here to download the Khan Academy app from iTunes

 

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Stunning new innovative resources site www.numberloving.co.uk

Laura Rees-Hughes and Sharon Derbyshire are teaching resource megastars! Many of their wonderful resources have been available from Craig Barton’s site  (www.mrbartonmaths.com) for a while, but they have now created a resources website to share all of their amazing creations. Please allow me to introduce: www.numberloving.co.uk.

The resources are a long way from ’10 questions about ….’ worksheets. On the Number Loving site you will find Top Trump card games, treasure hunt activities, QR code activities, matchup cards, quiz-quiz-trade activities, collective memory sheets, online investigations, revise and draw activities and much more. The resources will have your pupils doing ‘hands-on’ maths in engaging, active ways.

Laura has kindly agreed that I can feature some of her and Sharon’s resources on Great Maths Teaching Ideas. Here is a sample of some of their ideas:

Adding and Comparing Fractions Top Trump Cards

AFL Quadratics Match Up

Angles Musical Statues

Area and Volume Formula Match Up

Bingo Expanding Single Brackets

Circle Theorems Bingo

Loci and Constructions Murder Mystery

Volume QR Reader Treasure Hunt

I can’t recommend www.numberloving.co.uk highly enough! Definitely have a look when you get a moment.

You can follow Laura Rees-Hughes and Sharon Derbyshire on Twitter. Their Number Loving Blog is a fantastic read and available at this link.

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Maths is not calculating- Conrad Wolfram

Conrad Wolfram, founder of the amazing Wolfram Alpha site discussed on Great Maths Teaching Ideas previously, spoke recently about his concerns about the way maths education is delivered right across the world. In an engaging and persuasive talk, Wolfram argues that there is more to maths than calculating, yet this is what we are teaching pupils to do by hand 90% of the time. He believes that computers should be used for calculating and the maths curriculum should embrace the other areas of maths that computers cannot yet do such as formulating a problem, deciding what information you need to know and how you are going to use it and then interpreting the results.

I’ll go on the record saying that I believe Wolfram is right here. The current approach of trying to make pupils ‘more functional’ in their maths is an add-on to the current curriculum. Wolfram’s vision is where the ‘functionality’ pupils need to develop is the curriculum and we let the computers handle the solving of the quadratic equation.

This year I discovered Wolfram Alpha and how it can solve just about any question on the maths syllabus I teach. It can complete the square, factorise, calculate the sum of interior angles in polygons and solve cubic equations (without trial and improvement!) and pretty much anything else you’ll ever need. I was so energised when I discovered it as I thought it was going to be a tool pupils could really use to help them with their learning. In reality I could never see a way to get pupils as excited about it as they all realised they are investing large amounts of time learning how to solve things by hand that a computer can do faster, for free and without making mistakes.

You’re right Conrad.

Learning Without Frontiers Talk by Conrad Wolfram

What do you think?

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Information Is Beautiful infographics project

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!

Next, pupils watched this excellent TED talk by David McCandless that shows many examples of how he makes information beautiful.

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!

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Multiplying and dividing by 10, 100 and 1000- Who Wants To Be A Millionaire?

Who Wants to Be a Millionaire? (Philippine gam...

Image via Wikipedia

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.

Click here to download the PowerPoint Document

Click here to download the Excel Document

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MathsNet and NRich Maths 3D shape resource heaven

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.

UPDATE: MathsNet seems to be history, but the same links are available from this site: http://mathandmultimedia.com/2012/03/02/3d-math-applets/