Dividing Fractions- The Awkward Question


Cake fractions
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You are negotiating the shark invested waters of the Sea of Misconceptions which nestles itself within the vast barren plains in the province of Understanding Fractions, and you reach the point where you tell them that to divide one fraction by another you turn the second one upside down and then multiply them. The class is split. There are those pupils who accept what you said and want to get on with it and those who want to know why. In my experience the former group represents they larger proportion but nonetheless, having an answer as to why this works should be in every maths teacher’s armoury.

Let me start by saying that the following explanation isn’t my own. It was passed on to me by a fabulous teacher I had the privilege to spend a year on the PGCE with, Mr Swales. Continue reading

Mathematics and Multimedia Blog Carnival 6

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Welcome to the Mathematics and Multimedia Blog Carnival 6! Many thanks for Math Hombre for passing on the baton from their excellent Fifth Edition.

Six is a fantastic number, in fact, it’s a Perfect Number! It’s the smallest Perfect Number!

Before we dive into the best December posts from the Carnival submissions I’m going to set you a challenge! All the pictures in this edition of the Blog Carnival have a link to the number 6. Can you find all the links? If so, post the answers in the comments section below!

There were only a limited number of entries for this month’s carnival. Don’t worry; I have topped up the selection with my own finds from the outer reaches of the maths-edu-blog-o-shere…

So without further ado, here we go…

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No more guns and robots- using 3D imaging technology in the classroom

RealD glasses used in 3D movie theaters.

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You are teaching 2D views of 3D shapes. You think that the best way to do this may be to give them a physical object to hold and rotate in their hands. That way they’ll easily be able to draw the plans and elevations, won’t they? So you hand out the Multi-link cubes for them to create their own 3D shapes from which to draw some plans and elevations. Within 2 mins all the 12 year old boys have made guns or robots from their Multi-link cubes which may be slightly distracting from the lesson objective…

What’s the solution? Clear expectations, firm reprimands? Go with the tide, let them do it for an agreed 1 minute then they have to knuckle down? Possibly. Or, get them all to put on their 3D glasses to view a 3D shape projecting out of the board which can be rotated to suit whichever 2D view they want to draw? Continue reading

Dropbox- making life a whole lot easier

Image representing Dropbox as depicted in Crun...

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Have you ever lost important photos, music or document files through your computer harddrive or memory stick breaking? If not, are your files at risk from these failures? Do you sometimes want to work on a file that lives on your work computer? If so, doesn’t it get quite challenging after emailing it backwards and forwards a few times to remember what is the ‘latest version’? Do you ever want to share files with people that are too large to attach to an email?

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Real Life Vectors- Planes Landing In Crosswinds

I had a real challenge trying to convince my year 11s today of the awe-and-wonder of vectors and how we could have achieved little as a human race without them. I explained how I used to design buildings taking advantage of the wonderful addition properties of vectors by taking all the forces on a building and summing them such that I could design the building just to resist their single resultant force. They didn’t see the beauty of it so here’s my second ploy:

We’ve all seen the ‘canoeist crosses a river’ vector question where the the flow of water in the river ensures they take a diagonal path rather than one perpendicular to the bank. The following approach is an alternative take on this kind of problem.

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ANNOUNCEMENT: We have been selected to host the Mathematics and Multimedia Blog Carnival! Call for submissions!

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Great Maths Teaching Ideas is proud to announce that we have been selected to host the Mathematics and Multimedia Blog Carnival on 29th December 2010!

This consists of a monthly publication of the best blog articles in cyberspace that discuss connections between mathematical topics, difficult to teach topic discussions, proofs of mathematical curiosities that are accessible by secondary school students, using ICT to enhance learning and much more. The carnival, originally created by the excellent Mathematics and Multimedia blog, has grown significantly over the previous few months with an impressive readership and I’m very excited to get the opportunity to host the carnival on the Great Maths Teaching Ideas site.

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Using ICT to enhance learning- the BIG debate! Here’s one idea…

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This evening my department had a wonderful discussion about the potential future direction of ICT use within the department. Many people had lots of great ideas which filled me with enthusiasm and excitement of the opportunities to use ICT to enhance learning.

I’ve been giving a lot of thought to this recently as the day that pupils get their own netbooks to use in lessons seems on the horizon as computers become more ubiquitous and cheap to produce each year.

Whilst the day that pupils have ‘electronic exercise books’ that they write in using a graphic tablet still seems quite a way off, I am convinced that current ICT technology can help us improve our resource delivery to the students. Continue reading