Animated Triangles

5968 /www/nrich/html/content/id/5968/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> In the window below, you will see part of the National Film Board of Canada's website. Click on the arrow to watch the short film called "Notes on a Triangle". You can pause the film using the buttons underneath the screen (you may have to scroll down a little to see them). You may like to watch it a few times - it is just under five minutes long. <iframe name="Notes on a Triangle" src="http://www3.nfb.ca/animation/objanim/en/films/film.php?id=10581" style="width: 600px; height: 500px;">You are missing a link to a video of triangles dancing here because your browser does not show iframes.</iframe> How would you describe what happens in the film in just a few sentences? Now watch just the first 34 seconds. You might like to watch this part a few times. Can you describe what happens in this part? <a href="/content/id/5968/EquilateralTris.pdf">Here</a> is a sheet of triangles for you to print off and cut out (using coloured paper might be a good idea). Can you recreate some of the images in this first 34 seconds of the film? Please do send us photos of what you do. Now continue watching from the 34th second up to a minute. What happens in this section of the film? Try creating some of the images in this part using cut-out triangles. Again, we'd love to see what you do - please take pictures to send to us. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Luke from St Patrick's School responded to this problem. This is how he described the film: <div>It uses rotating, sliding and shifting (we can call this "translating") . Along with that the triangles are changing from iscoseles to equilateral to scalene and of course right angled!</div> Luke watched the first 34 seconds and said: It only uses equilateral and scalene triangles! Describing the next part, up to a minute, Luke wrote: The triangle(s) are rotating continuously. Thank you, Luke. I wonder whether anyone can add any more detail to Luke's comments? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Animated Triangles</h2> In the window below, you will see part of the National Film Board of Canada's website. Click on the arrow in the black and white rectangle to watch the short film called "Notes on a Triangle". You can pause the film using the buttons underneath the screen (you may have to scroll down a little to see them). You may like to watch it a few times - it is just under five minutes long. <iframe name="Notes on a Triangle" src="http://www3.nfb.ca/animation/objanim/en/films/film.php?id=10581" style="width: 600px; height: 500px;">You are missing a link to a video of triangles dancing here because your browser does not show iframes.</iframe> How would you describe what happens in the film in just a few sentences? Now watch just the first 34 seconds. You might like to watch this part a few times. Can you describe what happens in this part? <a href="/content/id/5968/Triangles.pdf">Here</a> is a sheet of triangles for you to print off and cut out (using coloured paper might be a good idea). Can you recreate some of the images in this first 34 seconds of the film? Please do send us photos of what you do. Now continue watching from the 34th second up to a minute. What happens in this section of the film? Try creating some of the images in this part using cut-out triangles. Again, we'd love to see what you do - please take pictures to send to us. </div> <h3>Why use this activity?</h3> The main aim of this problem is to give children the opportunity to talk about properties of triangles, symmetry and rotation in the context of a practical task. <h3>Possible approach</h3> Watching the film to begin with will stimulate lots of discussion amongst your class. (If you want to watch it directly from the National Film Board of Canada's website, go here: <a href="http://www3.nfb.ca/animation/objanim/en/films/film.php?id=10581" target="_blank">http://www3.nfb.ca/animation/objanim/en/films/film.php?id=10581</a>). You could ask them to watch it twice then talk about what they saw in pairs before having a whole group discussion. Children might notice the different ways in which the initial triangle is split during the film and it might be handy to have some large copies of the triangle available (cut out from <a href="/content/id/5968/EquilateralTris.pdf">this sheet</a>) so that the pupils can demonstrate what they saw in the film. Your class might also mention the triangles turning. This initial discussion is a good opportunity for you to praise well articulated descriptions of what the children have seen. For the main activity, show the two shorter sections in turn, as the problem suggests. Children could work in pairs to create an image (or more than one) from each part of the film. (It might be helpful to have triangles available which have been printed onto different coloured paper at this point, and perhaps a black sheet as the background for each pair.) In a plenary, you could show a few of their creations and ask the rest of the class how they think each was made from the original triangle. This will encourage visualisation and the use of appropriate vocabulary. The images would make a lovely wall display. <h3>Key questions</h3> How many triangles can you see now? How are they moving? How are they the same as the first triangle? How are they different from the first triangle? How many of the new triangle would fit into the old one? Can you tell me how the triangles have been split? Can you describe the way in which they are moving? <h3>Possible extension</h3> Encourage the children to use increasingly sophisticated language to describe and compare what they see. They may begin to identify the different kinds of triangles they see and to make suggestions about the size comparisons between them using numbers and fractions. Notions of rotation may also be expressed. <h3>Possible support</h3> Some children may need to stick to using colour to identify the traingles and compare them more generally in size looking for the bigger and smaller ones. They may also be able to count the triangles at different stages if you freeze the frames for them.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">How is the starting triangle split? Can you cut your own triangle in the same way? What happens to the new shapes then? You can always pause the film at any point so you can look carefully at the images. </mdoxml> 2 4 1 0 0 0 0 Animated Triangles Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles? Information and Communications Technology Animations 2D Geometry, Shape and Space Mixed triangles Transformations and their Properties Rotations Transformations and their Properties Symmetry Using, Applying and Reasoning about Mathematics Practical Activity