Curve Spotting

8287 /www/nrich/html/content/id/8287/ 1 2012-07-01T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">We've been collecting pictures! What do you think they are pictures of? Which of these pictures have curves in them? Can you see any circles? Can you see any spirals? Are there any pictures that don't have any curves at all? You could send us your ideas or photos of other circles and spirals you have found. Click on the images to make them bigger. <mdo:image class="fancyzoom" src="Aloe%20Plant%20Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Amazon-Curve.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Bacteria-Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Belize-Circle.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Butterfly%20Curves%201.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Butterfly%20Curves%202.JPG" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Cells%20Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Circuit-Board-Curves.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="DNA%20Spiral.jpg" style="height: 125px; width: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Double%20Slit%20Experiment%20Curves.png" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Drought%20Shapes.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Fractal%20Curve.png" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Fruit%20Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Galaxy-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Horns-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Leopard%20Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Lollipop-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Meteor-Crater-Circle.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Planets-Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Snail%20Shell%20Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Spiral%20Staircase.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Storm%20Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Sunflower-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Water%20Whirlpool.jpg" style="width: 125px; height: 125px;"></mdo:image></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">We had a few suggestion about what the $24$ pictures were from Brewers Hill Middle School in England. They were Kyle , who suggested, Succulent plant, leaf, bacteria/microbes, Great Barrier Reef, Butterfly, Moth, red/white blood cells, circuit board, DNA, light, land that has experienced drought, paisley pattern, oranges, lemons and limes, galaxy, gazelle, leopard, lollipops, crater, planets/solar system, snail shell, spiral stair case, satellite view of a hurricane, inside of a sunflower/helanthius whorl and a vortex in water. We had similar ideas from Molly, Annaleigh, Amber and Georgina all from the same school. Ms Wickens also joined in and added a few recognisable mathematical shapes as follows, 1. Aloe polyphilla (spiral) 2. chlorophyl 3. Prochlorococcus - the most common microbe in the world's ocean 4. Atoll reef - the Blue Hole in Belize 5. Diaethria anna aka 88 butterfly, found in wet tropical forests in Central America and South America 6. Bronze copper butterfly 7. red and white blood cells 8. circuit board 9. DNA - double helix 10. speed of light 11. dried river bed 12. spiral paisley pattern 13. citrus fruit slices - oranges, limes and lemons 14. andromeda galaxy 15. impala 16. leopard 17. spiral lollipops 18. meteor crater in Arizona 19. planets 20. snail shell 21. spiral staircase in the Vatican Museum 22. satelite view of a hurricane 23. helianthus whorl - centre of a sunflower 24. a vortex in water Thank you Brewers Hill for those suggestions and I hope that you'll be recognising shapes in all kinds of things that you see in the world around you. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Curve Spotting</h2> We've been collecting pictures! What do you think they are pictures of? Which of these pictures have curves in them? Can you see any circles? Can you see any spirals? Are there any pictures that don't have any curves at all? You could send us your ideas or photos of other circles and spirals you have found. Click on the images to make them bigger. <mdo:image class="fancyzoom" src="Aloe%20Plant%20Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Amazon-Curve.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Bacteria-Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Belize-Circle.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Butterfly%20Curves%201.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Butterfly%20Curves%202.JPG" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Cells%20Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Circuit-Board-Curves.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="DNA%20Spiral.jpg" style="height: 125px; width: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Double%20Slit%20Experiment%20Curves.png" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Drought%20Shapes.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Fractal%20Curve.png" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Fruit%20Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Galaxy-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Horns-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Leopard%20Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Lollipop-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Meteor-Crater-Circle.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Planets-Circles.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Snail%20Shell%20Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Spiral%20Staircase.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Storm%20Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Sunflower-Spiral.jpg" style="width: 125px; height: 125px;"></mdo:image><mdo:image class="fancyzoom" src="Water%20Whirlpool.jpg" style="width: 125px; height: 125px;"></mdo:image> </div> <h3>Why do this problem?</h3> <a href="https://nrich.maths.org/8287?part=index">This problem</a> provides lovely opportunities for mathematical talk. Children benefit from opportunities to describe the mathematical shapes they see around them in order to become more sophisticated in their language and descriptions. These images have been chosen to develop their understanding of curves, moving from informal language such as straight, curved, wavy towards more mathematical language about circles and spirals. Talking, prompted by appropriate questioning, will encourage children to observe the images carefully and identify what is important about them. The sophistication of the mathematical language used can be developed as far as the children can manage. <h3>Possible approach</h3> If you have an interactive white board you can display the images (which can be enlarged by clicking on them individually). Alternatively you could download this <a class="powerpoint" href="/content/id/8287/Curve%20Spotting2.pptx">powerpoint</a> and if you need paper copies print them from this. For a whole class activity you could ask the children to take turns to choose one of the images and describe it so that the rest of the class could work out which image they are describing. Descriptions are likely to focus firstly on colour, but listen out for the mathematical language of shape and pattern and if needed, introduce the vocabulary of circle and spiral. You could then give the children printed copies of the pictures and ask them to work in groups to sort them into sets. Give opportunities for them to explain why they sorted in the way that they did, again bringing out the vocabulary of shape and pattern. <h3> Key questions</h3> Can you see a curve in this one? Where? What's the difference between a circle and a spiral? Can you find any other circles/spirals around us? <h3>Possible extension</h3> Children could take photographs of curves they notice in their surroundings, and these could be used to start an interactive display. Make more durable versions of the images so that they can be used for sorting activities. Those children who have developed fine motor skills could be challenged to make a spiral, using apparatus such as that in <a href="http://nrch.maths.org/8293">Cuisenaire spirals</a> or even to draw an <a href="http://nrich.maths.org/5375">Archimedian spiral</a>. <h3> Possible support</h3> Provide materials for the children to make curves in free play time, both inside and out. Materials could be both continuous (such as skipping ropes, string or ribbon), or sets of objects (such as bottle tops, counters, stones). Bigger versions could be made outside and photographed to add to the display. <div class="framework">You can read about mathematical patterns in <a href="http://nrich.maths.org/2148">Pattern Power</a> Image attribution: Storm Spiral By NASA (http://visibleearth.nasa.gov/view_rec.php?id=6204)[see page for license], via Wikimedia Commons Fruit Circles public domain Aloe Plant Spiral By J Brew (Aloe polyphylla Schönland ex Pillans) [CC-BY-SA-2.0 (www.creativecommons.org/licenses/by-sa/2.0)], via Wikimedia Commons Snail Shell Spiral By Noel Feans (originally posted to Flickr as Spiral) [CC-BY-2.0 (www.creativecommons.org/licenses/by/2.0)], via Wikimedia Commons Sunflower Spiral By Clay Junell from austin, texas (sunflower) [CC-BY-SA-2.0 (www.creativecommons.org/licenses/by-sa/2.0)], via Wikimedia Commons DNA Sprial public domain Drought Shapes Tomas Castelazo Belize Circle public domain Galaxy Spiral public domain Planets Circles public domain Meteor Crater Circle public domain Leopard Circles By Patrick Giraud (Own work) [GFDL (www.gnu.org/copyleft/fdl.html), CC-BY-SA-3.0 (www.creativecommons.org/licenses/by-sa/3.0/) or CC-BY-2.5 (www.creativecommons.org/licenses/by/2.5)], via Wikimedia Commons Cells Circles public domain Bacteria Circles public domain Butterfly Curves 1 By Geoff Gallice from Gainesville (Diaethra clymena Uploaded by berichard) [CC-BY-2.0 (www.creativecommons.org/licenses/by/2.0)], via Wikimedia Commons Butterfly Curves 2 Super.lukas [CC-BY-SA-2.5 (www.creativecommons.org/licenses/by-sa/2.5)], via Wikimedia Commons Fractal Curve public domain Spiral Staircase By NormanB (Own work) [CC-BY-SA-3.0 (www.creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons Lollipop Spiral Personal blog (?) Amazone Curve public domain Electron Scattering Spiral CERN Double Slit Experiment Curves By Timm Weitkamp (Own work) [CC-BY-3.0-de (www.creativecommons.org/licenses/by/3.0/de/deed.en)], via Wikimedia Commons Water Whirlpool By This file is a Work of Kwj2772 (Own work) [CC-BY-SA-3.0 (www.creativecommons.org/licenses/by-sa/3.0) or CC-BY-SA-2.0-kr (www.creativecommons.org/licenses/by-sa/2.0/kr/deed.en)], via Wikimedia Commons Circuit Board Curves Stallio from Flickr </div></mdoxml> 2 3 1 0 0 0 0 Curve Spotting Can you spot circles, spirals and other types of curves in these photos? 2D Geometry, Shape and Space Circles Using, Applying and Reasoning about Mathematics Real world Using, Applying and Reasoning about Mathematics Selecting and using information Admin Lower primary mapping document