Biology measurement challenge

7424 /www/nrich/html/content/id/7424/ 1 2011-06-15T14:04:05 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/6308">Warm-up</a></li> <li><a href="http://nrich.maths.org/6505">Try this next</a></li> <li><a href="http://nrich.maths.org/6678">Think higher</a></li> <li><a href="http://plus.maths.org/content/philosophy-applied-mathematics">Read: mathematics</a></li> <li><a href="http://en.wikipedia.org/wiki/Cell_%28biology%29">Read: science</a></li> <li><a href="http://plus.maths.org/content/do-you-know-whats-good-you-maths-next-microscope">Explore further</a></li> </ul> <div> </div> Consider these objects, images for which are given below: <ol> <li>Mitochondria</li> <li>Arabis voch pollen</li> <li>Ring stage of Plasmodium falciparum</li> <li>Tuberculosis bacterium</li> <li>Human red blood cell</li> <li>Human nerve cell</li> <li>The eye of a needle</li> <li>Cat hair</li> <li>Snowflake crystal</li> </ol> How many do you recognise? Can you put them in order of length? Cross-sectional area? Volume? Once in order, how many of the smaller objects would fit into the larger objects? Discussion point: What measurement difficulties does this task raise? You can see the images, some of which contain scale information, below Mitochondria <a href="http://commons.wikimedia.org/wiki/File:Mitochondria,_mammalian_lung_-_TEM_%282%29.jpg" title="By Louisa Howard [Public domain], via Wikimedia Commons"><mdo:image alt="Mitochondria, mammalian lung - TEM (2)" src="http://upload.wikimedia.org/wikipedia/commons/e/e4/Mitochondria%2C_mammalian_lung_-_TEM_%282%29.jpg" width="640"></mdo:image></a> Arabis voch pollen <a href="http://commons.wikimedia.org/wiki/File:Arabis_voch1-1.jpg" title="By Marie Majaura (Own work) [CC-BY-SA-3.0 (www.creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons"><mdo:image alt="Arabis voch1-1" src="http://upload.wikimedia.org/wikipedia/commons/thumb/7/77/Arabis_voch1-1.jpg/800px-Arabis_voch1-1.jpg" width="800"></mdo:image></a> Ring stage of Plasmodium falciparum <a href="http://commons.wikimedia.org/wiki/File:Plasmodium_falciparum_in_Red_Blood_Cells.jpg" title="By Ernst Hempelmann (Original work by Ernst Hempelmann) [Public domain], via Wikimedia Commons"><mdo:image alt="Plasmodium falciparum in Red Blood Cells" src="http://upload.wikimedia.org/wikipedia/commons/thumb/9/91/Plasmodium_falciparum_in_Red_Blood_Cells.jpg/800px-Plasmodium_falciparum_in_Red_Blood_Cells.jpg" width="800"></mdo:image></a> Tuberculosis bacterium <a href="http://commons.wikimedia.org/wiki/File:Mycobacterium_tuberculosis_8438_lores.jpg" title="By Photo Credit: Janice Carr Content Providers(s): CDC/ Dr. Ray Butler; Janice Carr [Public domain], via Wikimedia Commons"><mdo:image alt="Mycobacterium tuberculosis 8438 lores" src="http://upload.wikimedia.org/wikipedia/commons/f/f5/Mycobacterium_tuberculosis_8438_lores.jpg" width="640"></mdo:image></a> Human red blood cell <a href="http://commons.wikimedia.org/wiki/File:SEM_blood_cells.jpg" title="By Bruce Wetzel (photographer). Harry Schaefer (photographer) (Image and description: National Cancer Institute) [Public domain], via Wikimedia Commons"><mdo:image alt="SEM blood cells" src="http://upload.wikimedia.org/wikipedia/commons/thumb/8/82/SEM_blood_cells.jpg/240px-SEM_blood_cells.jpg" width="240"></mdo:image></a> Human nerve cell <a href="http://commons.wikimedia.org/wiki/File:Myelinated_neuron.jpg" title="Roadnottaken [GFDL (www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (www.creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons"><mdo:image alt="Myelinated neuron" src="http://upload.wikimedia.org/wikipedia/commons/c/c1/Myelinated_neuron.jpg" width="500"></mdo:image></a> The eye of a needle <a href="http://commons.wikimedia.org/wiki/File:Eye_of_a_Needle.jpg" title="By crop by Peng (morguefile.com) [see page for license], via Wikimedia Commons"><mdo:image alt="Eye of a Needle" src="http://upload.wikimedia.org/wikipedia/commons/6/6e/Eye_of_a_Needle.jpg" width="240"></mdo:image></a> Cat hair <a href="http://commons.wikimedia.org/wiki/File:ESEM_BSE_cat_hair_No1194_10kV_1000x_680Pa.jpg" title="By Gerry Danilatos (Own work) [CC-BY-SA-3.0 (www.creativecommons.org/licenses/by-sa/3.0) or GFDL (www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons"><mdo:image alt="ESEM BSE cat hair No1194 10kV 1000x 680Pa" src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/64/ESEM_BSE_cat_hair_No1194_10kV_1000x_680Pa.jpg/500px-ESEM_BSE_cat_hair_No1194_10kV_1000x_680Pa.jpg" width="500"></mdo:image></a> Snowflake Crystal <a href="http://commons.wikimedia.org/wiki/File:Snow_crystals.png" title="See page for author [Public domain], via Wikimedia Commons"><mdo:image alt="Snow crystals" src="http://upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Snow_crystals.png/640px-Snow_crystals.png" width="640"></mdo:image></a> The URLS of these beautiful images are as follows: <ul> <li>Mitochondria - http://commons.wikimedia.org/wiki/File:Mitochondria,_mammalian_lung_-_TEM_%282%29.jpg</li> <li>Arabis voch Pollen - http://commons.wikimedia.org/wiki/File:Arabis_voch1-1.jpg </li> <li>Plasmodium falciparum - http://commons.wikimedia.org/wiki/File:Plasmodium_falciparum_in_Red_Blood_Cells.jpg</li> <li>Bacterium (tuberculosis) - http://commons.wikimedia.org/wiki/File:Mycobacterium_tuberculosis_8438_lores.jpg </li> <li>Human red blood - http://commons.wikimedia.org/wiki/File:SEM_blood_cells.jpg</li> <li>Nerve cell - http://commons.wikimedia.org/wiki/File:Myelinated_neuron.jpg</li> <li>Eye of a needle - http://commons.wikimedia.org/wiki/File:Eye_of_a_Needle.jpg</li> <li>Cat hair - http://commons.wikimedia.org/wiki/File:ESEM_BSE_cat_hair_No1194_10kV_1000x_680Pa.jpg</li> <li>Snow crystals - png: http://commons.wikimedia.org/wiki/File:Snow_crystals.png</li> </ul> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><h3>Why do this problem ?</h3> These interesting <a href="https://nrich.maths.org/7424">questions</a> will allow students to practise using different units of measurement whilst developing awareness of orders of magnitude in scientific contexts. Some also require students to find additional information. As with any problems involving approximation, they offer opportunity for classroom discussion and justification. <h3>Possible approach</h3> There are several parts to this question, some easier, some more challenging. The individual images could be used as starters or filler activities for students who finish classwork early. Enthusiastic students might work through them in their own time. If students disagree with each other, or with the answers provided, this could lead to productive discussion. <h3>Key questions</h3> Do you have all the information you need to decide where a particular image should fit in the list? If not, where can you find out what you need? What formulae will you need to use? How accurate do you think the answer is? What 'order of magnitude' checks could you make to test that your answer is sensible? <h3>Possible extension</h3> Challenge students to come up with their own images and questions about order of magnitude. <h3>Possible support</h3> Start with questions which seem most accessible and encourage whole class discussion of the values given. The article <a href="http://nrich.maths.org/6300">Getting Started with Solving Rich Tasks</a> might be helpful.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">The average dimension for each of the following objects is given in the table below: <table style="width: 518px; height: 512px;border-spacing:1px;" border="1"> <tbody> <tr> <td> </td> <td>Length</td> <td>Cross - Sectional Area</td> <td>Volume</td> <td>Modelling by which solid?</td> </tr> <tr> <td>Mitochondria</td> <td>1 $\mu$m</td> <td>0.79 $\mu$m$^2$</td> <td>0.79 $\mu$m$^3$</td> <td>Cylinder</td> </tr> <tr> <td>Arabis voch pollen</td> <td>30 $\mu$m</td> <td>706.9 $\mu$m$^2$</td> <td>14137 $\mu$m$^3$</td> <td>Sphere</td> </tr> <tr> <td>Ring stage of Plasmodium falciparum</td> <td>1.5 $\mu$m</td> <td>0.79 $\mu$m$^2$</td> <td>0.03 $\mu$m$^3$</td> <td>Ring</td> </tr> <tr> <td>Tuberculosis bacterium</td> <td>2 $\mu$m</td> <td>0.12 $\mu$m$^2$</td> <td>0.24 $\mu$m$^3$</td> <td>Cylinder</td> </tr> <tr> <td>Human red blood cell</td> <td>8 $\mu$m</td> <td>50 $\mu$m$^2$</td> <td>100 $\mu$m$^3$</td> <td>Disc</td> </tr> <tr> <td>Human nerve cell</td> <td>2 $\mu$m</td> <td>3 $\mu$m$^2$</td> <td>0.3 $\mu$m$^3$</td> <td>Disc</td> </tr> <tr> <td>The eye of a needle</td> <td>1 mm</td> <td>1 mm$^2$</td> <td>0.1 mm$^3$</td> <td>Cuboid</td> </tr> <tr> <td>Cat hair</td> <td>3 cm</td> <td>0.3 mm$^2$</td> <td>9 mm$^3$</td> <td>Cylinder</td> </tr> <tr> <td>Snowflake crystal</td> <td>1 cm</td> <td>0.79 cm$^2$</td> <td>0.17 cm$^3$</td> <td>Sphere</td> </tr> </tbody> </table> Therefore, we can roughly rank these objects by length, volume and cross - sectional area.</mdoxml> 2 4 0 0 0 1 0 Biology measurement challenge Analyse these beautiful biological images and attempt to rank them in size order. 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