6154 /www/nrich/html/content/id/6154/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/6308">Warm-up</a></li> <li><a href="http://nrich.maths.org/6146">Try this next</a></li> <li><a href="http://nrich.maths.org/6516">Think higher</a></li> <li><a href="http://lasp.colorado.edu/~bagenal/MATH/math2.html">Read: mathematics</a></li> <li><a href="http://en.wikipedia.org/wiki/SI_units">Read: science</a></li> <li><a href="http://en.wikipedia.org/wiki/Planck_units">Explore further</a></li> </ul> <div> </div> <br></br> <p>Some units are particularly well suited to a given measurement because they turn out to give a small, whole number of units. Understanding this concept gives you a feel for the order of magnitude of the quantities.<br></br> <br></br> What units would you measure these quantities in to make an approximation which was a reasonably small whole number?</p> <ul> <li>The volume of a bacterium</li> <li>The mass of an oak tree</li> <li>The area of a leaf</li> <li>The half-life of Uranium-235</li> <li>The area of a football pitch</li> <li>The average lifespan of a human</li> <li>The volume of a bath tub</li> </ul> <div>Can you reverse the process? For the following units, what physical phenomena might naturally be measured to be around 1 unit?</div> <br></br> <ul> <li>Millimetre</li> <li>Newton</li> <li>Angstrom</li> <li>Joule</li> <li>Volt</li> <li>Microgram</li> <li>Micrometre</li> <li>Hertz</li> <li>Parsec</li> </ul> <br></br> <h6>Send <a href="mailto:post16.nrich@maths.org?subject=Feedback%20on%20NRICH%20problem%20id%206154">feedback</a> on this problem</h6> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3>Phenomena to units</h3> Volume of a bacterium - Cubic micrometres $\mathrm{\mu m}^3$<br></br> Mass of an oak tree - Tonnes $(10^3\textrm{ kg})$<br></br> Area of a leaf - Square centimetres $(\textrm{cm}^2)$<br></br> Half-life of Uranium-235 - Millions of years<br></br> Area of a football pitch - Hectares<br></br> Average life-span of a human -Years<br></br> Volume of a bath tub - Cubic metres $(\textrm{m}^3)$<br></br> <br></br> <h3>Units to phenomena</h3> Millimetre - size of an amoeba<br></br> Newton - weight of an apple<br></br> Angstrom - atomic diameter of a hydrogen atom<br></br> Joule - kinetic energy of a table tennis ball travelling at $100\textrm{ km h}^{-1}$<br></br> Volt - voltage across an AA cell<br></br> Microgram - mass of $1\textrm{ mm}^3$ of air<br></br> Micrometre - mitochondrion<br></br> Hertz - frequency of tick-tock on a clock<br></br> Parsec - distance to Proxima Centauri (closest star other than the Sun)<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <h3>Why do this problem ?</h3> Use of units is a critical skill in the sciences, and one which often leads to confusion. <a href="http://nrich.maths.org/public/viewer.php?obj_id=6154&amp;part=">This problem</a> will encourage students to understand the relationships between various types of units, as well as possibly introducing them to new important scientific units. It will also help to embed the important skill of checking numerical answers to see if they make sense in terms of orders of magnitude, along with a sense of where units are of relevance in science.<br></br> <h3>Possible approach</h3> <div>This question works well through discussion in pairs. Remind the students that common sense works well when dealing with units: for example, a cubic mm is clearly far smaller than the volume of a bathtub.</div> <h3>Key questions</h3> <div>What suggestions for units are possible in each case?</div> <h3>Possible extension</h3> Continue the question for other, more exotic units of measure (such as those given in <a href="http://nrich.maths.org/public/viewer.php?obj_id=6153&amp;part=">New units for Old</a> ) <h3>Possible support</h3> <div>Remind students the formulae for the compound measures, such as volume.</div> <br></br> <div>Students might also struggle with the reasonably open nature of the question. Remind them that there is no 'correct' answer and common sense approximations will help.</div> <br></br></mdoxml> 5 3 0 0 0 1 0 Which units would you choose best to fit these situations? Applications biology Applications physics Measures and Mensuration Converting between units Measures and Mensuration Non-standard units Applications Maths Supporting SET Admin Discussion Applications STEM - physical world Applications STEM - living world