6462
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5
2011-02-01T00:00:01
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<p>Welcome to the <span style="font-weight: bold;">Core Scientific Mathematics</span> section of <a href="http://nrich.maths.org/6298">stemNRICH - Core</a>. This contains a set of activities designed to develop the basic applied mathematical skills needed to make the most of the study of a science in the final years of school or university.<br></br>
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<td colspan="5" style="padding:10px;"><span style="font-style: italic;">For more advanced mathematical problems please see the</span> <a href="http://nrich.maths.org/public/viewer.php?obj_id=6467&part=">Advanced Scientific Mathematics</a> <span style="font-style: italic;">section. For advanced activities more directly based around specific mathematical applications, please see</span> <a href="http://nrich.maths.org/public/viewer.php?obj_id=6139&part=">bioNRICH</a> , <a href="http://nrich.maths.org/public/viewer.php?obj_id=6463&part=">chemNRICH</a> , <a href="http://nrich.maths.org/public/viewer.php?obj_id=6465&part=">physNRICH</a> <span style="font-style: italic;">or</span> <a href="http://nrich.maths.org/public/viewer.php?obj_id=6466&part=">engNRICH</a></td>
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<th scope="col" width="100">Area of maths</th>
<th scope="col" width="25"><a href="http://nrich.maths.org/6103&part=">Style</a></th>
<th scope="col" width="30">Teacher Notes</th>
<th scope="col" width="150">Question</th>
<th scope="col">Description</th>
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<td rowspan="5" style="padding:10px;">Numbers</td>
<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6140&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6140&part=">Big and Small Numbers in Biology</a></td>
<td>10 individual questions using numbers big and small to calculate or estimate various quantities in simple biological contexts.</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6504&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6504&part=">Big and Small Numbers in Physics</a></td>
<td>10 individual questions using numbers big and small to calculate or estimate various quantities in simple contexts relevant to physics.</td>
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<td><mdo:image alt="" height="30" src="individual30x30.jpg" width="30"></mdo:image></td>
<td>-</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6516&part=">Constantly Changing</a></td>
<td>Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.</td>
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<td><mdo:image alt="" height="30" src="individual30x30.jpg" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/2312&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=2312&part=">Peaches Today, Peaches Tomorrow</a></td>
<td>A little monkey had 60 peaches. On the first day he kept 3/4 of his peaches, gave the rest away and then ate one. On the second day he kept 7/11 .... How many did he have left at the end?</td>
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<td colspan="4" style="padding:10px;"><span style="font-style: italic;">See also, in particular, the Dilution and Proportional Reasoning problems on the</span> <a href="http://nrich.maths.org/6463&part=">chemNRICH</a> <span style="font-style: italic;">pages</span></td>
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<td rowspan="3" style="padding:10px;">Algebra, equations and graphs</td>
<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/5608&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=5608&part=">Temperature</a></td>
<td>Is there a temperature at which Celsius and Fahrenheit readings are the same on a thermometer?</td>
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<td><mdo:image alt="" height="30" src="interactive30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/7502&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=7502&part=">What's that graph?</a></td>
<td>Which graphs, equations and physical processes go together?</td>
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<td rowspan="4" style="padding:10px;">Geometry and symmetry</td>
<td> <mdo:image alt="" height="30" src="interactive30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/4808&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/4808&part=">How Far Does it Move?</a></td>
<td>Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage. </td>
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<td><mdo:image alt="" height="30" src="investigate30x30.jpg" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/157&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=4832&part=">Semi-regular tessellations</a></td>
<td>Explore ways to symmetrically tile the plane with this beautiful interactivity.</td>
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<td><mdo:image alt="" height="30" src="individual30x30.jpg" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/157&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6157&part=">Efficient Packing</a></td>
<td>How will you go about calculation to pack small circles into a large square?</td>
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<td><mdo:image alt="" height="30" src="individual30x30.jpg" width="30"></mdo:image></td>
<td>-</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=295&part=">Ball Bearings</a></td>
<td>If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.</td>
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<td rowspan="6" style="padding:10px;">Curve fitting and sketching</td>
<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/7419&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=7419&part=">Fill me up</a></td>
<td>Imagine these flasks filling with water. How would the height of water vary over time?</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6160&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6160&part=">Real-life Equations</a></td>
<td>Relate these commonly used equations to points on a series of graphs. Which are possible and which are not?</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6301&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6301&part=">Equation Matcher</a></td>
<td>A series of graphs are given containing just 2 or 3 points. Which equations do the points rule out?</td>
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<td><mdo:image alt="" height="30" src="individual30x30.jpg" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6424&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6424&part=">Maths Filler</a></td>
<td>Can you work out how to make height-time charts as these unusually shaped vessels are filled up?</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6493&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6493&part=">Curve Match</a></td>
<td>Can you match these curves to the graphs?</td>
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<td><mdo:image alt="" height="30" src="individual30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/7499&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=7499&part=">Fill me up too</a></td>
<td>Analyse the volume of some commonly used scientific vessels.</td>
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<td rowspan="4" style="padding:10px;">Approximations and estimations</td>
<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/7500&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=7500">Place your orders</a></td>
<td>Can you sort these quantities into order of size?</td>
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<td><mdo:image alt="" height="30" src="investigate30x30.jpg" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6505&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6505&part=">Approximately Certain</a></td>
<td>Estimate these curious quantities sufficiently accurately that you can rank them in order of size.</td>
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<td><mdo:image alt="" height="30" src="investigate30x30.jpg" width="30"></mdo:image></td>
<td>-</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6453&part=">Global Warming</a></td>
<td>How much energy has gone into warming up the planet?</td>
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<td><mdo:image alt="" height="30" src="investigate30x30.jpg" width="30"></mdo:image><mdo:image alt="" height="13" src="blank10x10.jpg" width="12"></mdo:image></td>
<td><a href="http://nrich.maths.org/6508&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6508&part=">Carbon Footprints</a></td>
<td>Is it really greener to go on the bus, or to buy locally produced food?</td>
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<td rowspan="2" style="padding:10px;">Powers and roots</td>
<td><mdo:image alt="" height="30" src="interactive30x30.JPG" width="30"></mdo:image></td>
<td>YES</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6349&part=">A Question of Scale</a></td>
<td>This interactive page allows you to test your knowledge and skill using powers of 10 to place physical quantities in order of size.</td>
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<td><mdo:image alt="" height="30" src="interactive30x30.JPG" width="30"></mdo:image></td>
<td>YES</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6448&part=">Power Countdown</a></td>
<td>Try to hit the targets using the operations of powers and roots.</td>
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<td rowspan="6" style="padding:10px;">Data handling</td>
<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/5933&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=5933&part=">Data Matching</a></td>
<td>Use your skill and judgement to match the sets of random data</td>
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<td><mdo:image alt="" height="30" src="interactive30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/5801&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=5801&part=">Odd One Out</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=5801&part="></a> Develop your eye for patterns in data by trying to deduce the likely location of the odd ones out in six sets of random numbers</td>
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<td><mdo:image alt="" height="30" src="interactive30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6506&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6506&part=">Back Fitter</a></td>
<td>10 graphs are of noisy experimental data are given. Can you use the spreadsheet provided to find algebraic graphs which match them closely?</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/7367&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=7367">Who's the best?</a></td>
<td>Which countries have the most naturally athletic populations?</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/7360&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=7360">David and Goliath</a></td>
<td>It is suggested that heavier competitors are at an advantage in the shot put. Do the data support that claim?</td>
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<td><mdo:image alt="" height="30" src="interactive30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6990&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6990">Guessing the graph</a></td>
<td>Analyses these pieces of scientifc data and try to deduce the equation of the curve underlying the process.</td>
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<td rowspan="2" style="padding:10px;">Trigonometry</td>
<td><mdo:image alt="" height="30" src="individual30x30.jpg" width="30"></mdo:image></td>
<td>-</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=2357&part=">Far Horizon</a></td>
<td>An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?</td>
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<td><mdo:image alt="" height="30" src="investigate30x30.jpg" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6683&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/6683&part=">Perfect Eclipse</a></td>
<td>Find out why perfect eclipses are, in fact, perfect.</td>
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<td rowspan="3" style="padding:10px;">Units</td>
<td><mdo:image alt="" height="30" src="stopwatch30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6146&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6479&part=">Uniform Units</a></td>
<td>Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td>-</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6146&part=">Bigger or Smaller?</a></td>
<td>Develop your intuition for changing units by asking the simple question: will a unit change give me a larger or smaller number?</td>
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<td><mdo:image alt="" height="30" src="lips30x30.JPG" width="30"></mdo:image></td>
<td><a href="http://nrich.maths.org/6154&part=note">YES</a></td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6154&part=">Choose Your Units</a></td>
<td>Which would be the most sensible units in which to measure these objects?</td>
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<td rowspan="3" style="padding:10px;">Algorithms and decision making</td>
<td><mdo:image alt="" height="30" src="slips30x30.JPG" width="30"></mdo:image></td>
<td>-</td>
<td><a href="http://nrich.maths.org/public/viewer.php?obj_id=6957&part=">How would you score it?</a></td>
<td>How would you devise a scoring system to score a 'guess the weight' competition?</td>
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<th width="15" scope="col">STATUS</th>
<th width="25" scope="col"><a href="http://nrich.maths.org/6103&part=">Style</a></th>
<th width="30" scope="col"><a href="http://nrich.maths.org/6103&part=">Use in</a></th>
<th width="30" scope="col"><a href="http://nrich.maths.org/6103&part=">Yrs</a></th>
<th width="150" scope="col">Question</th>
<th scope="col">Description</th>
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<td colspan="6">Stage 3</td>
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<td>DRAFT</td>
<td>.</td>
<td>M|S</td>
<td>7-11</td>
<td><a href="http://nrich.maths.org/7417&part=">Certainly
approximate</a></td>
<td>Can you rank these curious physical quantities in order of
size?</td>
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<td>DRAFT</td>
<td>.</td>
<td>.</td>
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<td><a href="http://nrich.maths.org/7421&part=">Lining up for
line graphs</a></td>
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<td>DRAFT</td>
<td>.</td>
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<td><a href="http://nrich.maths.org/7419&part=">Fill me
up</a></td>
<td>See how quickly the level of liquid rises in these
vessels.</td>
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<td>PUBLISHED</td>
<td>.</td>
<td>.</td>
<td>.</td>
<td><a href="http://nrich.maths.org/6044&part=">Reaction
timer</a></td>
<td>This problem offers you two ways to test reactions - use them
to investigate your ideas about speeds of reaction. </td>
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<td colspan="6">Stage 4</td>
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<td>DRAFT</td>
<td>.</td>
<td>M|S</td>
<td>11</td>
<td><a href="http://nrich.maths.org/7415&part=">Get in
line</a></td>
<td>Link together the physical processes with their equation and
graphs. Discuss the mathematical modelling assumptions made.</td>
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<td>DRAFT</td>
<td>.</td>
<td>M</td>
<td>.</td>
<td><a href="http://nrich.maths.org/7109&part=">Speedo</a></td>
<td>What can we know for certain about a car journey where we
infrequently looked at the speedometer?</td>
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<td>PUBLISHED</td>
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<td><a href="http://nrich.maths.org/6990&part=">Guessing the
graph</a></td>
<td>Can you suggest a curve to fit some experimental data? Can you
work out where the data might have come from? </td>
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<td>PUBLISHED</td>
<td>.</td>
<td>.</td>
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<td><a href="http://nrich.maths.org/7033&part=">How do you
react?</a></td>
<td>To investigate the relationship between the distance the ruler
drops and the time taken, we need to do some mathematical
modelling... </td>
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<td>PUBLISHED</td>
<td>.</td>
<td>M</td>
<td>.</td>
<td><a href="http://nrich.maths.org/6630&part=">Mach
attack</a> </td>
<td>Think about breaking the sound barrier.</td>
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<td>DRAFT</td>
<td>.</td>
<td>M</td>
<td>.</td>
<td><a href="http://nrich.maths.org/7360&part=">David and
Goliath</a></td>
<td>Can you find the relationship between strength and size from
this data taken from weightlifting?</td>
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<td colspan="6">Mixed stage 3/4 science/maths</td>
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</tr>
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</tr>
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<td>.</td>
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</tr>
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</tr>
</tbody>
</table>
<br></br></mdoxml>
2
3
0
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1
1
Core Scientific Mathematics
This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.
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