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Welcome to the Core Scientific Mathematics section of stemNRICH  Core. 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.
For more advanced mathematical problems please see the Advanced Scientific Mathematics section. For advanced activities more directly based around specific mathematical applications, please see bioNRICH , chemNRICH , physNRICH or engNRICH  
Area of maths  Style  Teacher Notes  Question  Description 

Numbers  Image

YES  Big and Small Numbers in Biology  10 individual questions using numbers big and small to calculate or estimate various quantities in simple biological contexts. 
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YES  Big and Small Numbers in Physics  10 individual questions using numbers big and small to calculate or estimate various quantities in simple contexts relevant to physics.  
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  Constantly Changing  Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.  
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YES  Peaches Today, Peaches Tomorrow  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?  
See also, in particular, the Dilution and Proportional Reasoning problems on the chemNRICH pages  
Algebra, equations and graphs  Image

YES  Temperature  Is there a temperature at which Celsius and Fahrenheit readings are the same on a thermometer? 
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YES  What's that graph?  Which graphs, equations and physical processes go together?  
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Geometry and symmetry  Image

YES  How Far Does it Move?  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. 
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YES  Semiregular tessellations  Explore ways to symmetrically tile the plane with this beautiful interactivity.  
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YES  Efficient Packing  How will you go about calculation to pack small circles into a large square?  
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  Ball Bearings  If a is the radius of the axle, b the radius of each ballbearing, 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.  
Curve fitting and sketching  Image

YES  Fill me up  Imagine these flasks filling with water. How would the height of water vary over time? 
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YES  Reallife Equations  Relate these commonly used equations to points on a series of graphs. Which are possible and which are not?  
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YES  Equation Matcher  A series of graphs are given containing just 2 or 3 points. Which equations do the points rule out?  
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YES  Maths Filler  Can you work out how to make heighttime charts as these unusually shaped vessels are filled up?  
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YES  Curve Match  Can you match these curves to the graphs?  
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YES  Fill me up too  Analyse the volume of some commonly used scientific vessels.  
Approximations and estimations  Image

YES  Place your orders  Can you sort these quantities into order of size? 
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YES  Approximately Certain  Estimate these curious quantities sufficiently accurately that you can rank them in order of size.  
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  Global Warming  How much energy has gone into warming up the planet?  
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YES  Carbon Footprints  Is it really greener to go on the bus, or to buy locally produced food?  
Powers and roots  Image

YES  A Question of Scale  This interactive page allows you to test your knowledge and skill using powers of 10 to place physical quantities in order of size. 
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YES  Power Countdown  Try to hit the targets using the operations of powers and roots.  
Data handling  Image

YES  Data Matching  Use your skill and judgement to match the sets of random data 
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YES  Back Fitter  10 graphs are of noisy experimental data are given. Can you use the spreadsheet provided to find algebraic graphs which match them closely?  
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YES  Who's the best?  Which countries have the most naturally athletic populations?  
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YES  David and Goliath  It is suggested that heavier competitors are at an advantage in the shot put. Do the data support that claim?  
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YES  Guessing the graph  Analyses these pieces of scientifc data and try to deduce the equation of the curve underlying the process.  
Trigonometry  Image

  Far Horizon  An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see? 
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YES  Perfect Eclipse  Find out why perfect eclipses are, in fact, perfect.  
Units  Image

YES  Uniform Units  Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length? 
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  Bigger or Smaller?  Develop your intuition for changing units by asking the simple question: will a unit change give me a larger or smaller number?  
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YES  Choose Your Units  Which would be the most sensible units in which to measure these objects?  
Algorithms and decision making  Image

  How would you score it?  How would you devise a scoring system to score a 'guess the weight' competition? 
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