Core Scientific Mathematics

Stage: 4 and 5 Challenge Level:

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.

Area of maths	Style	Teacher Notes	Question	Description
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
Numbers		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.
		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.
		-	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.
		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		YES	Temperature	Is there a temperature at which Celsius and Fahrenheit readings are the same on a thermometer?
		YES	What's that graph?	Which graphs, equations and physical processes go together?
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Geometry and symmetry		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.
		YES	Semi-regular tessellations	Explore ways to symmetrically tile the plane with this beautiful interactivity.
		YES	Efficient Packing	How will you go about calculation to pack small circles into a large square?
		-	Ball Bearings	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.
Curve fitting and sketching		YES	Fill me up	Imagine these flasks filling with water. How would the height of water vary over time?
		YES	Real-life Equations	Relate these commonly used equations to points on a series of graphs. Which are possible and which are not?
		YES	Equation Matcher	A series of graphs are given containing just 2 or 3 points. Which equations do the points rule out?
		YES	Maths Filler	Can you work out how to make height-time charts as these unusually shaped vessels are filled up?
		YES	Curve Match	Can you match these curves to the graphs?
		YES	Fill me up too	Analyse the volume of some commonly used scientific vessels.
Approximations and estimations		YES	Place your orders	Can you sort these quantities into order of size?
		YES	Approximately Certain	Estimate these curious quantities sufficiently accurately that you can rank them in order of size.
		-	Global Warming	How much energy has gone into warming up the planet?
		YES	Carbon Footprints	Is it really greener to go on the bus, or to buy locally produced food?
Powers and roots		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.
Powers and roots		YES	Power Countdown	Try to hit the targets using the operations of powers and roots.
Data handling		YES	Data Matching	Use your skill and judgement to match the sets of random data
		YES	Odd One Out	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
		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?
		YES	Who's the best?	Which countries have the most naturally athletic populations?
		YES	David and Goliath	It is suggested that heavier competitors are at an advantage in the shot put. Do the data support that claim?
		YES	Guessing the graph	Analyses these pieces of scientifc data and try to deduce the equation of the curve underlying the process.
Trigonometry		-	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?
Trigonometry		YES	Perfect Eclipse	Find out why perfect eclipses are, in fact, perfect.
Units		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?
		-	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?
		YES	Choose Your Units	Which would be the most sensible units in which to measure these objects?
Algorithms and decision making		-	How would you score it?	How would you devise a scoring system to score a 'guess the weight' competition?
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