This collection of STEM resources is based on the living world. Resources are listed in order of stage.
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bioNRICH
bioNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of the biological sciences, designed to help develop the mathematics required to get the most from your study of biology at A-level and university.
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Mathematical issues for biologists
STEM students at university often encounter mathematical
difficulties. This articles highlights the 8 key problems for
biologists.
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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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chemNRICH
chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study of chemistry at A-level and university.
problem
Favourite
Discuss and choose
Age
5 to 11
Challenge level
This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.
problem
Maths is everywhere!
Age
11 to 16
Challenge level
Maths is everywhere in the world! Take a look at these images. What mathematics can you see?
problem
Food chains
Age
11 to 14
Challenge level
When a habitat changes, what happens to the food chain?
problem
Big and small numbers in the living world
Age
11 to 16
Challenge level
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
project
Terrariums
Build a mini eco-system, and collect and interpret data on how well the plants grow under different conditions.
problem
Natural shapes
Age
14 to 16
Challenge level
How does shape relate to function in the natural world?
problem
Biology measurement challenge
Age
14 to 16
Challenge level
Analyse these beautiful biological images and attempt to rank them in size order.
problem
Genetics
Age
14 to 16
Challenge level
A problem about genetics and the transmission of disease.
problem
Packing 3D shapes
Age
14 to 16
Challenge level
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
problem
Favourite
Ratios and dilutions
Age
14 to 16
Challenge level
Scientists often require solutions which are diluted to a
particular concentration. In this problem, you can explore the
mathematics of simple dilutions
problem
Dilution series calculator
Age
14 to 16
Challenge level
Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?
problem
Robot camera
Age
14 to 16
Challenge level
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
problem
Exact dilutions
Age
14 to 16
Challenge level
Which exact dilution ratios can you make using only 2 dilutions?
problem
Peas in a pod
Age
14 to 16
Challenge level
What is the chance this pea plant will look like its parents?
list
Disease Dynamics - understanding the spread of diseases
A chance to explore the mathematics of networks as applied to epidemics and the spread of disease.
problem
Big and small numbers in biology
Age
14 to 16
Challenge level
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
problem
Mixed up mixture
Age
14 to 16
Challenge level
Can you fill in the mixed up numbers in this dilution calculation?
problem
The genes of Gilgamesh
Age
14 to 16
Challenge level
Can you work out the parentage of the ancient hero Gilgamesh?
problem
Bigger or smaller?
Age
14 to 16
Challenge level
When you change the units, do the numbers get bigger or smaller?
problem
Bio graphs
Age
14 to 16
Challenge level
What biological growth processes can you fit to these graphs?
problem
Alternative record book
Age
14 to 18
Challenge level
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
problem
Time to evolve
Age
14 to 16
Challenge level
How many generations would link an evolutionist to a very distant
ancestor?
problem
Why multiply when you're about to divide?
Age
16 to 18
Challenge level
A brief introduction to PCR and restriction mapping, with relevant
calculations...
problem
Fitting flat shapes
Age
16 to 18
Challenge level
How efficiently can various flat shapes be fitted together?
problem
Graphic biology
Age
16 to 18
Challenge level
Several graphs of the sort occurring commonly in biology are given.
How many processes can you map to each graph?
problem
Favourite
Real-life equations
Age
16 to 18
Challenge level
Here are several equations from real life. Can you work out which measurements are possible from each equation?
problem
Is your DNA unique?
Age
16 to 18
Challenge level
Use combinatoric probabilities to work out the probability that you are genetically unique!
problem
Population dynamics - part 3
Age
16 to 18
Challenge level
Third in our series of problems on population dynamics for advanced students.
list
Population Dynamics Collection
Age
16 to 18
Challenge level
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
problem
Favourite
Blood buffers
Age
16 to 18
Challenge level
Investigate the mathematics behind blood buffers and derive the
form of a titration curve.
problem
Population dynamics - part 2
Age
16 to 18
Challenge level
Second in our series of problems on population dynamics for advanced students.
problem
Favourite
Mixing pH
Age
16 to 18
Challenge level
Use the logarithm to work out these pH values
problem
Population dynamics
Age
16 to 18
Challenge level
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
problem
Population dynamics - part 1
Age
16 to 18
Challenge level
First in our series of problems on population dynamics for advanced students.
problem
Favourite
Very old man
Age
16 to 18
Challenge level
Is the age of this very old man statistically believable?
problem
pH temperature
Age
16 to 18
Challenge level
At what temperature is the pH of water exactly 7?
problem
Population dynamics - part 4
Age
16 to 18
Challenge level
Fourth in our series of problems on population dynamics for advanced students.
problem
Extreme dissociation
Age
16 to 18
Challenge level
In this question we push the pH formula to its theoretical limits.
problem
Branching processes and extinction
Age
16 to 18
Challenge level
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
problem
Population dynamics - part 6
Age
16 to 18
Challenge level
Sixth in our series of problems on population dynamics for advanced students.
problem
Catalyse that!
Age
16 to 18
Challenge level
Can you work out how to produce the right amount of chemical in a
temperature-dependent reaction?
problem
Favourite
Chi-squared faker
Age
16 to 18
Challenge level
How would you massage the data in this Chi-squared test to both
accept and reject the hypothesis?
problem
Population dynamics - part 5
Age
16 to 18
Challenge level
Fifth in our series of problems on population dynamics for advanced students.
problem
Reaction types
Age
16 to 18
Challenge level
Explore the rates of growth of the sorts of simple polynomials
often used in mathematical modelling.
problem
Favourite
Stats statements
Age
16 to 18
Challenge level
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
problem
Drug stabiliser
Age
16 to 18
Challenge level
How does the half-life of a drug affect the build up of medication
in the body over time?
problem
Population ecology using probability
Age
16 to 18
Challenge level
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
problem
Whose line graph is it anyway?
Age
16 to 18
Challenge level
Which line graph, equations and physical processes go together?
article
Genetic intrigue
Dip your toe into the fascinating topic of genetics. From Mendel's
theories to some cutting edge experimental techniques, this article
gives an insight into some of the processes underlying a
fundamental biological discipline.
problem
Predator - prey systems
Age
16 to 18
Challenge level
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
problem
Bird-brained
Age
16 to 18
Challenge level
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.