In these resources, maths is used as a tool to explore some aspect of the physical sciences. Some might be best used in the maths lesson, with reference made to the science. Others could be taught as cross-curricular topics.
Stage 3 is roughly 11-14 years and Stage 4 roughly 14-16 years. The stars indicate how easily most learners can get into the problem, although most problems contain enough depth to challenge and stimulate all.
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Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems.
Investigate how avalanches occur and how they can be controlled
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.
Design and test a paper helicopter. What is the best design?
Making a scale model of the solar system
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?
This problem offers you two ways to test reactions - use them to
investigate your ideas about speeds of reaction.
Examine these estimates. Do they sound about right?
Make your own pinhole camera for safe observation of the sun, and find out how it works.
We need computer programmers! Logo is a great entry-level programming language - and you can create stunning graphics while you learn.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
When you change the units, do the numbers get bigger or smaller?
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
Is it really greener to go on the bus, or to buy local?
Which dilutions can you make using only 10ml pipettes?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Have you ever wondered what it would be like to race against Usain Bolt?
How much energy has gone into warming the planet?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the distribution of molecular masses for various hydrocarbons
Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.