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stemNRICH - The Physical World

Welcome to the Physical World collection of stemNRICH resources.

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.


Back to main STEM pages.
 

Problems with teacher support


The following problems contain detailed teacher support concerning how we might use the task in schools.  However, since these problems are intended to be rich mathematical activities they can be used effectively in many ways and at many levels of sophistication, both in the classroom and by individuals.

Curve Spotting

Age 5 to 7
Challenge Level Yellow star

Can you spot circles, spirals and other types of curves in these photos?

Maths Trails - Encouraging Purposeful Outdoor Learning

Age 5 to 11

In this article, Becky Moseley outlines key considerations for Primary teachers wanting to create a maths trail in their own locality.

Observing the Sun and the Moon

Age 7 to 14
Challenge Level Yellow star

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.

Playground Snapshot

Age 7 to 14
Challenge Level Yellow starYellow star

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?

Troublesome Triangles

Age 7 to 14
Challenge Level Yellow star

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.

Avalanche!

Age 7 to 14
Challenge Level Yellow star

Investigate how avalanches occur and how they can be controlled

Helicopters

Age 7 to 16
Challenge Level Yellow star

Design and test a paper helicopter. What is the best design?

Make Your Own Solar System

Age 7 to 16
Challenge Level Yellow star

Making a scale model of the solar system

Pinhole Camera

Age 11 to 14
Challenge Level Yellow star

Make your own pinhole camera for safe observation of the sun, and find out how it works.

Does This Sound about Right?

Age 11 to 14
Challenge Level Yellow star

Examine these estimates. Do they sound about right?

Temperature

Age 11 to 14
Challenge Level Yellow starYellow star

Is there a temperature at which Celsius and Fahrenheit readings are the same?

Reaction Timer

Age 11 to 14
Challenge Level Yellow star

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

stemNRICH - The Physical World

Age 11 to 16
Challenge Level Yellow star

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

Programming: Moiré Patterns

Age 11 to 16

We need computer programmers! Logo is a great entry-level programming language - and you can create stunning graphics while you learn.

Choose Your Units

Age 14 to 16
Challenge Level Yellow star

Which units would you choose best to fit these situations?

Carbon Footprints

Age 14 to 16
Challenge Level Yellow star

Is it really greener to go on the bus, or to buy local?

Investigating the Dilution Series

Age 14 to 16
Challenge Level Yellow starYellow starYellow star

Which dilutions can you make using only 10ml pipettes?

Constantly Changing

Age 14 to 16
Challenge Level Yellow starYellow star

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Big and Small Numbers in the Physical World

Age 14 to 16
Challenge Level Yellow star

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

A Question of Scale

Age 14 to 16
Challenge Level Yellow starYellow star

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?

Speed-time Problems at the Olympics

Age 14 to 16
Challenge Level Yellow star

Have you ever wondered what it would be like to race against Usain Bolt?

Global Warming

Age 14 to 16
Challenge Level Yellow starYellow star

How much energy has gone into warming the planet?

Far Horizon

Age 14 to 16
Challenge Level Yellow starYellow starYellow star

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Perfect Eclipse

Age 14 to 16
Challenge Level Yellow starYellow starYellow star

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Guessing the Graph

Age 14 to 16
Challenge Level Yellow starYellow starYellow star

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Big and Small Numbers in Chemistry

Age 14 to 16
Challenge Level Yellow starYellow star

Get some practice using big and small numbers in chemistry.

Big and Small Numbers in Physics

Age 14 to 16
Challenge Level Yellow star

Work out the numerical values for these physical quantities.

How Do You React?

Age 14 to 16
Challenge Level Yellow starYellow star

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Bigger or Smaller?

Age 14 to 16
Challenge Level Yellow star

When you change the units, do the numbers get bigger or smaller?

Electric Kettle

Age 14 to 16
Challenge Level Yellow star

Explore the relationship between resistance and temperature

Heavy Hydrocarbons

Age 14 to 18
Challenge Level Yellow starYellow star

Explore the distribution of molecular masses for various hydrocarbons

Molecular Sequencer

Age 14 to 18
Challenge Level Yellow starYellow star

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.

Alternative Record Book

Age 14 to 18
Challenge Level Yellow star

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

chemNRICH

Age 14 to 18
Challenge Level Yellow star

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.

physNRICH

Age 14 to 18
Challenge Level Yellow star

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

Approximately Certain

Age 14 to 18
Challenge Level Yellow starYellow star

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Construct the Solar System

Age 14 to 18
Challenge Level Yellow star

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Problems without specific teacher support


The following problems are without specific teacher notes. These are often problems which would be difficult to fit into a typical curriculum area at school or are very open ended. They will be interesting for students interested in the general subject area to explore alone or for teachers to explore for ideas to bring to their own classrooms.

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Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Crossing the Atlantic

Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

Fixing the Odds

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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