# 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.

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### 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.

### Avalanche!

##### Age 7 to 14Challenge Level

Investigate how avalanches occur and how they can be controlled

### Observing the Sun and the Moon

##### Age 7 to 14Challenge Level

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 14Challenge Level

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 14Challenge Level

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.

### Helicopters

##### Age 7 to 16Challenge Level

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

### Make Your Own Solar System

##### Age 7 to 16Challenge Level

Making a scale model of the solar system

### Temperature

##### Age 11 to 14Challenge Level

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

### Reaction Timer

##### Age 11 to 14Challenge Level

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

### Pinhole Camera

##### Age 11 to 14Challenge Level

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 14Challenge Level

Examine these estimates. Do they sound about right?

### 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.

### stemNRICH - The Physical World

##### Age 11 to 16Challenge Level

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

### Guessing the Graph

##### Age 14 to 16Challenge Level

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 16Challenge Level

Get some practice using big and small numbers in chemistry.

### Big and Small Numbers in Physics

##### Age 14 to 16Challenge Level

Work out the numerical values for these physical quantities.

### How Do You React?

##### Age 14 to 16Challenge Level

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 16Challenge Level

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

### Electric Kettle

##### Age 14 to 16Challenge Level

Explore the relationship between resistance and temperature

##### Age 14 to 16Challenge Level

Which units would you choose best to fit these situations?

### Carbon Footprints

##### Age 14 to 16Challenge Level

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

### Investigating the Dilution Series

##### Age 14 to 16Challenge Level

Which dilutions can you make using only 10ml pipettes?

### Constantly Changing

##### Age 14 to 16Challenge Level

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 16Challenge Level

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

### A Question of Scale

##### Age 14 to 16Challenge Level

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 16Challenge Level

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

### Global Warming

##### Age 14 to 16Challenge Level

How much energy has gone into warming the planet?

### Far Horizon

##### Age 14 to 16Challenge Level

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 16Challenge Level

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

### physNRICH

##### Age 14 to 18Challenge Level

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

### Approximately Certain

##### Age 14 to 18Challenge Level

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

### Construct the Solar System

##### Age 14 to 18Challenge Level

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

### Heavy Hydrocarbons

##### Age 14 to 18Challenge Level

Explore the distribution of molecular masses for various hydrocarbons

### Molecular Sequencer

##### Age 14 to 18Challenge Level

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 18Challenge Level

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

### chemNRICH

##### Age 14 to 18Challenge Level

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.

### 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.