# Modelling Scientific Exploration and Discovery - July 2010, All Stages

This month our problems and games model the process of scientific exploration and discovery. When you first begin tackling a problem, you might make some observations which could lead to a tentative, incomplete theory or hypothesis. You might try something rather random to test your hypothesis, which you subsequently modify. Then you will become more systematic in your testing and your hypothesis will be reconstructed based on your new insight. At any time, the theory you have is the one that best fits the evidence you have gathered so far.

## Problems

### Our Numbers

##### Stage: 1 Challenge Level:

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

### I Like ...

##### Stage: 1 Challenge Level:

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

### Light the Lights

##### Stage: 1 Challenge Level:

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

### Fit These Shapes

##### Stage: 1 and 2 Challenge Level:

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

### Which Numbers? (1)

##### Stage: 2 Challenge Level:

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

### Light the Lights Again

##### Stage: 2 Challenge Level:

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

### Which Numbers? (2)

##### Stage: 2 Challenge Level:

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

### Reaction Timer

##### Stage: 3 Challenge Level:

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

### Four Coloured Lights

##### Stage: 3 Challenge Level:

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

### Charlie's Delightful Machine

##### Stage: 3 and 4 Challenge Level:

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

### A Little Light Thinking

##### Stage: 4 Challenge Level:

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

### How Do You React?

##### Stage: 4 Challenge Level:

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

### Guessing the Graph

##### Stage: 4 Challenge Level:

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

### Spectrometry Detective

##### Stage: 5 Challenge Level:

From the atomic masses recorded in a mass spectrometry analysis can you deduce the possible form of these compounds?

### The Not-so-simple Pendulum 1

##### Stage: 5 Challenge Level:

See how the motion of the simple pendulum is not-so-simple after all.

### Black Box

##### Stage: 5 Challenge Level:

This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?

### The Real Hydrogen Atom

##### Stage: 5 Challenge Level:

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms

### The Not-so-simple Pendulum 2

##### Stage: 5 Challenge Level:

Things are roughened up and friction is now added to the approximate simple pendulum