# Modelling Scientific Exploration and Discovery - July 2010, Stage 2&3

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

### Fit These Shapes

##### Age 5 to 11 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)

##### Age 7 to 11 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

##### Age 7 to 11 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)

##### Age 7 to 11 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

##### Age 11 to 14 Challenge Level:

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

### Four Coloured Lights

##### Age 11 to 14 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

##### Age 11 to 16 Challenge Level:

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