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

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?

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? (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

Stage: 2 Challenge Level:

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

Featured Solution

Table Patterns Go Wild!

There were lots of patterns to notice and explain in this problem. Have a look at the solutions we received.

Go to last month's problems to see more solutions.

Articles & Games

Rocking Chairs, Railway Games and Rayboxes

In this article for teachers, Alan Parr looks at ways that mathematics teaching and learning can start from the useful and interesting things can we do with the subject, including modelling scientific enquiry.

White Box

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.