Investigation strategies

Example of problem posing with question openers

What is 2 + 2? 4

Why? What do we mean by (WDWMB) "2"? by "+"? What if not (WIN) base 10?

What if base 3? What if mod 3?

What other problems have the solution 4?

How many?

In general, how many pairs of numbers add up to n? In general, how many sets of numbers add up to n?

WDWMB "set"?

WIN addition?

What is 2 x 2? Also 4.

What other pairs of numbers have the same sum as product?

How many?

WDWMB "number"?
In general, how many pairs of numbers have product n?
In general, how many sets of numbers have product n?

What is 2 – 2? 0.

What other pairs of numbers have difference 0?

How many?
Is it necessary that they are the same number?

Why?

WIN subtraction of a number from itself to get 0?

What if adding a number to itself gets 0?
What if multiplying a number by itself gets 0?
In general, what if multiplying a pair of numbers gets 0?

Is it necessary that one of the numbers must be 0?

Why?
Under what conditions might the product not be 0?

What is 2/2? 1.

What other pairs of numbers have quotient 1?

How many?
Is it necessary that they are the same number?

Why?

WIN dividing a number by itself gets 1?

What if adding a number to itself gets 1?
What if multiplying a number by itself gets 1?
In general, what if dividing a pair of numbers gets 1?