# The rounding question

Yesterday I presented some of the children in my class with this question:

The news reported today that 2000 people have contracted a rare tropical illness. This figure is known to have been rounded to the nearest 100 people. What is the largest possible number of people that could have the condition?

It was fascinating to see the thought progression that so many of the children went through. It looked something like this:

Preliminary idea (in some cases): 1900 or 2100
Idea 1: 1999
Realisation that you can go above 2000
Idea 2: 2040
Realisation that units column can increase
Idea 3: 2044
Realisation that the units column does not determine whether rounding up or down
Idea 4: 2049
Occasional error: 2049.999999
Awareness, in this context, that the answer must be whole number.

It was amazing to see how uniform this pattern of thinking was with different groups of children, particularly as children came to the counter-intuitive realisation that you have to find a number that will round down In order to find the maximum number of people.

There’s no place quite like the classroom!