Denominator Focussed Thinking
Number Between

RicardoIntroduction
Playing the game "Number Between" illustrates that Ricardo believes any number of hundredths (in this case 45) is smaller than any number of tenths (in this case 4). He does not perceive 45 hundredths (0.45) as 4 tenths and 5 hundredths.

Comments: Text in italics
Interviewer: Text in red
Ricardo: Text other colour

0.3 - 0.5

Interviewer:
In this game you have type a number which fits on the numberline. You can see the two endpoints on the screen. For this turn they are point 3 and point 5.

Ricardo:
Easy, point 4

0.4

Interviewer:
OK, the computer has accepted your answer and now it will change the numberline for your next turn.

0.4 - 0.5

Ricardo:
But there is no number between 4 and 5, so there is no number between 4 tenths and 5 tenths! (pause)...

Interviewer:
Why don't you try something like point four five?

Ricardo:
That's too small because point four five is 45 hundredths. It's smaller than point 4 and point 5 because they are both tenths.