Whole Number Thinking
Make the Biggest and Smallest Numbers

CaitlinIntroduction
In this interview, Caitlin shows her whole number thinking. She correctly makes the biggest number, as is predicted from whole number thinking. However, when making the smallest number, she shows that she cannot distinguish between 3.01 and 3.1. To Caitlin, both of these are 3 wholes and 1 extra bit.

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

Interviewer:
I have a number that starts 3 point something something and you get to choose the rest of the number.

3.--

Interviewer:
Here are the cards to choose from...

3.-- 1234567890

Interviewer:
.
..marked 0,1,2,3,4,5,6,7,8 and 9. I'm going to ask you to make the biggest number that you can by choosing any two of these cards.

Caitlin:
Any cards?

Interviewer:
Yes

3.98

Caitlin selects the 9 and 8 cards and puts them in place, correctly making the biggest number.

Interviewer:
OK, now we'll put those cards back

3.--

Interviewer:
...and could you make another number, this time as small as you can?

3.1

Caitlin selects the 1 card and places it alone. Interviewer reminds her to use two cards.

Interviewer:
OK, what if you have to choose two of the cards to make your number?

3.01

Caitlin selects the 0 card and makes 3.01.

Interviewer:
Could we just look at those two numbers that you made? Did you make it bigger or smaller when you changed it?

3.1Caitlin:
Ummm, I think they're the same...because the zero doesn't matter...

Caitlin thinks 3.01 is the same as 3.1, that each is 3 wholes and 1 3.01extra bit.