Chapter 4.5, Problem 8P

AThe exchanges that follow are taken from Developing Children ‘s Understanding of the Rational Numbers: A New Model and an Experimental Curriculum by Joan Moss and Robbie Case [53, p. 135]. “Experimental Si” and “Experimental S3” are two of the fourth-grade students who participated in an experimental curriculum described in the article.*

*From Journal for Research in Mathematics Education, Vol. 30, No. 2, 122—147 by Robbie Case and Joan Moss. Copyright© 1999 by National Council for Teachers of Mathematics (NCTM). Used by permission of National Council for Teachers of Mathematics (NCTM).

Experimenter: What is 65% of 160?

Experimental S1: Fifty percent (of 160) is 80. I figure 10%, which would be 16. Then I divided by 2, which is 8 (5%) then 16 plus 8 um.. . 24. Then I do 80 plus 24, which would be 104.

For each of the two students’ responses, write strings of equations that correspond to the student’s method for calculating 65% of 160. State which properties of arithmetic were used and where. (Be specific.)

Write your string of equations in the following form:

   $\begin{array}{l}\hfill \\ 65\%.160=someexpression\hfill \\ \begin{array}{l}=.:\\ =someexpression\end{array}\hfill \end{array}$