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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:
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