Box 8–7 Mentally Graphing to Find the Solution to an Equation
Toward the end of a study of equation solving by means of a graphical representation, a seventh grader was asked to solve the equation 7x+4=5x+8 (an equation whose solution is x=2). Rather than graph the two expressions, the student took a “shortcut.”
Interviewer: Can you solve 7x+ 4=5x+8?
Jer: Well, you could, see, it would be like start at 4 and 8, this one would go up by 7, hold on, 8, 8 and 7, hold on, no, 4 and 7, 4 and 7 is 11. They’d be equal, like, 2 or 3 or something like that.
Interviewer: How are you getting that 2 or 3?
Jer: I’m just like graphing it in my head.
SOURCE: Kieran and Sfard, 1999, p. 15. Used by permission of the author.