Mark and Jan share $47 but Mark gets $5 more than Jan. How much do they each get?
Les knew that he would take $5 off $47, divide the remainder ($42) in 2 equal parts to get 2 lots of $21 and then increase Mark’s amount by the initial $5. This is a good solution. But how does Les think about this problem in algebra? He began by writing 5 + x = 47 and described his thinking to the interviewer this way: Les: x is what is left out of $47 if you take $5 off it. Interviewer: what might the x be? Les: Say she gets $22 and he gets $27 (He hasn’t found the answer of $21 at this stage, but guesses $22). They are sharing two x’s. Interviewer: What are the two x’s? Les: Unknowns…they are two different numbers, 22 and 27. Interviewer: So what is this x? (pointing to 5 + x = 47) Les: That was what was left over from $47, so its $42. Les’ good problem solving skills cannot connect with his algebra learning, because he thinks of x as any unknown quantity, rather than it representing one quantity throughout the problem. In his interview, he thinks about x as three quantities: $42, J
