Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 364: 123

There may be three approaches for evaluation. Approach 1: true evaluation for solution and provide zero credit to the student. Approach 2: check step-wise evaluation with understanding to solve the question and may give 3 to 4 credits. Approach 3: just do blind check. Since answer is right give him full credits that are10 out of 10. But this third approach is not at all right for true professional teacher.

Consider, \[-3\left( x-6 \right)=2-x\]and solution provided by the student is; \[\begin{align} & -3x-18=2-x \\ & -2x-18=2 \\ & -2x=-16 \\ & x=8 \end{align}\] Detail analysis of the calculation worked by the student: First step: Calculated by student is \[-3x-18=2-x\]. This is wrong since right calculation is \[-3x+18=2-x\] If student should have followed the right step wise approach to solve it as below: \[\begin{align} & \left( -3x \right)-\left( -3\times 6 \right)=2-x \\ & -3x-\left( -18 \right)=2-x \\ & -3x+18=2-x \end{align}\] But he jumps to write one step instead of writing three steps and reaches to one wrong calculation out of two calculations of this step. Zero credit for this step in any way. Second step: Student worked it as \[-2x-18=2\]. Yes, he calculated right for what he got in first step. But right calculation would have been; \[\begin{align} & -3x+18=2-x \\ & -2x+18=2 \end{align}\] So, according to right calculation student is wrong and till here he did wrong. Third step: Student calculated wrong even for his own calculated previous step. According to him he should write\[-2x=16\] but he wrote\[-2x=-16\]. Subtract 18 from both sides of the equation; \[\begin{align} & -2x-18=2-18 \\ & -2x=-16 \end{align}\] So, according to student’s calculation he reaches to right but he did wrong so no credit goes to him for this step. Fourth step: Student wrote\[x=8\]. He did right for his own calculation of previous step. But according to his own way of calculations he should get the answer as\[x=-8\]. So, though he approaches to right answer but he did wrong. He reaches to right answer in spite of doing wrong calculations. Reason for this is that he did two sign mistakes in his calculation. So, it nullifies the sign mistakes and accidentally numbers for which he did these sign mistakes does no effect to get the right answer. According to above analyses there are three approaches to analyze this. Approach 1: His understanding for sign calculations is poor. He did total wrong working, jumped steps leads him to do mistakes. He should not get any credit. Thus zero credit goes to him. Approach 2: If step wise analysis is to be taken into consideration then in its own way he did two steps right and two steps wrong and overall approach to attend the question is poor since he jumped the steps in between the calculations. He has poor understanding for sign calculations. At the most 3 to 4 credits can be given to him. Approach 3: Just do blind check. That is just check the answer which is of course right answer and give full credit to this student that is 10 out of 10 credits. But this will not be fair at the part of the true teacher. So, there may be three approaches for evaluation. Approach1: true evaluation for solution and give zero credit to the student. Approach2: check step-wise evaluation with understanding to solve the question and may give 3 to 4 credits. Approach3: just do blind check. Since answer is right give him full credit that is 10 out of 10. But this third approach is not at all right for true professional teacher.