Been meaning to post about this since I did the exam marking in the summer, but have been seriously busy (haven’t we all?) and just as I’m about to revise T&I with some of my one to one students its prompted me to finish the post that was started so long ago. To some of you that mark exams, or make a point of reading the mark schemes it wont be news, but based on the questions I marked I suspect that the exact requirements for getting full marks on these kind of questions in an exam haven’t quite got to everyone.
Consider this question:
Its obvious that the first trial will be 4.5 (as it’s halfway between 4 and 5), you then work through successive trials until you get two numbers on the number line next to each other – one of which is “too big” and one of which is “too small”. It is then a matter of making your choice between these two numbers – in this case its a choice between 4.6 and 4.7
Many students seemed to use a method that involved working out how far away the solution for 4.6 and 4.7 were away from 110 and then choosing the one with the smallest difference. I’ve shown what I mean below:
The above would only gain 3 out of 4 marks … I still think the fact that they have used a “difference method” shows that the student has an understanding of the value of x that they are trying to find has to be the closest value to 110, but no! in order to get full marks you need to do “one more trial” (which is how I’m referring to it now, when I teach it … Trial & Improvement AND one more trial” … this time to two decimal places … like this:
May or may not be news!