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!