Trialling \(x=7\) gives \(252\) which is too small and \(x=8\) gives \(320\) which is too big. The positive solution must be one of these two, but which one?
From my experience, students tend to look at \(252\) and \(320\) and use those to determine which one is closer, but they should actually trial \(x=7.5\) giving \(285\) which is too small and therefore conclude that \(x=8\). For years, I struggled to explain why they need to do this, because this shortcut seems to work for an overwhelming proportion of questions, so I set out to find something that broke that habit.
Well, the question above does just that. \(252\) and \(320\) are both equidistant from the \(286\) so it provides no additional information. Students have to rely on testing \(x=7.5\)
I did produce a series of questions that did this, but it seems that every question I created, the midpoint trial value was always too small and so it always rounded up. I don't want to create new misconceptions, but did want to share this one example as a wake-up call for those not going to one extra level of accuracy.
If I can generate some questions that round down, expect a worksheet.
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