Why do this problem?
encourages students to get into the real meaning of
graphical representation without getting bogged down in algebraic
calculations or falling back into blind computation. It will also
encourage them to think about error in measurement.
There are two levels at which the graphical data can be
interpreted. At a basic level, the students can easily see if a
measurement increases or decreases from point to point or whether
the measurement is positive or negative. At a more advanced level,
they can suggest some rate of change of the measurements from point
to point: although there are no units on the charts, there are
certain key points (the grid lines) which allow some 'indirect'
by-eye measurement. Students will need to realise this more subtle
point to make full progress. (Note that the points have been
carefully placed by the question setter!)
The question of the accuracy of the 'by-eye' measurements can
raise interesting discussion about the accuracy of the
measurements. Since no context is given in the question it is
natural to assume total accuracy, but would this be the case in
- We only have two measurements, but what information can we
deduce from these?
- How can we relate this information to the equations?
Think of other equations which might match the points on the
graphs. How many could you think of?
Let students leaf through a science textbook searching for
graphs and charts. Do they notice that the same shapes of charts
appear frequently? For each chart they find, which measurements
would be a possibility?