Event 1.5
Nicole: Another way you can think about it is as a subtraction sum. They are saying that
the three times two ex plus one exceeds the two, twice two ex plus three, obviously the
three times two ex plus one is the bigger one, so you take your bigger one minus the
smaller one [Lecturer listens and writes up on the board: see Fig. 4] and the difference
between them is 13.
L: [looking at class] Follow? So we can interpret this as saying, take the smaller one
from the larger one, the gap is 13. So there are at least 3 ways that we can write this
thing. [points to new equation written on the board]
This interjection by the student enabled the movement to E1.5 and the fixing of an
instance of contingent necessity.
L: Ok. That is subtraction to get 13. This one is balancing, so we are dropping the
bigger one by 13 to make it equal to the smaller one [writing second equation on the
board: see Fig. 5]. The other way is what Nathi was saying, [writing third on the board]
add 13. So in other words we increase the smaller one so that it is the same size as the
bigger one.
L: At the end of the day when we solve this we are going to get the same
answer. In fact the next step of all three equations could be identical. But the
meaning behind these three is slightly different. Ok. Is the answer going to come
out to be negative five?
(Students shake their heads)