Conversion factors and units. These are really equations. The problem was that a person received 676 pieces of mail a year. How much mail was received each week?

 

We first write

 

1 year = 52 weeks, or 1 year/52 weeks = 1.

 

We then multiply 676 by 1:

 

676/1 year * 1 year/52 weeks.

 

This gives x ≈ 13. To check, if x = 14, it comes out to 2 per day, or 365*2 per year. The answer is reasonable, as 676 < 365*2. This must be written. The work must include the checking.

 

Note that if we ask how much mail per day, we can say 1 year = 365 days. The teacher can mention that this equation is not strictly true, as there are no mail deliveries on Sundays and holidays; furthermore, some years are leap years. However, the teacher should say that we will assume a year has 365 days because otherwise the problem is too complicated. The point is that we do not ignore the reality of the complexity of the problem, but we do not actually do the work.

 

Some students were trying to figure how many days there are in a year excluding Sundays. One girl said 365 – 52. A boy said 52*6. I mentioned to them that these numbers are not the same. “Which is correct?” as the girl. I told her that both are approximately correct. However, it is best at this level to avoid the issue completely, just briefly mentioning the problem, but not actually using a number different from 365. It may be used, however, as a challenge for the brighter students.

 

SEE THE BOOK FOR MORE DETAILS.