# New Cuyama

Alignments to Content Standards: N-Q.A

On a road trip in California, Lisa saw a sign which made her laugh and take a picture:

## IM Commentary

The purpose of this task is to provide a fun context to examine the pitfalls of disregarding units when reporting and manipulating quantities. Teachers might use this as a discussion-starter about appropriate and careful use of units. In this particular example, the units of the three quantities are so diverse that it is not surprising Lisa laughed when looking at the ''arithmetic'' on this sign.

Teachers are encouraged not to let students dismiss the example in a single sentence. For a famous example, lack of attention to units caused quite a stir with the loss of the expensive Mars orbiter described here http://www.cnn.com/TECH/space/9909/30/mars.metric.02/index.html?_s=PM:TECH. There are situations where objects of different kinds can be meaningfully added by viewing them from a different, more general perspective. For example, 10 hippos and 13 giraffes could be added to make 23 animals. In the case of this problem, however, it is hard to find a general category which encompasses the three types of units which are being added: people, feet above sea level, and years. We could, however, say that these are all ''things'' and that if we add them together we do indeed get 4663 ''things.'' While technically accurate, this is not a very interesting way of reasoning. Moreover, it can readily lead to further problems: we have 1 foot is the same as 12 inches but if feet and inches are both viewed as ''things'' then we find that 1 ''thing'' is equal to 12 ''things.''

A detailed discussion of the pitfalls of being cavalier with units touches on quite a few of the Standards for Mathematical Practice, e.g., MP3 (critiquing the reasoning of others), and MP6 (precision with language and units).

The arithmetic is performed correctly on the sign (ignoring the units that should be attached to the numbers). So $$562 + 2150 + 1951 = 4663.$$