Tell students the meaning of mean lower low water (MLLW), which is used as a reference point in the tables of water levels. The MLLW is an average of low tides, taken over a long period of time. Zero depth on U.S. maps corresponds to the MLLW. For this reason, many low tides are close to 0. People often think of 0 in this context as meaning “sea level” but, of course, the sea level varies, and when studying this variation, another reference point is needed.

Students may begin with a hypothesis of one (or two) tides every 24 hours, either from experience or from a quick look at the data. As they test their model for future days, they should realize that 24 hours is not accurate. A better estimate is close to 25 hours. (From tidal data collected in Boston, an estimate of 24 hours and 45 minutes is used in the provided solution.) Note that the time between moonrises is about 24 hours and 50 minutes. This is no coincidence—the gravitational pull of the Moon is the main reason for the tides. The times vary slightly, depending on the location on Earth.

Although the choice of where to investigate the tides is left to the individual classroom, the tides at many locations are extremely complex and perhaps not appropriate for modeling because they would require a sum of trigonometric functions with different periods. The tides in Boston (and at most locations along the eastern coast of the United States) are relatively regular, with a period of a little more than 12 hours. The tides along the Gulf Coast can be more complex, but the period is usually twice as much—a little less than 25 hours. We recommend using these locations.

Show students a table of the water levels in Boston on July 4–5, 2018, and ask them what they notice and wonder.