Modeling Prompt

Tell students the meaning of mean lower low water (MLLW) used as a reference point in the table of water levels. This is an average of low tides taken over a long period of time: 0 on this scale corresponds to this average level of low tides. For this reason, many of the low tides are pretty 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.

Many 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 closer to 25 hours (24 hours and 50 minutes is the estimate that comes from studying the tides at Boston in the provided solution). Note that the orbit of the moon around the earth takes about 24 hours and 50 minutes. This is no coincidence as the gravitational pull of the moon is one of the main contributing factors in the tides.

The choice of location to investigate the tides can be left to the individual classroom but it is important to realize that at many locations the tides are extremely complex and perhaps not appropriate for modeling as they would require a sum of trigonometric functions with different periods. The tides in Boston (and most locations on the east coast of the United States) are relatively regular with a period of a little over 12 hours. The tides along the gulf coast can be more complex but here the period is usually twice as much, a little less than 25 hours. We recommend using these locations.

Many websites provide data for tides (both current and historical). Make sure to check the regularity of the tides in a given location before assigning that location to students. If the class uses a different location, the data can either be recorded in advance or students can be directed to a particular website.

Since the tides can fluctuate substantially, especially if there are strong weather events in the area (for example an incoming hurricane or tropical storm), make sure to check the tides for the dates you choose to assign. The sample student response is written for Boston on the dates of July 4 and 5, 2018, testing the period on July 11, 2018 for accuracy. Note: for these particular dates and location, the water level starts at a level which is not near the maximum, midline, or minimum value so that students will need to think carefully about a horizontal shift.

If students use the Boston data for July 4th and 5th, they'll also need the corresponding data for July 11th and 12th so they can check the accuracy of their model. That data is in the table shown here.

You will construct a model for the tides in Boston for July 4 and July 5, 2018 and then use your model to make predictions about future tides. Here are the water levels during this two day period. The water level is given relative to the mean lower low water.

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

Tell students that the table shows the water level in Boston over a two day period in July 2018. 

Discuss with students the measurements given in the table and the meaning of mean lower low water level (the reference point for the tide levels). This is an average value for low tide levels taken over a long period of time. A positive value means that the water level is above this mean lower water level while a negative value means that it is below the mean lower water level.

Tell students that they are going to try to model the water level and make predictions about the tides for future days.

After students have made their model, they'll need to check it with the data for July 11th and 12th. That data is in the table shown here.

The table shows the water level at different times in Boston on July 4 and July 5 2018. The water level is given relative to the mean lower low water level.