The Moon and Math.

  We are in the time of the year in Alaska, when we will often see the moon for 24 hours or longer at a time.  There are times when it does not set but circles around the sky.  It is an awesome sight.

The moon and its phases offers some great math opportunities for the classroom in geometry and in measuring time.  Two different aspects of something we see all our lives.

Lets start with the relationship between the time of day and the visibility of the moon based on its phase. It is important to remember the moonlight we see is actually sunlight bouncing off the moon.  Consequently, the phase of the moon is determined by the relationship between the moon, the earth and the sun. 

So the geometry involved is as follows.  When the moon is between the earth and the sun, we observe it as a new moon because we are looking at the moon without illumination. Two weeks later when the moon is on the other side of the earth from the sun, the moon is fully illuminated and we see it as the full moon.  The two quarter moons occur in between when the moon is half lit. When all this is happening, the moon is rising as the sun is setting during the full moon.

Add in an activity that uses a spreadsheet to determine the next full moon.  The moon's orbit is 29.5 days long so its a matter of adding that amount to the current time of moon rise.  However, if you want to make it a bit more interesting follow the link to get the in depth equations to create a wonderful sine wave visualization of the moons cycle.  The equation even goes so far as to include the percent of the phases of the moon.  The author has them adjust the equation to make it a bit more accurate.  See if you could coordinate this activity with the science class when they are studying phases of the moon.

Of course NASA has a 128 page book filled with various science and mathematical activities for grades 3 to 12 on lunar math.  It includes a list of math topics covered in this book.  I took a look at some of the activities for younger students and with a bit of adjustment, they could be used in the high school. 

This lesson geared for middle school seems to tie the geometry of moon phases and spread sheet into one nice long lesson.  It has everything needed and all the links for supplemental materials. 

Finally, there is a four lesson unit in the NCTM middle school magazine which integrates science, math, and literacy on using moon phases to measure time.  Lesson one is focused on lunar phases and how they work.  The second lesson focuses on what make a good standard unit because we measure things in standard units such as feet or meters.  The third lesson focuses on the Hopi because their astronomers did a good job of marking time. This lesson includes the lunar cycles based on the Hopi names for the moons.  The final lesson looks at the ways different cultures describe time.

Have a good day and let me know what you think.  I love getting feedback.