7th Grade Students Delve Into Geometry
Open-ended problem solving? Look no further than Dr. Geraghty's 7th grade math class.
After completing a geometry chapter, Dr. Geraghty decided it was time for a deeper challenge! The math class was randomly broken into groups and told to calculate the volume of a golf ball taking the dimples into consideration. Those were the only directions given to the students! Dr. Geraghty believes it is important for students to experience problems that may not have a single correct answer. There is no standard for a golf ball and some information about its geometry is unknown.
While three of the four groups used similar approaches, all took at least slightly different routes that led to some interesting discussions. One group measured the diameter of the golf ball with a straight ruler. This action led them to discuss other more accurate ways to do the measurement, either by indirect means or by using different equipment. Several groups approximated the dimples as hemispheres, which prompted the class to discuss whether selecting hemispheres would under- or over-estimate the volume of the dimples. The class also discussed ways to approximate dimensions of the dimples. Groups used different units, allowing students to convert between metric and English units, including converting cubic units. One group took the less mathematical, but more accurate route of measuring the displacement of water by a submerging the golf ball in a measuring cup. This lesson was a great opportunity to discuss the technique of utilizing displacement, possible sources of error, conversion from mL to cm3 (and to grams) and density in general.
Despite all of the different calculations performed and the lack of an official standard golf ball volume, all groups came up with volumes that were quite close to each other. Congratulations to our 7th grade problem solvers!