Tech Directions - November 2007 - (Page 27)

See the Math with Your Binoculars! By Harry T. Roman htroman49@aol.com OU and your students will find a very practical math application right there in a pair of common binoculars. Follow the procedure described here to get a bit of math practice and analysis. Y Analyzing the Data I recently conducted this activity with students at the elementary school that I attended many years ago. Table l shows my raw data for 21 8th-grade students. In analyzing the table, we see a strong and peaked statistical distribution around 6.0 cm. If you plot the data shown, you get an almost perfect distribution curve. Now, let’s go back to that measurement made on the binocular eyepieces. When I measured the eyepieces on my pair, the closest spacing was 5.0 cm and the largest spacing was 7.0 cm—perfectly bracketing the end points of my data set! Actually, you’d need a sample of about 100 students for statistical validity. I may have been lucky with my data set to have the scores work out so balanced with only 21 students. You can suggest that in addition to measuring their classmates’ eye distances, they also measure those of their parents and younger brothers and sisters, or other children from lower school grades. Then have them construct data sets and graphs of their findings for each group and compare the results. Perhaps doing the experiment with young children would show different data distributions because their heads are still growing. How might that data look compared with that for teenagers and adults? Will Taking Measurements Locate a pair of binoculars and a centimeter (cm) scale ruler. Have students use the ruler to measure the distance between the centers of the binoculars’ two eyepieces, first with the eyepieces pushed in to their closest separation, and then again with them at their greatest separation. Here comes the fun and interesting part. Students next take turns measuring the distance between their classmates’ eyes. They should do the measuring while each student stares forward, keeping his or her eyes as motionless as possible. Holding the ruler near each student’s nose, measure the separation between the centerlines of his or her eyes. Next, construct a frequency histogram of the number of times a measured value was recorded. (See Table 1 for an example.) Harry T. Roman is an electrical engineer, inventor, and technology education supporter, East Orange, NJ. the data be centered at larger values for the adults? From the data between the age groups, it may be possible to conclude something about changes in head size with age, as well as eye spacing. Do you think data sets would vary between the races of people around the world? If binoculars are Table 1—Sample Measurement Results Distance Between Centerline of Eyes 7.0 cm 6.6 cm 6.0 cm 5.5 cm 5.0 cm Recorded Scores 1 4 12 3 1 sold worldwide, how might the manufacturer design them to accommodate different facial and eye separation features? The class of students I used for my experiment was evenly divided between Hispanic, white, and African-American students. Might that have influenced why my data set was so neatly distributed? There is mathematical support behind the design of most products. All we have to do is put on our binoculars and take a close look. Have your students give it a try! www.techdirections.com APPLIED MATH 27 http://www.techdirections.com

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Tech Directions - November 2007 Technically Speaking Contents Direct from Washington The News Report Technology’s Past Technology Today Mastering Computers Video Game Programmers Learn to “Pitch” Project Teaches Students to Diagnose an Ailing Windows OS See the Math with Your Binoculars! Fire Safety Technician ACTE Convention and Career Tech Expo Hands-On Activities More than Fun

Tech Directions - November 2007

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