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Do You Measure Up?

Participants: Pamela Frederick & Sandra Kowalowski

Overview:
This unit will cover the topics of ratio and proportion. These topics are found primarily in Key Idea #5 – MEASUREMENT, but through the incorporation of other content and activities, we will address key ideas 3 – 6 also.

Students will address these topics through a variety of activities. First and foremost, students will use algebra skills for calculations. They will also learn to translate language (verbal information) into algebraic expressions /equations.

The golden mean, .61803, is a ratio seen extensively in nature, ranging from the DNA helix at the microscopic level to flowers and spirals in shells, from the proportions of the human body and our EKG heart rhythm to the planets in our solar system. The Ancient Greeks and others discovered this relationship and used it in art and architecture. It is still used today. This relationship will be explored and analyzed in class. Students will then continue to investigate it as an individual project using computers and the Internet. As a culminating activity, students will present their findings to the class.

Other class activities will involve map readings and shadows. The map lab will hone measuring skills using the metric system and require map-reading skills to calculate ratios. Students will use these ratios to form proportions to calculate linear distances between two locations. The shadow lab will allow students to measure objects (including themselves) and their shadows.

They will then use a proportion to calculate the height of an object that is too tall to measure in the conventional sense. This exercise will enlighten the students as to the difficulties involved with measuring in the ‘real world’, which will lead to a discussion of the sources of error in measurement and its effect on calculations.

Finally, students will estimate the height of an object using the 45°-45°-90° triangle ratio. This trigonometric relationship between the two sides of a right triangle will be used to determine the height of the object using a one-to-one relationship. This crude estimation will then be compared to calculations from the shadow lab and results will be discussed in class.

This unit is designed for Pre-Math I or Math I part 1 students and has an instructional time of approximately 10 days.

NYS Learning Standards Addressed:

Math, Science, & Technology:

• Standard 1 Analysis, Inquiry, Design: Mathematical Analysis 1 - 3
• Standard 3 Mathematics: Key Ideas 2 - 6

English Language Arts:

• Standard #3: Students will read, write, listen & speak for critical analysis and evaluation.