“Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry” - Richard Feynman
Introduction
The scale of the known universe is truly immense, from quantum level interactions that affect molecular affinities to collisions of whole galaxies. In fact, even the nucleus of an atom, which is tiny in comparison to the whole atom, is made of smaller parts, called nucleons, and even the nucleons (protons, neutrons) are made up of smaller parts. Our humble existence is predicated on these interactions. No other field of science, besides physics, truly seeks to understand this broad scope of knowledge. As a result, many students struggle with contextualizing content and the related quantities associated with cosmic energy outputs and extreme distances in physics. Scientists have utilized the base ten numeral system for hundreds of years to accurately represent quantities; from the distances between particles in an atom to the energy output of a quasar. This rather sophisticated but very powerful and simple to use, mathematical tool is often not discussed sufficiently in the classroom, which creates deficits in areas of scientific notation, unit representation, exponential arithmetic and significant digits.
The electromagnetic spectrum provides a practical context to integrate the concept of scale, and refine skills of scientific notation, due to the inherent inverse relationships between wavelength and frequency. The District of Columbia has adopted the Common Core standards which requires high school students to use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media (HS-PS4-1). Students continually struggle with articulating these mathematical relationships, and these difficulties serve as the impetus for this unit. After three years in DCPS, I am keenly aware of the importance of truly understanding quantities and groups of quantities with respect to the base unit, implementation of scientific notation, and explorations of scale. All three of these basic topics are fundamentally important to all STEM fields. This 3-4 week unit seeks to enhance understanding of the relation between mathematics and physics through the continual implementation of scientific notation throughout the year, with a concentrated emphasis on SI units systems. In addition, students will develop a sense of scale through base ten numeration with the electromagnetic spectrum. The size of each relevant wavelength will be compared to metric distances to provide a familiar frame of reference. The culminating work will occur during the months of September to November as well as March; students will conduct several inquiry investigations (i.e., calculating wave speed in various media and developing EM spectrum mind maps that depict relationships based in data). It is my hope that this unit will motivate students to think critically about their physical environment as well as refine their number sense to provide valuable insight in comparing like quantities in a base ten system.
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