Students are introduced to the challenge question, which revolves around proving that …
Students are introduced to the challenge question, which revolves around proving that a cabinet x-ray system can produce bone mineral density images. Students work independently to generate ideas from the questions provided, then share with partners and then with the class as part of the Multiple Perspectives phase of this unit. Then, as part of the associated activity, students explore multiple websites to gather information about bone mineral density and answer worksheet questions, followed by a quiz on the material covered in the articles.
In their reading from activity 1 of this unit, students should have …
In their reading from activity 1 of this unit, students should have discovered the term "logarithm." It is at this point that they begin their study of logarithms. Specifically, students examine the definition, history and relationship to exponents; they rewrite exponents as logarithms and vice versa, evaluating expressions, solving for a missing piece. Students then study the properties of logarithms (multiplication/addition, division/subtraction, exponents). They complete a set of practice problems to apply the skills they have learned (rewriting logarithms and exponents, evaluating expressions, solving/examining equations for a missing variable.) Then they complete a short quiz covering what they have studied thus far concerning logarithms (problems similar to the practice problems). They consider how what they have learned moves them closer to answering the unit's challenge question.
Students revisit the mathematics required to find bone mineral density, to which …
Students revisit the mathematics required to find bone mineral density, to which they were introduced in lesson 2 of this unit. They learn the equation to find intensity, Beer's law, and how to use it. Then they complete a sheet of practice problems that use the equation.
Students examine an image produced by a cabinet x-ray system to determine …
Students examine an image produced by a cabinet x-ray system to determine if it is a quality bone mineral density image. They write in their journals about what they need to know to be able to make this judgment. Students learn about what bone mineral density is, how a BMD image can be obtained, and how it is related to the x-ray field. Students examine the process used to obtain a BMD image and how this process is related to mathematics, primarily through logarithmic functions. They study the relationship between logarithms and exponents, the properties of logarithms, common and natural logarithms, solving exponential equations and Beer's law.
Students continue an examination of logarithms in the Research and Revise stage …
Students continue an examination of logarithms in the Research and Revise stage by studying two types of logarithms—common logarithms and natural logarithm. In this study, they take notes about the two special types of logarithms, why they are useful, and how to convert to these forms by using the change of base formula. Then students see how these types of logarithms can be applied to solve exponential equations. They compute a set of practice problems and apply the skills learned in class.
In this activity, students will explore two given websites to gather information …
In this activity, students will explore two given websites to gather information on Bone Mineral Density and how it is measured. They will also learn about X-rays in general, how they work and their different uses, along with other imaging modalities. They will answer guiding questions as they explore the websites and take a short quiz after to test the knowledge they gained while reading the articles.
Students complete an exercise showing logarithmic relationships and examine how to find …
Students complete an exercise showing logarithmic relationships and examine how to find the linear regression of data that does not seem linear upon initial examination. They relate number of BMD scanners to time.
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