Nanotechnology and Human Health

Teaching Strategies

I teach three 90-minute block periods a day during each semester, for a total of 6 classes per year. I use an interactive SmartBoard in my classroom daily, and I prepare lessons using Notebook software. In a lot of ways my Notebook files are similar to Power Point presentations, in that the lesson flow is generally dictated by the slides. The difference comes from some of the interactive capabilities and links on the SmartBoard, but the strategies I describe in this section can be used anywhere there is access to the internet.

After the obligatory introductions for a new semester, and before introducing students to the Nanoscale World, I will do a Pre-Assessment Activity about nanoscale materials to assess their level of understanding of Nanotechnology. The next step is to get students thinking about how small nanoscale is. There are several interactive websites listed in the Teacher Resources section in the Appendix that can help students visualize relative sizes of common objects, from galaxies down to atoms, and I will let those images swirl in their minds for a little while.

To introduce the science of Nanotechnology, I will focus on the structure of carbon. My students should have some background in atomic structure and bonding, either from Earth Science or Chemistry, so I will start with a KWL activity. KWL evaluates what students already Know, what they Want to Know, and later, what they Learned. Based on the results, I will evaluate how much I need to review about the structure of carbon and the reasons it can bond covalently with four other atoms. I will use links to one or two websites (also in the Teacher Resources section) to show the structures of graphite, diamond, buckyballs and carbon nanotubes. From the visuals of the different structures, we will discuss the different properties of each carbon allotrope, and why they might be useful for different end products. It will be important for students to be familiar with buckyballs and carbon nanotubes since they are both commonly used in Nanotechnology research.

Since one of my objectives is for students to find the relevance of Nanotechnology to themselves, I will have them do some research outside of class to learn how it could be used in their (vocational) career area, or in any area of interest. Because Nanotechnology has a future in computers/internet, cell phones, cosmetics, medical and green energy applications, every high school teenager should be able to find something of interest to him/her. In addition, a large percentage of the students I teach in Precalculus are in Nursing, Electrical, Computer or Pre-Engineering career areas, all of which are areas with important connections to Nanotechnology. Students will create Power Point presentations, either individually or in pairs, of their findings to share with their classmates early in the semester. The presentations will be done at a rate of only one or two a day to leave adequate time for math instruction.

The mathematics lessons will be spread throughout the semester and will vary depending on the math course. In all courses, the first lesson will relate to size. To understand the significance of Nanotechnology, students need to grasp the scale of nanoparticles (10 ^-9 meters, or approximately 1 billionth of a meter). To accomplish this, and to emphasize what they saw on the interactive websites at the very beginning, students will create 3-dimensional models having complex shapes. One example I can envision is attaching an empty toilet paper tube to an ice cream cone (cylinder plus cone). During the Geometry unit in the Integrated Math 2 course, I will have them first cover their models with appropriately-sized cut-out squares (in ², cm ², mm ²) and count the squares to measure surface area. If their models are too small for individual cutout squares, students can create a net to cover the model and draw a grid of squares on the net to count the overlap. After this activity, these models should look like mosaic masterpieces that we can display in the classroom to continually reinforce the overlapping concept of area, discussed in the Background section. For other classes, I can use the models on display to reinforce the overlapping/coverage definition of area. With the conceptual understanding of area, students can then use the combination of appropriate formulas (i.e. the sum of the areas of each part of their complex shape) to verify their surface area measurements. Next, I will have them fill their 3-dimensional models with cubes, sand, or water, if possible, to measure volume. If it's not possible, I can demonstrate the filling of classroom manipulative models made for this purpose. Students will also use a combination of appropriate formulas to calculate the volume of their models.

Again, using the models, I will have students address another math standard - the effects of scaling on surface area and volume of three-dimensional solids. They will enlarge or shrink the model and then build it, using their creativity, from whatever materials they choose. Finally, through discussion and calculation, students will determine how many repeated "shrinkings" by the same factor they used for their models, of their smaller model it would take to reach nanoscale. During this activity, they will be able to describe sizes in multiple ways: different units, decimals, fractions and scientific notation.

At this point, I will need to give some instruction about the importance of the surface area- to- volume (S/V) ratio in the study of nanoscale particles. As similar (same shape) particles get smaller, S/V increases. That is, there is more surface area available, compared to volume, for reactivity with the environment. This is a significant fact that affects the properties of nanomaterials: once again, students will know "WHY" they need to learn the effects of scaling in geometry. Students will use their two models to compare the changes in first, dimensions, second, surface area and third, volume by dividing to find the three scale factors. This hands-on activity will clearly demonstrate the fact that changes in dimensions (scaling) affect surface area and volume differently and will confirm that S/V increases as linear dimensions decrease. While these geometric concepts only apply directly to the objectives of one of our district's integrated math courses, I can reinforce the concepts via warm-up activities in upper-level courses.

Revisiting the student-created models, and multiple divisions, may be just the thing that students need to comprehend why negative exponents are inverses of the corresponding positive ones (i.e. multiplication and division are inverse operations). I will begin by multiplying and dividing by tens and relate the results to what they already know about scientific notation. As I discussed in the Background section, I can illustrate other exponent properties using this idea of repeated divisions, multiplications. Exponents are a topic in my district's Integrated Math 1 course, used again in Integrated Math 2, and then in Intermediate Algebra and Precalculus, so getting a solid foundation of understanding will go a long way. With all that I have learned about Nanotechnology, and my enthusiasm for it, I'm sure I will find other ways to interject more examples of the topic throughout all of the courses I teach!