Nanotechnology and Human Health

Classroom Activities

Lesson 1 – What is a nanometer? What is Nanotechnology?

This lesson will take place on the first day of the semester, after all introductions and paperwork are complete.

Pre-Assessment: One side of the classroom will be designated as "True" and the other side "False." I will ask questions about nanomaterials and applications from Chapter 1 in the book Nanoscale Science: Activities for Grades 6-12. ¹⁶ Students will move to the side of the room that represents their answer to each question, and we will discuss the answers to each to introduce the field of Nanotechnology.

Instruction: Define nanometer as one billionth of a meter and ask students to name things that are that small. Show a video (refer to links in the Teacher Resources section) that illustrates relative sizes of common materials. There are several videos to choose from, and I will experiment with different ones to determine which my students prefer. Introduce and define Nanotechnology using another video or Power Point presentation with general background information.

Assignment/Assessment: Students will work individually or in pairs to research a Nanotechnology application of interest to them. Research will be done outside of class, and they will create a Power Point presentation to share with their classmates. Students will present their findings at a rate of 1-2 per day over several weeks. Presentations must have a minimum of three slides that cover:

1. Student Biography: name(s), career area, post-graduation plans, other interests
2. Nanotechnology Application: how it is used, how it works, fun facts/illustrations
3. Reason for choosing Application (above) and Source(s) of Information

Lesson 2 – Size and Scale

This lesson will cover more than one day, depending on the course and level of the students. It will begin on the second day of the semester to lay more of a foundation for the study of Nanotechnology, but the mathematics may be spread throughout the course.

Warm-up/Pre-Assessment: Several topics can be used as mathematics warm-up activities and repeated as often as necessary. A) Convert between decimals and scientific notation. B) Calculate area of basic and/or composite geometric figures. C) Apply scale factors and calculate surface area and volume of resulting objects.

Instruction: Set up discussion of size and scale by reading the poem "One Inch Tall" by Shel Siverstein or an excerpt from Gulliver's Travels and/or by showing video clips from old movies such as King Kong, The Incredible Voyage, or A Bug's Life (Teacher Resources). Discussion should focus on whether it is physically possible for the animals or people depicted to exist, followed by examples from nature where size matters (elephants versus geckos and ants). This discussion will lead into basic chemistry instruction about the element carbon. The amount of chemistry instruction will be determined by the KWL activity described in the Strategies section. I will show internet images of the four common allotropes of carbon, along with some of their properties, and give examples of how some properties change at the nanoscale (i.e. strength and conductivity).

Scientific notation and the geometry topics surface area, volume, and "scaling" (enlarging/shrinking by a scale factor) will be embedded within this lesson. At this stage, I want students to demonstrate how to convert between very large (millions) or very small numbers (billionths) and scientific notation by multiplying or dividing by 10 repeatedly, representing the number of repetitions with an exponent on 10. They will also use their calculators to add, subtract, multiply and divide numbers at the extremes to ensure that they recognize the notation using "E" followed by the exponent on 10, and that they look for "answers" shown in scientific notation on the screen.

Students will use materials of their choice to create "complex" 3-dimensional models made from two or more basic shapes. They will first measure appropriate (linear) dimensions for their models. Next they will measure the surface area in one of two ways: cover the model with cut-out squares of appropriate size or cover the model with a net having a square grid on it, and count the number of squares. Students will then compare their measured areas with the sum of the areas calculated by area formulas for each piece of their models. If possible, students will measure volume by filling their models with a known volume of water, sand, cubes, etc. All students will calculate the volume of their models using appropriate formulas. Finally, all models will be displayed in the classroom as visual reminders that surface area is a measure of overlapping squares.

To study the effects of applying scale factors on surface area and volume, students will enlarge or shrink their models by a factor of 10 or 100, depending on the size of their original models, by multiplying each of its original dimensions. They will build it and then calculate the surface area and volume of their second model. Finally they will compare the new versus original measurements by completing a table:

Assessment: Students will complete additional rows in the table and summarize the relationship between the scale factor and the changes in surface area and volume. Students will also verbalize the pattern for the ratio of surface area to volume as the linear dimensions decrease.

Extension for Precalculus: Students will create one graph of both surface area and volume versus one of the linear dimensions in the table above. They will create a second graph using the same data on a logarithmic plot. Students will then verbalize and explain the differences between the two graphs.

Lesson 3 – Exponents

This lesson can be inserted into any math course when rules of exponents are being taught or reviewed.

Warm-up (sample): Rewrite each expression showing all factors individually.

1. x ⁴x ⁵x 2. p ⁸/p ⁴ 3. (4h) ³ 4. (k ⁶) ² 5. (2d ³) ⁴

[KEY: 1. xxxxxxxxxx, 2. (pppppppp)/(pppp), 3. 4h4h4h, 5. 2ddd2ddd2ddd2ddd, etc.]

Instruction: Relate exponents to nanometers and scientific notation by asking questions such as: "How many nanometers are in 5 meters?" "How many meters is 3 nm?" "Starting with a length of 5 m, how many times must you divide by 10 to get a length less than 100 nm?" Starting with a length of 5 m, how many times must you divide by 5 to get a length less than 1 nm?" If necessary, review how 100 nm or 1 nm will be displayed on the calculator screen. Discuss the meaning of the base (10) and positive versus negative exponents in scientific notation. Relate the concept of multiplication and division being inverse operations to the negative sign in an exponent indicating the inverse of multiplying repeatedly.

Emphasize the meaning of symbolic exponent rules by having students verbalize them. The following table gives examples of how to verbalize five basic rules when the exponents are integers. (NOTE: The symbolic rules apply for real numbers as exponents, but the meanings may not make sense.)

Assessment: Practice rewriting expressions with exponents in simplest form and verbalizing their meaning. Practice can be in the form of worksheets, matching cards with symbolic expressions to corresponding cards with written meanings (group activity or interactive SmartBoard activity), or displaying a written meaning on the screen and students writing the corresponding symbolic expression on dry erase boards or paper at their seats for the teacher to check.