Scale and Relative Size
Carrie Persing, 6-12 Math Department Chair, MathScience Innovation Center
Developed with funding from the Mathscience Innovation Center
Major
Understanding
A nanometer is a billionth of a meter. How do scientists see and manipulate
objects that small? This lesson will help students understand the size of a
nanometer in relation to their own size.
Grade/Subject
Grade 7: Math
Objectives
Student will solve practical problems using proportional reasoning and
fractions.
Student will investigate concepts of powers of ten.
Time
Anticipatory Set: How Small Is Nano
Activity: Carbon Nanotubes
Activity: What is that?
Activity: Can You Build It?
Activity: MiniMe
Closure
Materials
For Teacher:
 PowerPoint presentation
5 min
10 min
10 min
10 min
20 min
5 min
For Groups:
 Journal
 SEM cards
 Metric tape measures
 4 meters of rope, paper towel tube, dowel rod, toothpick, pencil lead
 30 Small LEGO® bricks and a LEGO® base
 Pair of oven mitts
 Model Magic
 Pipecleaners
21st Century
Curriculum
Nanotechnology: Size & Scale, Tools & Instrumentation
State and National
Correlations
Virginia Standards of Learning: 2009 Math 6 (6.6), 2009 Math 7 (7.4)
NCTM Standards: Students will solve problems involving scale factors using
ratio and proportion.
Scale and Relative Size
http://MathInScience.info
© MathScience Innovation Center, 2007
Instructional
Strategies
1. Anticipatory Set (slides 1-3)
1.1. Ask students if they know how small a nanometer is. Discuss that in
Greek “nano” means dwarf and in science, it means billionth.
1.2. Show students the video from nisenet.org (Intro to Nano). Discuss
what they discovered about nanometers and nanotechnology watching
the video.
1.3. Record their thoughts on the board or chart paper.
1.4. Explain that students are going to complete a few activities that will
help them understand the size of a nanometer.
2. Activity: Carbon Nanotubes (slides 4-5)
2.1. Explain that length in nanometers is an important unit of measure for
nanotechnology.
2.2. One exciting design in nanotechnology is carbon nanotubes. They are
made up of bonded carbon atoms and have the highest strength-toweight ratio of any material but have a diameter of about 4 nm.
Baseball bats are now being designed using carbon nanotubes in order
to make them lighter and stronger. NASA is using carbon nanotubes to
design lighter spacecraft.
2.3. Even though carbon nanotubes are 200 times stronger than steel, they
are about 1,000 times thinner than the width of an average piece of
human hair! That is pretty small.
2.4. First, have students compare the diameter of their wrist to the diameter
of a piece of hair.
2.5. You will need to be outside or in an open area for this activity. Have
all but four or five students form a circle with the 4 meters of rope.
Hand the other cylindrical items to the other students. They will stand
in the middle of the circle.
2.6. Let’s say that the 4 meters of rope represent a single piece of hair that
has been magnified 100,000 times. Now look at each object and decide
which would represent a carbon nanotube (4 nm). If the hair is 4
meters, the object would have to be 0.4 mm (pencil lead).
3. Activity: What Is That (slides 6-9)
3.1. Ask students how we could possibly see an object as small as a
nanotube. Would a regular microscope work?
Scale and Relative Size
http://MathInScience.info
© MathScience Innovation Center, 2007
3.2. Explain that scientists must use either an Atomic Force Microscope
(AFM) or Scanning Electron Microscope (SEM) in order to see nanosized objects.
3.3. Show students slide 8. It is an image made by an SEM. Ask if they can
tell what it is. (pollen)
3.4. Pass out a set of SEM cards to groups. Tell students that their job is to
try and figure out what each picture represents. They can record their
guesses in their journals.
3.5. After students have had time to discuss in their groups and make
predictions, bring up slide 9. Ask students what they thought each
image was. With each click, the image will disappear and reveal what
the object was (a: bee leg; b: Horsefly Claw; c: Wasp Antennae; d:
Grasshopper Head; e. Fly antennae; f: Moth fly head)
3.6. If one billion grains of salt fit in a tub what fraction of that is one
grain? (one billionth)
3.7. If you would like to create cards of your own with objects like a staple,
porcupine quill, toilet paper, etc., go to
http://www.mos.org/sln/sem/quill.html
4. Activity: Can You Build It? (slides 10-11)
4.1. Pass out a bag of LEGO® bricks to each group.
4.2. Pass out oven mitts or mittens to half of the groups.
4.3. Show the picture on slide 10 and tell the students they have two
minutes to build it.
4.4. Discuss what happened. Why couldn’t the groups with mittens on
complete their building?
4.5. Scientists have to be able to manipulate objects at the nanoscale, but
normal tools will not work. They have been able to create tools at that
level like tweezers and lasers that will help.
5. Activity: Mini Me (slides 12-15)
5.1. In order for students to better understand a scale they cannot see, they
will try to model themselves at a smaller scale.
5.2. Place students in groups of 4. Ask then to measure each other’s height,
arm spam, and length of leg to the nearest centimeter. They will record
Scale and Relative Size
http://MathInScience.info
© MathScience Innovation Center, 2007
their data in the journal.
5.3. Ask students to calculate their measurements to be 1/10 and 1/100
smaller. Discuss how small that would be. Explain that by shrinking
by 1/10, students move from the meter scale to the centimeter scale.
5.4. Pass out model magic, pipe cleaners and scissors to each group.
5.5. Explain that they are going to create a “mini me” to model themselves
at 1/10 and 1/100 of their size. The pipe cleaners need to be cut the
appropriate lengths for their height, arm span and legs. The model
magic will be shaped around the pipe cleaners to form a body and
head.
Closure
After students have created their “mini me,” ask how many times they think
they would have to shrink themselves to become the smallest size visible to the
human eye (1,000). How about nano size? (10 million). Tell students to
imaging their 1/10 “mini me” as an atom. A normal-sized person would be as
tall as the distance around the Earth. End the lesson reviewing what they
learned about nano scale and nano technology. Show the video “How Small is
Nano?” from www.nisenet.org for a great illustration of scale and powers of
ten.
Extensions
1. DragonflyTV
Materials: Internet access
Students can be in groups of four for this activity. Dragnonfly TV on PBS
has six different shows about nanotechnology. Show 1 introduces students
to size and scale and nanotechnology. There are five different sections for
Show 1. Have groups pick a section they would like to look at. They will
go to http://pbskids.org/dragonflytv/nano/index.html and click on Show 1
and then the section they have chosen. Each group will report back to the
class what was learned.
Assessment
1. How can scientists see objects at the nano scale?
Answer: atomic force or scanning electron microscope
2. How many times stronger is a carbon nanotube than steel?
Answer: 200
3. If Sam is 56 inches tall, what height would he be if he were 10 times
smaller?
Answer: 5.6 inches
References
University of Wisconsin
The nanotube and mitten challenge were adapted from this site.
http://mrsec.wisc.edu/Edetc/
Duke University
Scale and Relative Size
http://MathInScience.info
© MathScience Innovation Center, 2007
Dr. Frederik Nijhout’s Entomology class takes SEM pictures of insects each
year and posts them on this site. The SEM sorting card pictures came from
here.
http://www.biology.duke.edu/dukeinsects/about.php
NISE Network
The videos used in this PowerPoint came from nisenet. It has videos, activities,
posters and much more to teach nanotechnology.
http://www.nisenet.org/
MathScience Innovation Center
Information on educational programs available to students, teachers and school
divisions, and procedures for registering for programs.
http://msinnovation.info
Scale and Relative Size
http://MathInScience.info
© MathScience Innovation Center, 2007