Lesson 3 – Inferences From Proxy Variables Mock AFM

This is the third lesson of the Observing Beyond our Senses module. In this lesson, students will learn about observation. Observation is the skill of recognizing and noting some fact or occurrence in the natural world. Observation includes the act of measuring. To infer is to arrive at a decision or logical conclusion by reasoning from evidence. Scientists use observations to make inferences.


See the NGSS listed in the left-hand menu and below. When applicable, connections to 21st Century Learning Skills and other published standards are also included in the chart below. In addition, for this lesson, here is a breakdown of:

What Students Learn
  • Observation is the skill of recognizing and noting some fact or occurrence in the natural world. Observation includes the act of measuring.
  • To infer is to arrive at a decision or logical conclusion by reasoning from evidence.
  • Scientists use observations to make inferences.
  • Additional information can improve the validity of inferences.
  • Proxy variables can be used to make observations.
  • An Atomic Force Microscope (AFM) uses repulsive force as a proxy variable to make observations of surfaces at the atomic scale. Processing the data with of visualization software, scientists infer surface structure from these observations.
  • Increased resolution can provide additional information.
  • Design solutions involve tradeoffs.
What Students Do
  • Make observations and generate inferences about differing types of data.
  • Use “touch” data to draw an unknown object in a bag.
  • Make inferences about the identify of the object from the drawings.
  • Use a mock Atomic Force Microscope (AFM) to infer surface structure from “touch” data processed with Excel into a 3D graph.
  • Brainstorm ways to improve the design of their mock AFM & evaluate the trade-offs.
  • Evaluate the limitations of utilizing proxy variables to take measurements.
  • Evaluate the limitations of observation to infer patterns or make predictions.
Aligned Washington State Standards
Washington Science Standards (Next Generation Science Standards)

Performance expectation(s): 

HS-PS2-3 Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision.* (*This PE will not be fully completed at the end of this lesson or module.)

HS-PS2-6 Evaluate the claims, evidence, and reasoning that the complex interactions in ecosystems maintain relatively consistent numbers and types of organisms in stable conditions, but changing conditions may result in a new ecosystem.

HS-ESS2-2 Analyze geoscience data to make the claim that one change to Earth’s surface can create feedbacks that cause changes to other Earth systems.

HS-ETS1-1 Analyze a major global challenge to specify qualitative and quantitative criteria and constraints for solutions that account for societal needs and wants.

HS-ETS1-2 Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

HS-ETS1-3 Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics, as well as possible social, cultural, and environmental impacts.

The bundle of performance expectations above focuses on the following elements from the K-12 Science Education Framework:

Highlighted Science and Engineering Practice(s)

Highlighted Disciplinary Core Idea(s)

Highlighted Crosscutting Concept(s)

SEP-1: Asking questions and defining problems

SEP-6: Constructing Explanations and Designing Solutions

SEP-4: Analyzing and interpreting data

SEP-8: Obtaining, Evaluating, and Communicating Information

HS-PS2.A: Forces and Motion

HS-ETS1.A: Defining and Delimiting an Engineering Problem

HS-ETS1.C: Optimizing the Design Solution

PS2.B: Types of Interactions

ESS2.A: Earth Materials and Systems

ESS2.D: Weather and Climate

CCC-2: Cause and Effect

CCC-3: Scale, Proportion and Quantity

CCC-6: Structure and Function

CCC-7: Stability and Change


Prior to beginning this lesson, if there is time, we recommended an optional reading activity.  Students would read a short article on innovative techniques to measure brain activity. This article specifically discusses brain neurology as a system and the need for novel ways to “see” into it. Taken from the August 2011 HHMI Bulletin, vol. 24, No. 3. “Let’s Get Small” by Helen Fields. This may help students understand the application of instruments and technology that help us answer questions that may have been unanswerable before!  You can discuss the article. Or have them take notes and then come back to this article after the activity below to discuss observation, inferences, scale and proportion.

For implementing the rest of this lesson, please note: There are additional materials needed for this lesson. The paper bags with items for the warm-up activity should be assembled and taped shut before class. The mock AFM boxes can be assembled ahead of time, or students could assemble them in class. If assembled during class, the surfaces should be inserted into the boxes without students seeing them so have students trade boxes or one class make them for use in another class. Students will also need computer access (one per group) to plot the mock AFM data on the premade Excel file. See Making the AFM Teacher Directions (Word Doc | Google Doc).

Materials (for ~25 students, ~8 groups of ~3):
Vanilla for scent
-Paper lunch bags (per student)
-Collection of items of similar size and shape (pack of gum, eraser, used (EMPTY) lighter, USB drive, 9Vbattery). See powerpoint slide #10. (1 per student)
-Probe sticks (one per group) that have been marked in 0.2cm resolution (wooden skewers from the grocery store work well).
-Rulers (one per group)
-AFM box (1 per group)
-marking pen(1 per group)
-1cm x 1 cm graph paper (and somewhat smaller 0.5 cm x 0.5 cm if completing the ‘fine’ resolution data collection).
-box about the size of a shoe box (one per group)

Warm-up: How does observation lead to inference? (There is a student worksheet that goes with these slides Word Doc | Google Doc.)

(PowerPoint | Google Slides)
    • What distinguishes an observation from an inference? Before students enter, have the classroom smelling of vanilla. Ask students to describe the smell [slide 2] using descriptive words (data) then ask them to make inferences about what the smell implies (cookies?, air freshener?). Do the same for shadow [slides 3-7]. Encourage observations of the picture first, rather than inference (not “it’s a shadow from a man’s face,” but “it’s a contoured region of low light surrounded by higher light intensity“). To assess their understanding of the difference between the two terms, slide 8 returns to the wind speed activity. Students are asked to identify the observations and inferences used to arrive at a wind speed value. Be sure they know the difference between observation and inference before they move on. Student groups could share in a whole class discussion or you could check in with each group as they discuss the trade-offs. The term “proxy variable(s)” is introduced to describe measuring/observing something we reasonably infer to be an indicator of something we cannot directly observe with our senses.
    • How can we use proxy variables to make observations? How does additional information help our inferences? (PowerPoint, Student Activity) (Slide 9) Hand out paper bags containing one of the items on the material list (pack of gum, flash drive, 9V battery, lighter, or eraser). Students should make a drawing based on their observations about the object, but cannot open the bag for direct visual observations. Ask students what they think is in their bag (inference).(Slide 10) Discuss the different approaches to make observations (probably some form of touch data) used to make inferences. Once many have made guesses as to the object’s identity, show the possibilities and ask if they can make a stronger inference with the additional data.
    • If you could not rely on visual observations, how could you make inferences about your environment? (slide 11) Students are asked to consider how they could make observations about two different sidewalks without visual stimuli. Often we need to rely on other characteristics to “see” objects, such as a bat’s echolocation or a shark’s electroreception. Specifically, we can use touch to determine the shape of an object. Push students to specify details about the process: What would the edge feel like? How would you know if there’s a bump, an incline, or step up/down? Slide 12 illustrates the use of a cane to transmit the “touch” data through a probing process. Slide 13 illustrates tactile surface features built to aid the visually impaired in detecting boundaries such as sidewalk to street or transit crossings. Once students identify the purpose, questions can be posed concerning how notable the features need to be (this will set up a future signal to noise discussion) or how regular/large the pattern would need to be to distinguish the “touch” data from natural occurring variations in the surface.
  1. Mock Atomic Force Microscope
    • How can we use touch data to see things that are very small? (PowerPoint | Google Slides)

      Slides 14, 15, & 16 Introduce the concept of using “touch” data to make observations at scales too small to see with the human eye. Slide 17 introduces the Atomic Force Microscope. Since atoms repel each other, we could probe a surface with a very fine tip and record the feedback from the changing topography. Repulsion data from dragging a small ‘cane” across a surface is visualized with computer software so that inferences about atomic structure can be made. Slides 18 & 19 show examples of data used to visualize the hexagonal structure of carbon in graphite and the repeating “steps” in gold.

      Teacher background: Chemical analysis has shown that graphite is composed of carbon, but more analysis is needed to show the geometry of the atomic structure. This is what an Atomic Force Microscope (AFM) does (http://virtual.itg.uiuc.edu/training/AFM_tutorial/). Basically, a fine tip is dragged along a sample surface while a laser reflects off the back of the tip to a light sensor. As the surface dips and bumps the tip moves in or out, changing the reflected angle of the laser. The light sensor uses this subtle change to determine how the tip must have moved and therefore the geometry of the sample surface. Displaying the bumps as bright regions and dips as dimmer regions, a pattern emerges. Noticing the periodicity, a structure can be deduced for graphite; hexagonal layers of carbon atoms. Similar instruments such as the Scanning Tunneling Microscope (STM) yield similar data (an STM does not measure touch, but the proximity to a surface by how much current flows from the tip to the surface). Notice how either method deduces a hexagonal layered structure for graphite. Gold, for example, appears smooth to the eye, but exhibits “steps” when viewed with an AFM on a relatively large scale of half of a micrometer. Upon magnification, “strips” appear on the formerly smooth surface. At maximum magnification, the actual atoms of gold can be seen on the surface of these strips. These are the hexagonally arranged bumps.

  2. Collecting Data with a mock Atomic Force Microscope
    • Gross Data Collection

      Handout mock AFM boxes (or have students assemble them in class) and marked probe sticks. The provided surfaces should be hidden inside (box opaque and lids taped down) (slide 20). Instruct student groups that they are NOT to open the box. Demonstrate how students will use proxy “touch” data collected as probe stick measurements to infer the surface structure. To help interpret the data visually, the measurements can be directly entered into the premade Excel File Lesson 3 3D Plot Mock AFM: using the Sheet named Student Data Gross.

      Guiding Questions for a whole class discussion regarding the processed data:

      1. Is there enough data to infer the structure of the surface?
      2. Is there enough data to infer a predictable pattern? Teacher Notes: The cast shapes intentionally vary so that how easily the structure can be inferred & the pattern predictability varies considerably from group to group. At this point, each group’s answers to these two questions should be ambiguous.
      3. How could we improve our data collection design to generate stronger inferences about your unknown surface? (slide 21)
        Teacher Notes: Student answers may vary. One key idea that students should recognize is that some means of achieving greater resolution could provide additional useful data. Ask students to extrapolate what new data could be revealed by shrinking the tip size of the probe stick within the grid they just used or conversely to use their current tip size to take measurements at smaller and smaller grid intervals (0.05 cm x 0.05cm, etc. ). Drawing out the extrapolations on whiteboards in groups can help them visualize the effect of the change.

        While students are discussing the effect of the changes, the teacher should be circulating to change out the screen (graph paper with smaller squares) for the fine data collection, ensuring that students do not see into the box.

    • Fine Data Collection (optional)
      Have students repeat the process using the fine data collection screen (0.5 cm intervals) and the Sheet named Student Data Fine within the same Excel spreadsheet. Once the fine data collection & graphing is complete, collect the boxes and set out the surfaces for students to view.
    • Students should then complete the Post Mock AFM Worksheet (Google Doc | Word Doc).

Career Connection

Based on how much time you have available, choose a career-connected activity below. In each case, recap what your students just learned in the lesson to the activity.

A homework/ outside of class B 5-10 minutes in class C half of class period (~25 minutes) D entire class period (~50 minutes)
Give handout for students to watch Dana’s video and answer questions at home as homework. A & Brainstorm on interview questions for Dana using a whiteboard or projector. A & Have students imagine a job like Dana’s that works with sensors and proxy variables. Students prepare written explanations of the proxy variable, and the education necessary to do this work. C & Have students prepare a set of interview questions for the person/job they’ve identified or described in C. This could start with students taking 3 minutes on their own, then pair-and-share, then share to class and evaluate questions.

Example interview questions for Dana:

  • What skills did you already have when you started this project?
  • How did you develop the other skills that you did not acquire through the communications major?


How will I know they know?

  • Review students identified observations & inferences for the wind speed challenge.
  • Review students’ suggestions to improve the mock AFM.
  • Review students’ mock AFM worksheets. Use example graphs (slides 22-27) to see if students can identify the structures they describe.



  • Students who do not visualize graphs well may benefit from additional or introductory work. This Student Graphing Extension Activity (Word Doc | Google Doc) requires 2 odd shaped bottles (obtain at vintage shops), a plastic champagne glass, and a plastic ‘party’ glass, ruler, graduated cylinder and container for water. It generally takes 80 minutes to complete and gives students an understanding of slope and y-intercept…and the importance of looking at axes labels.