### Summary

In addition to the associated lesson, this activity functions as a summative assessment for the Using Stress and Strain to Detect Cancer unit. In this activity, students create 1-D strain plots in Microsoft ExcelÂ® depicting the location of a breast tumor amidst healthy tissue. The results of this activity function as proof of the accuracy and reliability of students' breast cancer detection designs.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Biomedical engineers conducting cancer research have shifted their attention toward tumor classification since finding characteristics common to all types of malignant breast cancer increases the validity in cancer diagnosis. One characteristic that distinguishes breast cysts from cancerous tumors is a dense fibrous area surrounding the lesion. This occurs as the body attempts to ward off the malignant tumor. Benign tumors are found to be much softer. On a very basic level, in this activity, students apply this concept to Young's modulus of elasticity. In generating the strain graph, the malignant region is depicted with a much higher modulus of elasticity indicting a stiffer region with less deformation. This understanding is applied in the generation of the strain graph as well as the brochures generated as part of the associated lesson's assessment.

### Pre-Req Knowledge

A complete understanding of Hooke's law, stress, strain and the associated relationships.

### Learning Objectives

After this activity, students should be able to:

- Model a tumor in normal tissue using a stress strain relationship.
- Depict a tumor using a graph in excel.
- Describe the advantages and disadvantages of this imaging technique.
- Explain how breaking down the problem can lead to an achievable solution.

### More Curriculum Like This

**Stress, Strain and Hooke's Law**

Students are introduced to Hooke's law as well as stress-strain relationships. Through the lesson's two-part associated activity, students 1) explore Hooke's law by experimentally determining an unknown spring constant, and then 2) apply what they've learned to create a strain graph depicting a tumo...

**Using Stress and Strain to Detect Cancer!**

Students are presented with a biomedical engineering challenge: Breast cancer is the second-leading cause of cancer-related death among women and the American Cancer Society says mammography is the best early-detection tool available. This three lesson/three activity unit provides hands-on activitie...

**Presenting Painless Breast Cancer Detection!**

This lesson culminates the unit with the Go Public phase of the legacy cycle. In the associated activity, students depict a tumor amidst healthy body tissue using a Microsoft Excel® graph.

**Applying Hooke's Law to Cancer Detection**

Students explore Hooke's law while working in small groups at their lab benches. They collect displacement data for springs with unknown spring constants, k, by adding various masses of known weight.

###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### NGSS: Next Generation Science Standards - Science

- Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Motion and Stability: Forces and Interactions (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards - Math

- Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Summarize, represent, and interpret data on a single count or measurement variable (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Summarize, represent, and interpret data on two categorical and quantitative variables (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- Telemedicine reflects the convergence of technological advances in a number of fields, including medicine, telecommunications, virtual presence, computer engineering, informatics, artificial intelligence, robotics, materials science, and perceptual psychology. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Use computers and calculators to access, retrieve, organize, process, maintain, interpret, and evaluate data and information in order to communicate. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Document processes and procedures and communicate them to different audiences using appropriate oral and written techniques. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Maryland - Science

- Motion and Stability: Forces and Interactions (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Tennessee - Math

- Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Summarize, represent, and interpret data on a single count or measurement variable (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Summarize, represent, and interpret data on two categorical and quantitative variables (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

###### Tennessee - Science

- Solve problems related to velocity, acceleration, force, work, and power. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

Each student needs a copy of the attached handout (doc).

### Introduction/Motivation

Today we will finally complete our unit and it will be your task to create an image depicting a tumor amidst healthy breast tissue. You will each receive a handout with an image which, after making the appropriate calculations, should be depicted in a graph generated in Microsoft ExcelÂ®. Please read the instructions on your assignment and ask any me any questions you may have. Today's assignment is worth 50 points, like your brochure. Together the two assignments are worth 100 points, equal to a test grade. Not to worry though! You all are more than prepared to create your challenge solution. Please clear everything from your desks and remember this is an individual assessment so please only look at your computer screen.

### Vocabulary/Definitions

cancer: A malignant and invasive growth or tumor tending to recur after removal and to metastasize to other sites.

force: An influence on a body or system, producing a change in movement or in shape or other effects.

spring: An elastic body such as a wire of steel coiled spirally that recovers its shape after being compressed, bent, or stretched.

strain: Deformation of a body or structure as a result of an applied force beyond limit.

stress: The physical pressure, pull, or other force exerted on a system by another, producing a strain. Measured by the ratio of force to area.

### Procedure

Background

This activity provides students with the first portion of the Go Public phase of the legacy cycle. Students create strain plots without any aids. They are graded on their solutions. This activity tests students on their comprehension of the material presented thus far, which includes the concepts of Hooke's law, stress, strain and biomedical imaging techniques.

With the Students

Hand out tp students the Show Me the Tumor! Handout. Explain that they may not use their notes or any other aids. This is an individual assessment, which along with the take-home portion, will count as a test grade.

### Attachments

### Investigating Questions

- What fundamental concepts does this method of cancer detection rely upon?
- Is this method reliable?
- Is this method of tumor detection cost effective?
- Is this method reasonable for clinical use?
- Are there any other methods to detect tumors in tissue? If so compare to the method used in this activity.

### Assessment

*Activity Embedded Assessment:* Grade on the accuracy of their graphs as well as their supporting calculations.

### References

Dictionary.com. Lexico Publishing Group,LLC. Accessed December 28, 2008. (Source of vocabulary definitions, with some adaptation)

### Contributors

Luke Diamond ; Meghan Murphy### Copyright

© 2013 by Regents of the University of Colorado; original © 2007 Vanderbilt University### Supporting Program

VU Bioengineering RET Program, School of Engineering, Vanderbilt University### Acknowledgements

The contents of this digital library curriculum were developed under National Science Foundation RET grant nos. 0338092 and 0742871. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.

Last modified: July 20, 2017

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