Are students the only things that experience stress and strain? No, it’s a common phenomenon that is a key for engineers to understand materials that we use to make virtually everything around us. In this 2-day lesson, students investigate the relationship between tensile force applied and resulting elongation of a metal spring. Measurement skills will be practiced. Results will be converted into mathematical expressions (formulas) with two variables. Data will be graphed by hand and with a graphing calculator, then assessed for best fit curve. The curve equations obtained from the graphs will be compared to each other and to the the mathematical formula obtained from measurements. Statistical analyses of class results will be conducted. Finally, students will evaluate possible causes of variations. Applications to the real world: Engineers are often faced with problems of selecting appropriate materials for different applications. Adjacent to the school where this lesson was taught is a prestressed reinforced concrete bridge, made with twisted cable reinforcing that acts like a spring. Societal impact: Virtually every item of modern society – such as planes and rockets, bridges, buildings, cars, artificial joints, MP3 players, computers, appliances and retractable pens -- reflects an engineering material choice. Different materials have different properties and therefore are suited (or not) for particular applications. Career connections: Understanding properties of materials, and expressing them mathematically are necessary for every engineering discipline. Data about material properties needs to be repeatable to give consistent results that can be relied on. Statistics are important for analyzing engineering research results to produce useful factors for design. Catch: video of engineering tests of various materials destructive (things breaking under tension); stretch a variety of materials (silly putty, fruit roll-ups, crepe paper, rubber bands) and engage class in observing their behavior (elongation, thinning then breaking). Brief PowerPoint instruction on stress types, relationship between force and elongation in tension Different materials behave in different ways. Math is essential to understand and predict properties of materials so engineers can select appropriate materials and designs. Students will learn the engineering concepts of stress and strain and understand how math is used to define behavior of materials Students will use measurement and analytical skills to explore behavior of an elastic material. They will: measure applied force and resulting elongation within specified accuracies record data accurately in written tables graph the data and define a best fit line for the graph compute the slope of the line, and an equation for the line create mathematical expressions (formulas) for the data compute mean, median, mode and standard deviation of data from the class interpret graphs evaluate data for possible causes of variations/inaccuracy MA-HS-1.4.1: Students will apply ratios, percents and proportional reasoning to solve real-world problems (e.g., those involving slope and rate, percent of increase and decrease) and will explain how slope determines a rate of change in linear functions representing real-world problems. MA-HS-3.3.1: Students will apply algebraic concepts and graphing in the coordinate plane to analyze and solve problems (e.g., finding the final coordinates for a specified polygon, midpoints, betweenness of points, parallel and perpendicular lines, the distance between two points, the slope of a segment). MA-HS-4.1.1: Students will analyze and make inferences from a set of data with no more than two variables, and will analyze problems for the use and misuse of data representations. MA-HS-4.1.2: Students will construct data displays for data with no more than two variables. MA-HS-4.2.3: Students will: identify an appropriate curve of best fit (linear, quadratic, exponential) for a set of two-variable data; determine a line of best fit equation for a set of linear two-variable data and apply a line of best fit to make predictions within and beyond a given set of two-variable data. MA-HS-5.1.1: Students will identify multiple representations (tables, graphs, equations) of functions (linear, quadratic, absolute value, exponential) in real-world or mathematical problems. MA-HS-5.3.3: Students will model, solve and graph first degree, two-variable equations and inequalities in real-world and mathematical problems.  Working in groups of 2-3, students measure the initial length of the spring.  Then they sequentially add bolts to the spring as weights, and measure the resulting length after each bolt is added. They record information in a data table, then graph it.  Groups create mathematical formulas with x and y variables to describe their observations. They then draw a “best fit” line on the data graph, and compute the slope of the line. They use the slope to write an equation describing behavior of the material, and compare it to the formulas they created from the graph.  Students use graphing calculators to plot the data and obtain a line equation. Calculator values are compared to the manually derived values.  Values for slopes from various class groups will be shared. Mean, median, mode and standard deviation of the values are computed.  The class brainstorms on factors that could affect test results. These were results for the target class, Algebra 2. Lesson was taught in all classes of partner teacher (Geometry, Algebra 2, and Honors Calculus). Even the Honors Calculus students improved – by an average of 15%. Stress-Strain Springs Carol Clinton 1, Peggy Dunn 1 Department of Civil and Environmental Engineering, University of Cincinnati, Cincinnati OH; 2 Newport High School, Newport, KY AbstractActivityConclusions Goals Pictures Objectives State Standards Assessment Results References and Acknowledgments Assistance provided by: Dr. Richard Miller, University of Cincinnati Ms. Peggy Dunn, Newport High School Project STEP is funded through NSF Grant # DGE Overall I would rate this lesson as: Excellent (35%) Good (48%) Average (12%) Fair (4%) What did you like most about today’s lesson : activity, group work (playing with the spring), seeing how the graphing and equations are alike, real-life examples, fun What did you like least : using graphing calculator, pre and post tests / writing