Mathematical Modeling- Linear Approximations
Students investigate the idea of linear approximation. Students apply mathematical modeling, specifically linear approximation, to an already collected data set to make a prediction. In this lesson, students first engage in a warm-up that is not a perfectly linear data set, being exposed to this for the first time. Students take on the role as a packaging engineer to learn the process to apply linear approximation modeling: collecting data, creating a graph, drawing a line-of-fit, creating a model in the form of an equation, defining the model’s variables, and evaluating with the model. Students ultimately use their linear model to predict the net weight of cereal in grams contained by 260 square inches of cardboard packaging.
Often in the real-world, situations are not perfect and require a model, such as the linear model shown, to make a prediction.Copyright Algebraic & Geometric Error. (2014, September 13). Retrieved June 27, 2018, from http://darkpgmr.tistory.com/143
Engineers deal with real-world problems, and often in real-world problems, numbers and data do not follow a perfect model like they often do in a mathematics classroom. To accommodate for this, engineers use mathematical modeling to investigate the relationship between variables, which allows them to make an accurate prediction of situational outcomes. Engineers follow the engineering design process while they work, and throughout this lesson, the process of collecting data, creating a model, testing the model, and making necessary amendments to the model post-testing are applicable to the engineering design process. In this lesson, students more specifically explore how packaging engineers apply mathematical modeling to help determine packaging variations for cereal and even offer a suggestion of linear approximation model to Battle Creek Cereal’s executive team that can be used to create skews of packaging based on square inches of cardboard packaging used and the net weight of the cereal in grams.
After this lesson, students should be able to:
- Investigate relationships between quantities by using points on scatter plots.
- Model an approximately linear situation.
- Apply lines of fit to make and evaluate predictions.