Judgement with Jellybeans
Students collect data and apply mathematical modeling, specifically linear approximation, to predict what will happen in a specific situation. In this activity, students collect data to determine the number of Jelly Belly jelly beans it takes to fill up the respective tube. Students plot their data, graph a linear approximation model, and write an equation representing their model. Students use their linear model to predict the number of Jelly Belly jelly beans that are in a similar cylindrical tube with a given height. Students discuss the accuracy of their results and limitations in their model and data collection process. They then apply their predictions to make suggestions to Jelly Belly for potential packaging of jelly beans based on quantity instead of net weight.
Can you determine the number of Jelly Belly jelly beans it takes to fill up a cylindrical tube?Copyright 2021 Linnaea Mallette, Public Domain https://www.publicdomainpictures.net/en/view-image.php?image=284746&picture=jelly-beans-background
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 activity, 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 activity, students more specifically explore how packaging engineers apply mathematical modeling to help determine optimal packaging for jelly beans and even offer a suggestion of linear approximation model to Jelly Belly’s logistics team to switch their packaging system from a net weight model to a model based on quantity and cost-effective packaging.
After this activity, 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.