Derivatives in Motion: Rate, Graph, Dash!

High School Grade Project 1 week

Derivatives in Motion: Rate, Graph, Dash!

Stefanie Trapani

1-pager

Purpose

This project aims to immerse students in the practical application of calculus by analyzing their own physical activity data. Through hands-on experiences, students will explore how derivatives and regression analysis can provide insights into the dynamics of movement and predict future trends. The project encourages students to engage with mathematics in a meaningful way, connecting abstract concepts to real-world scenarios, thereby enhancing their understanding and appreciation of the subject.

Learning goals

Students will develop a comprehensive understanding of calculus concepts, specifically derivatives, and their application in analyzing physical activity data. They will learn to calculate average and instantaneous rates of change, and apply regression analysis to predict trends. Through graphing and data visualization, students will enhance their ability to interpret and communicate findings effectively. Additionally, they will cultivate skills in collaboration, problem-solving, and self-assessment, reflecting on the real-world relevance of mathematics in everyday life.

Standards

Common Core - CCSS.MATH.CONTENT.HSF.IF.B.6: Calculate and interpret the average rate of change of a function over a specified interval.
Common Core - CCSS.MATH.CONTENT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
Common Core - CCSS.MATH.CONTENT.HSS.ID.B.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Products

Throughout the project, students will develop a comprehensive multimedia presentation that showcases their analysis of physical activity data using calculus principles. This presentation will include detailed graphs, data visualizations, and photographs that illustrate their understanding of average and instantaneous rates of change. Students will also produce a regression function model based on their data, demonstrating their ability to apply derivatives for predictive analysis. Additionally, students will engage in self-assessment and peer review activities to refine their work and ensure clarity and accuracy in their final product.

Launch

Kick off the project with an engaging 'Data Dash' event where students participate in a group physical activity, such as a relay race or a hike, while using Strava to record their data. This shared experience will provide real-world data for analysis and set the stage for the project. Students will have the opportunity to connect physical activities with mathematical concepts, fostering curiosity and enthusiasm for the upcoming tasks.

Exhibition

Host a "Calculus in Motion" showcase where students present their multimedia projects to peers, teachers, and family members. Set up stations where each group can display their graphs, data, and analysis, allowing attendees to interact with the presentations and ask questions. Encourage students to demonstrate their understanding by explaining how derivatives and regression analysis were applied to their physical activity data. Include a Q&A session where students can discuss the insights they gained and the real-world applications of their findings. Conclude with a reflection circle where students share their learning experiences and how the project has changed their view of mathematics.

Plan

Week 1	Day 1	Day 2	Day 3	Day 4	Day 5
Activities	Data Dash Kickoff - Participate in a group physical activity while using Strava to record data for analysis, laying the groundwork for the project. (20 min) Introduction to Derivatives - Engage with interactive simulations to explore the concept of derivatives and how they relate to rates of change in physical movement. (25 min)	Data Collection and Reflection - Review and discuss the data collected during the Data Dash, reflecting on initial insights and questions that arise. (15 min) Calculating Average Rate of Change - Learn and practice using the definition of a derivative to calculate the average rate of change between different time intervals from the collected data. (30 min)	Graphing and Visualization - Create graphs and data visualizations to represent the average rate of change in physical activity, enhancing comprehension of the data. (20 min) Exploring Instantaneous Rate of Change - Use calculus principles to determine the instantaneous rate of change at different points in the data, applying derivatives practically. (25 min)	Introduction to Regression Analysis - Learn how to find a regression function that models the collected data and apply it to predict trends. (20 min) Derivative of Regression Function - Calculate and interpret the derivative of the regression function to understand its implications on physical activity trends. (25 min)	Refinement and Self-Assessment - Use a rubric for self-assessment to evaluate work against project criteria, setting goals for refinement before final presentation. (20 min) Project Presentation Preparation - Develop a multimedia presentation that includes graphs, data analysis, and interpretations, demonstrating understanding of derivatives and regression analysis. (25 min)
Deliverables	1. Day 1: Participation in the 'Data Dash' event with recorded data on Strava. 2. Day 2: Initial analysis of the recorded data to calculate average rate of change over specified intervals. 3. Day 3: Interactive simulation completion showing understanding of derivatives in context. 4. Day 4: Graphs and data visualizations illustrating average and instantaneous rates of change. 5. Day 5: Preliminary regression function and derivative calculations with a draft multimedia presentation outline.
Preparation	1. Secure and test Strava app access for all students on their devices. 2. Plan and organize the 'Data Dash' event, including location, logistics, and safety measures. 3. Prepare interactive simulations and resources that demonstrate derivatives with physical activity data. 4. Gather graphing materials and software tools for data visualization and analysis. 5. Ensure access to computers or tablets for data entry and analysis tasks. 6. Develop a rubric for self-assessment and provide copies to students for guidance throughout the project.