"Calc Your World: Everyday Math Magic!"

11th Grade Lesson 45 minutes

"Calc Your World: Everyday Math Magic!"

Barry F

CCSS.Math.Practice.MP1

CCSS.Math.Content.HSF-BF.A.2

CCSS.Math.Content.HSF-IF.B.6

Self Directed Learning

Academic Mindset

+ 1 more

1-pager

Purpose

Students will engage in a hands-on exploration of calculus concepts applied to real-world scenarios, such as population growth and disease spread, with guidance from Detroit City Government representatives. This project-based learning experience will foster critical thinking and problem-solving skills, encouraging students to reflect on the impact of calculus in understanding natural phenomena. Through collaborative activities and self-directed learning, students will build academic confidence and a sense of belonging while addressing authentic community questions.

Learning goals

Students will explore how calculus concepts, such as sequences and rate of change, can be applied to model real-world phenomena like population dynamics and disease spread. They will engage in self-directed learning by using feedback to refine their understanding and problem-solving skills. Through collaboration with the Detroit City Government, students will critically analyze community data to understand the impact of calculus in predicting trends and making informed decisions.

Standards

[Common Core] CCSS.Math.Practice.MP1 - Make sense of problems and persevere in solving them.
[Common Core] CCSS.Math.Content.HSF-BF.A.2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
[Common Core] CCSS.Math.Content.HSF-IF.B.6 - 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.

Competencies

Self Directed Learning - Students use teacher and peer feedback and self-reflection to monitor and direct their own learning while building self knowledge both in and out of the classroom.
Academic Mindset - Students establish a sense of place, identity, and belonging to increase self-efficacy while engaging in critical reflection and action.
Critical Thinking & Problem Solving - Students consider a variety of innovative approaches to address and understand complex questions that are authentic and important to their communities.

Products

Students will create a predictive model using calculus to analyze population growth or disease spread within Detroit, applying real data provided by the city government. They will compile their findings into a presentation that outlines their process, insights, and predictions, and present it during the reflection session. Additionally, students will develop a personal learning journal documenting their self-directed learning journey, including feedback received and self-reflection on their academic mindset and problem-solving strategies.

Launch

Begin the lesson with a hands-on activity where students analyze real-world data on Detroit's population growth over the past decade. Using graphing calculators or software, students will calculate the average rate of change and discuss factors influencing these changes. Then, introduce a brief case study on how calculus models the spread of diseases, highlighting recent local health data. This launch will set the stage for exploring calculus applications in understanding dynamic systems.

Exhibition

Students will create a visual presentation that illustrates how calculus can be used to model and predict population growth or the spread of diseases. This presentation will be shared with a representative from the Detroit City Government, who will provide feedback and discuss real-world applications in the community. Students will have the opportunity to showcase their understanding by explaining their models and predictions to peers and community members, fostering a collaborative learning environment.

Rubric

Competency Progression Rubric Competency-first rubric

Category	Learning Goal	Stage 1	Stage 2	Stage 3	Stage 4
Deeper Learning Competencies	Self Directed Learning	I can independently use feedback from my teacher and peers to adjust my approach when modeling population growth or disease spread using calculus I actively seek out resources to deepen my understanding of arithmetic and geometric sequences, and apply them to real-world data from Detroit I demonstrate perseverance by calculating and interpreting the average rate of change over specific intervals, using graphing tools and software, and clearly explaining my process and findings in both my predictive model and personal learning journal	I can use feedback from my teacher and peers to adjust my approach when analyzing real-world data, and I can describe how I applied calculus concepts to develop a model that predicts population growth or disease spread in Detroit I can explain the steps I took and how I utilized graphing tools to calculate the average rate of change, making connections between the data and the factors influencing these changes	I can effectively use feedback from my teacher and peers to adjust my learning strategies while developing a predictive model that accurately applies calculus to real-world scenarios I can demonstrate perseverance by calculating and interpreting the average rate of change using real data, and I confidently present my findings to the Detroit City Government, showcasing my understanding of how calculus can predict population growth or disease spread	I can independently analyze real-world community data using calculus concepts, such as sequences and average rate of change, to create predictive models I effectively use feedback from peers and experts, including insights from the Detroit City Government, to refine my models and presentations, demonstrating my understanding and problem-solving skills Through self-reflection, I track my learning progress and adapt my strategies to improve my academic mindset and contribute meaningfully to community discussions
Deeper Learning Competencies	Academic Mindset	I can identify factors that influence population growth and disease spread using calculus concepts like sequences and rate of change I use feedback to refine my understanding, and I confidently present my predictive models to classmates and community members, showing how calculus helps make informed decisions in real-world scenarios	I can analyze real-world data about Detroit's population growth using graphing tools and apply calculus concepts like sequences and rate of change to create models I interpret the average rate of change confidently and use feedback to enhance my understanding, which helps me present my findings clearly to my peers and community representatives	I can confidently use calculus concepts, like sequences and rate of change, to create models that explain real-world data on population growth or disease spread I actively engage with feedback from my peers and teachers to refine my understanding and improve my predictions I present my findings in a clear and organized manner, demonstrating my ability to connect mathematical concepts to authentic community issues	I confidently apply calculus concepts to real-world data by creating predictive models for population growth or disease spread in Detroit I can effectively communicate my insights and findings through a visual presentation, demonstrating my understanding of average rate of change and sequences I actively seek and incorporate feedback from peers and community representatives to refine my models, showcasing my ability to persevere and solve complex problems
Deeper Learning Competencies	Critical Thinking & Problem Solving	I can use real-world data to create a predictive model by identifying the factors that influence population growth or disease spread I am able to calculate the average rate of change using graphing technology, interpret my results accurately, and discuss how different variables impact these changes in a way that deepens my understanding and helps me solve complex problems	I can analyze real-world data to identify patterns and calculate the average rate of change using graphing tools I discuss how these calculations are influenced by various factors, using them to make informed predictions about population growth or disease spread I apply feedback from peers and teachers to refine my approach and improve my models	I can effectively analyze real-world data by applying calculus concepts to model population growth or disease spread I calculate the average rate of change using graphing calculators or software, accurately interpreting and estimating from graphs and tables I engage in thoughtful discussions about factors influencing these changes, demonstrating persistence in solving complex problems and using feedback to refine my understanding	I can confidently apply calculus concepts to analyze real-world data, creating a predictive model that accurately reflects population growth or disease spread in Detroit I effectively use feedback to refine my model and clearly communicate my insights and predictions during presentations, demonstrating a deep understanding of the factors influencing these dynamic systems