Explore how linear functions and the concept of slope can be applied to real-world scenarios, such as urban planning. Collaborate with community partners to model and analyze proportional relationships, like traffic flow or population growth, using linear equations. Develop a deeper understanding of mathematical concepts while enhancing your skills in communication, teamwork, and problem-solving through hands-on experiences and community engagement.
Learning goals
By the end of this project, you will be able to graph proportional relationships and interpret the unit rate as the slope, enhancing your understanding of linear functions. You will construct and analyze linear equations to model real-world scenarios, such as traffic flow or population growth, and effectively communicate your findings to community stakeholders. Additionally, you will develop socio-emotional skills through teamwork and public presentation, reflecting on your growth in both mathematical and collaborative capacities.
Standards
CCSS.Math.Content.8.EE.B.5 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
CCSS.Math.Content.8.F.A.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
CCSS.Math.Content.8.F.B.4 - Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Products
Develop a detailed traffic flow model or population growth projection using linear equations, which you will present to the city planning department. Create visual aids such as graphs or charts to illustrate the linear relationships and their implications in urban planning. Compile a project portfolio that includes your mathematical models, visual aids, and a reflective essay or blog post on your learning journey.
Launch
Kick off the project by visiting the local city planning department to observe real-world applications of linear functions in urban planning. Engage in a hands-on activity where you measure and graph traffic flow or population data from your community. Discuss with city planners how these graphs help in decision-making processes, setting the stage for your project work. This experience will provide a practical context for understanding slope and proportional relationships.
Exhibition
Host an interactive community showcase event where you present your project findings on how linear functions are applied in urban planning. Invite city planners and community members to engage in a Q&A session, allowing you to demonstrate your understanding of linear equations through models of traffic flow or population growth. Create visual displays and digital presentations to effectively communicate your insights and encourage dialogue with attendees.
Week 1
Day 1
Activities
Kick-off Meeting with City Planners - Visit the local city planning department to learn about real-world applications of linear functions in urban planning (30 min)
Exploration of Proportional Relationships - Measure and graph traffic flow or population data from your community, discussing its implications with city planners (30 min)
Deliverables
1. Detailed traffic flow or population growth model using a linear equation.
2. Visual aids (graphs/charts) illustrating the linear relationships.
3. Reflective essay or blog post on the project experience.
Preparation
1. Arrange a visit to the local city planning department.
2. Collect traffic flow or population data for modeling.
3. Prepare graphing tools and software for data analysis.
4. Provide materials for creating visual aids (poster boards, markers, digital tools).
5. Organize a practice session for the community showcase presentation.
