City Sports & Activity Center: Create Functions from Real-World Situation
Modeling Linear Relationships: City Sports & Activity Center (8.F.B.4)
Help students learn how to construct and interpret linear functions using realistic, connected scenarios from a city-run Sports and Activity Center. In this worksheet, students act as operations analysts, building linear models to represent costs, usage, and attendance across multiple center services.
This activity focuses on modeling from context, not just identifying equations, making it ideal for mastering CCSS 8.F.B.4.
Short Storyline (Student Context)
A city operates a large Sports and Activity Center and tracks memberships, rentals, attendance, and resource usage using linear models. Different departments record data in descriptions, tables, graphs, and data points. Students analyze this information to build functions that help the city understand and predict costs and usage.
What Students Will Do
Across several connected scenarios, students will:
- Read real-world descriptions and data
- Identify the rate of change (slope)
- Identify the initial value (y-intercept)
- Construct linear functions in the form y = mx + b
- Use tables, graphs, and data points to build models
- Interpret what slope and intercept mean in context
- Make predictions using their equations
Scenarios Included
All problems fit within one consistent context:
- Membership fees at the sports center (build function from word problem)
- Gym locker rental costs (build function from table)
- Swimming pool water usage (build function from two points)
- Fitness class attendance growth (build function from graph)
- Equipment rental charges (build function from word problem)
Each scenario highlights a different way linear relationships appear in real life.
Skills & Standards Covered
- Construct linear functions from real-world situations
- Determine rate of change and initial value from:
- Written descriptions
- Tables
- Graphs
- Two data points
- Interpret slope and y-intercept in context
- Write and use equations to make predictions
Aligned to CCSS: 8.F.B.4
Why Teachers Love This Worksheet
- Strong emphasis on modeling, not memorization
- Uses one cohesive, realistic context
- Clear progression from information → equation → interpretation
- Perfect for interactive and auto-graded platforms
- Supports randomization, giving each student unique values
- Encourages mathematical reasoning and explanation
- Works well for classwork, homework, or assessment
Learning Objective
Students will construct linear functions to model real-world relationships by determining the rate of change (slope) and initial value (y-intercept) from descriptions, tables, graphs, and data points. Students will write equations in the form y = mx + b and interpret the meaning of slope and intercept in context.
Randomization Available
This worksheet supports randomization, meaning each student may receive different values, tables, graphs, or data points while practicing the same modeling skills. This promotes independent reasoning and reduces copying.
💡 Tip: When assigning this activity to your classroom, you can optionally enable randomization to give each student a unique version of the problems. When you re-assign the same worksheet, each student will get a new set of questions, helping them master the content through repeated practice.
