Comparing Delivery Performance: Algebraic & Tabular Functions
This real-world worksheet helps students master 8.F.A.2 by comparing two linear functions represented in different ways: one as an algebraic equation and the other as a table of values. Students act as analysts comparing how two companies perform across key business operations.
Instead of abstract graphs or motion-only examples, this activity uses authentic company operations to make rates of change meaningful and engaging.
What Students Will Do
Students compare Company A and Company B across four interconnected scenarios:
- Daily production output
- Warehouse inventory growth
- Order backlog reduction
- Raw material usage
In each scenario:
- One company follows a rule-based algebraic model
- The other records measured data in a table
- Students identify slope (rate of change) and y-intercept (starting value)
- Students determine which function changes faster and explain why
Skills Covered
- Compare linear functions represented algebraically and numerically
- Identify and interpret rate of change from equations and tables
- Interpret y-intercepts in real-world contexts
- Compare positive and negative slopes
- Extend patterns to make predictions (e.g., after 10 hours)
- Justify comparisons using numerical evidence
Why Teachers Love This Activity
- Directly aligned to CCSS 8.F.A.2
- Focuses on representation comparison, not just computation
- Uses realistic production and supply chain scenarios
- Clear, repeatable structure builds student confidence
- Includes increasing and decreasing functions
- Ideal for practice, assessment, or small-group work
Built for Interactive Classrooms
- Supports randomization, so each student can receive different equations and tables
- Prevents copying while reinforcing the same reasoning process
- Auto-gradable friendly for digital platforms
- No prior worksheets required; full context included
Learning Objective
Students will compare two linear functions represented in different ways - algebraic form and tabular form, by identifying and interpreting rate of change and initial value, and will determine which function increases or decreases faster in real-world operational contexts such as production, inventory, and supply chain management.
Randomization Available
This worksheet supports randomization, meaning each student can receive different tables and algebraic rules while practicing the same comparison skills. Randomization helps prevent copying and encourages independent reasoning.
💡 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.
