Unit Plan 19 (Grade 7 Math): Circles—Radius, Diameter, Circumference
7th graders explore the proportional relationship between a circle’s diameter and circumference to derive C = πd and C = 2πr. Through measurement, modeling, and error analysis, they apply formulas accurately with clear unit reasoning.
Focus: Develop and use formulas C = πd and C = 2πr; relate diameter and circumference via proportional reasoning.
Grade Level: 7
Subject Area: Mathematics (Geometry • Measurement & Proportional Reasoning)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students investigate circles by measuring, modeling, and reasoning proportionally. They measure real objects to see that circumference is proportional to diameter and that the constant of proportionality is π. They connect radius and diameter, choose between C = πd or C = 2πr, attend to units, and solve practical problems (for example, wheel rotations, edging a circular garden, labels around cans). Area of a circle is previewed only as an extension.
Essential Questions
- How do radius, diameter, and circumference relate, and why is π the same for all circles?
- When should I use C = πd versus C = 2πr, and how do I keep my units straight?
- How do measurement and proportional reasoning help me build and trust a model?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Define and convert among radius (r), diameter (d = 2r), and circumference (C).
- Use proportional reasoning and measurement to justify C = πd and C = 2πr.
- Solve multi-step problems involving circumference with correct units and rounding.
- Interpret the slope of a C–d graph as an estimate of π and discuss sources of measurement error.
- Communicate clear conclusion statements that answer the question asked.
Standards Alignment — CCSS Grade 7
- 7.G.4: Know the formulas for the circumference (and area) of a circle and use them to solve problems; give an informal derivation of the relationship between circumference and area. (This unit focuses on circumference and the proportional C–d relationship; area is introduced as an extension.)
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (use tools), MP.6 (precision).
Success Criteria — Student Language
- I can find r and d, choose C = πd or C = 2πr, and show my units.
- I can explain why C is proportional to d, and why the constant is π.
- I can estimate π from data and explain measurement error.
- I can solve a real problem and write a clear conclusion with units and rounding.