Unit Plan 14 (Grade 7 Math): Scale Drawings & Maps
7th graders apply proportional reasoning to interpret and create scale drawings. They compute real measurements, convert units, and explain why perimeter scales by k and area by k², producing accurate, labeled diagrams that demonstrate mathematical precision.
Focus: Use scale factors to reproduce and interpret drawings; compute missing lengths and areas under scaling.
Grade Level: 7
Subject Area: Mathematics (Geometry • Ratios & Proportional Relationships)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students use scale and proportional reasoning to interpret and create scale drawings and maps. They compute actual lengths, redraw figures at a new scale, and reason about how perimeter and area change under scaling. Emphasis: reading scale statements (for example, “1 cm represents 2 m”), converting units, and explaining why lengths scale by k while areas scale by k².
Essential Questions
- How do I read a scale statement and use it to move between drawing and real-world measurements?
- Why do lengths multiply by the scale factor k, while areas multiply by k²?
- How do I create a new scale drawing that’s accurate and easy to read?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Interpret scale statements and convert units to compute actual lengths and distances from drawings and maps.
- Determine and use a scale factor (k) to reproduce a figure at a different scale; label and justify all new measurements.
- Explain and apply perimeter and area scaling: perimeter scales by k, area by k².
- Choose efficient methods (proportions, unit rates, scale factors) and communicate results with units and reasonableness checks.
- Design or revise a scale drawing (diagram, room plan, or map segment) that meets given constraints.
Standards Alignment — CCSS Grade 7
- 7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas and reproducing a scale drawing at a different scale.
- 7.RP.2 (connection): Recognize and represent proportional relationships (use equations and tables with k as constant of proportionality).
- Mathematical Practices: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (tools), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can read a scale (for example, “1 cm : 3 m”) and convert correctly.
- I can find or use the scale factor k and explain what it means.
- I can compute actual lengths and areas from a drawing and check if my answers are reasonable.
- I can explain why perimeter scales by k and area scales by k².
- I can make a new scale drawing that is neat, labeled, and accurate.