Unit Plan 21 (Grade 7 Math): Surface Area—Prisms and Pyramids
7th graders explore surface area through nets and formulas for right prisms and pyramids, applying SA = 2B + Ph and SA = B + ½Pl. They distinguish slant height from height, use precise units, and solve real-world material and coverage problems.
Focus: Nets and formulas for surface area of right prisms and right pyramids; interpret units and context.
Grade Level: 7
Subject Area: Mathematics (Geometry • Measurement & Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students build intuition for surface area (SA) by unfolding 3D solids into nets and summing the areas of the faces. They compute SA for right prisms and right pyramids, distinguish lateral area from total surface area, and use appropriate square units. For prisms, students connect the structure SA = 2B + Ph (B = area of base, P = perimeter of base, h = prism height). For pyramids, they reason from nets that SA = B + (1/2)·P·l where l is slant height (and sum triangle areas when faces differ). Contexts include packaging, paint/film coverage, and materials cost.
Essential Questions
- How do nets help us see and calculate the surface area of prisms and pyramids?
- What is the difference between height and slant height, and why do square units matter?
- How can we use structure (repeated faces, base + lateral faces) to compute SA efficiently and explain our method?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Draw and interpret nets for right prisms and right pyramids; label dimensions and faces clearly.
- Compute surface area by summing face areas; for prisms, use SA = 2B + Ph; for pyramids, use SA = B + (1/2)·P·l (or sum of triangular lateral faces when l varies).
- Identify and use slant height (l) for pyramids and distinguish it from vertical height.
- Solve real-world SA problems (materials/covering/cost) with unit conversions, rounding, and reasonableness checks.
- Explain their method with diagrams, formulas, and unit-based conclusions.
Standards Alignment — CCSS Grade 7
- 7.G.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Extended here to right pyramids through nets and triangle sums.)
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (use tools), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can draw or use a net and add up the face areas to get surface area.
- I can calculate SA for a right prism using SA = 2B + Ph and for a right pyramid using SA = B + (1/2)·P·l (or by summing triangle areas).
- I can tell the difference between height and slant height and choose the right one.
- I can include square units, convert units if needed, and round reasonably.
- I can write a clear conclusion that answers the question (for example, how much paper/paint is needed).