Technology · Technology exploration · Source checked October 13, 2026

Could a roof become a power station?

Explore how sunlight becomes electricity—and how to plan an array.

Original editorial illustration; not a scientific image or measured diagram.

The story

Photovoltaic cells convert sunlight into electrical energy. Cells connect into panels, and panels connect into arrays. The mathematics of a proposed array helps us explore space, energy, and cost before anything is installed.

Read the source: US Department of Energy · Photovoltaic technology basics ↗

Explore the evidence

Illustrative classroom scenario, not Tower School measurements or a supplier quote: a rectangular usable roof is 12 m × 8 m; each panel occupies 2 m × 1 m and produces 1.5 kWh on a modeled day. Ignore gaps, shading, structural limits, and equipment space.

Choose your way in

Allow 15–25 minutes. Work in your binder: show calculations, label units, and explain what your result means. Read the story first; choose a task with your teacher.

Design an arrayGrade 6 · Area and decimal multiplication

Sketch a layout of panels. How many fit if they align in rows with no gaps? Find modeled daily energy for that layout. Explain why area division alone may fail for other roof shapes.

A hint

List the known quantities and their units. Identify the quantity you need. Use a sketch, table, or equation to connect them.

Check your reasoning · Open after an attempt

Roof area = 96 m²; panel area = 2 m²; 48 panels fit in a 6-by-8 arrangement; 72 kWh/day. Shape and dimensions can prevent an area-based count from fitting.

Account for shadeGrade 7 · Percent

Suppose shading reduces modeled daily energy by 15%. What energy remains from the 48-panel array? A building uses 90 kWh that day. What percent of that use could the shaded array cover?

A hint

List the known quantities and their units. Identify the quantity you need. Use a sketch, table, or equation to connect them.

Check your reasoning · Open after an attempt

72 × 0.85 = 61.2 kWh. 61.2/90 = 68%. This is a simplified daily comparison, not a guarantee of simultaneous supply.

Compare installation plansGrade 8 Algebra 1 · Systems of equations

Illustrative costs: Plan A costs $2,000 plus $300 per panel; Plan B costs $5,000 plus $240 per panel. Write both functions. Find their intersection. Which is cheaper for the 48-panel roof?

A hint

List the known quantities and their units. Identify the quantity you need. Use a sketch, table, or equation to connect them.

Check your reasoning · Open after an attempt

A(n)=2000+300n; B(n)=5000+240n. Intersection: 50 panels and $17,000. At 48: A=$16,400; B=$16,520. A is cheaper by $120; the intersection exceeds this roof’s capacity.

Look beyond the answer

Which number or assumption most affects your conclusion? What additional evidence would make your answer more useful?