Area of a circle

Warm-up

Put a rectangle on the board and ask for its area. Easy — base times height. Then draw a circle next to it and ask the same question. Let the silence sit. Most students know the words “π r squared” but can't say why, and a few will admit they don't know it at all. That gap is the lesson.

Explore

Hand out the paper circles. Students cut along the printed lines to make wedges, then lay them in a row — point up, point down, point up — so the teeth interlock. As they work, the ragged strip starts to look suspiciously like a rectangle. Ask: “What shape are you making? What are its sides?”

Formalize

Now make it precise. The rectangle's height is the radius, r. Its width is half the distance around the circle — and since the circumference is 2·π·r, half of that is π·r. Area of a rectangle is width × height, so:

Area = (π·r) × r = π·r²

Drive the closing idea home: nothing was added or thrown away. The circle and the rectangle are the same paper, so they have the same area — and the more wedges you cut, the straighter the rectangle's edges become.

Practice

Students work the 18-problem practice set; circulate and look for anyone squaring the diameter instead of the radius. For the exit ticket, one question on a slip: “A pizza has a radius of 14 cm. What is its area? Show the formula you used.”

Exit ticket

Students work the 18-problem practice set; circulate and look for anyone squaring the diameter instead of the radius. For the exit ticket, one question on a slip: “A pizza has a radius of 14 cm. What is its area? Show the formula you used.”