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Geometry and Measurement 6-8 / Week 07 / Build Day
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Week 07 · Circles

Build Day

Build Day: The round window
// String around a can, and a little more than three
⏱ about 20 min

Build Day: The Round Window

Saturday at the Blueprint Table, the clubhouse wall lies flat. Rocket holds the can over it. "Window goes here."

"Trace it, then measure before anyone cuts," Raven says. "Diameter first."

Rocket traces the can and measures across. "8 centimeters. So the edge is 3.14 times 8." He works it out. "25.12."

"And the clear sheet inside?" Raven asks. "What do you notice about which formula you need?"

"Inside, so area. Radius 4. 3.14 times 4 times 4." Rocket grins. "50.24 square centimeters of sheet."

Nova hovers over the traced circle, her light a perfect ring. "Check it with string before the scissors," she says.

Rocket wraps the string around the trace. Nova hums. "Twenty-five and a bit. Build on."

  1. A circle has a center, a radius r and a diameter d = 2 × r.
  2. The circumference is the distance around: C = π × d = 2 × π × r. It is a little more than three diameters.
  3. Pi is the circumference divided by the diameter, the same for every circle. We use 3.14.
  4. Wedges laid as a near-rectangle show the area: half the circumference times the radius, A = πr².
  5. Edge questions use C in centimeters. Inside questions use A in square centimeters.
◇ FAMILY CIRCLE HUNT
Together, pick four round things: a lid, a can, a plate, a roll of tape. Measure each diameter.
Each person predicts the circumference with 3.14 before anyone wraps string. Then wrap and compare.
Pick one round thing and work out its area in square centimeters.
Trace the round window on the clubhouse wall. A grown-up cuts it out with scissors, inside the line.
For a grown-up
This week your student learned the parts of a circle, C = πd and A = πr², with 3.14 for π.
Ask them why the circumference is "a little more than three diameters." The string measurements are the answer.
You cut the window out of cardboard yourself, with scissors. Check every can and lid for a smooth edge first.
Safety first
A grown-up cuts cardboard, with scissors only, never a craft blade. Students cut paper.
Cans are empty with a smooth rolled rim. Lids are plastic or smooth metal. String stays on the table.
BUILD DAY CHECK
  • Read the question.
  • Tap your answer.
A circle with diameter 8 cmThe window trace has diameter 8 cm. How long is its edge, in centimeters? (Use 3.14 for π.)
A circle with radius 4 cmThe window has radius 4 cm. How much clear sheet fills it, in square centimeters? (Use 3.14 for π.)
A plate has circumference 37.68 cm. What is its diameter in centimeters? (Use 3.14 for π.)
A round tray has diameter 24 cm. What is its radius in centimeters?
Build Day checkTrue or false?
3.14 × 8 = 25.12?
The window's area uses the diameter squared.?
One full turn of a can rolls it one circumference.?
WHY THIS EXERCISEThe window is the first round part of the clubhouse, and every number on it was measured, not guessed.
Draw the clubhouse wall with the round window. Label the diameter, the radius, the circumference and the area.

Great building, crew. Next week: angles on the roof frame, and sticks that cross in pairs.

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