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Geometry 9-12 / Week 12 / Friday
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Week 12 · Modeling the Set and Opening Night

Friday

Opening Night
// Every prop a shape, every plan a number
⏱ about 20 min

Friday: Opening Night

The house lights dim. Comet and Wren stand at the back of the theater as the curtain rises on their set.

The column stands straight. The turntable turns. The lamp dish throws a clean beam across the honeycomb panel.

"Twelve weeks," Comet whispers. "Chalk and string, flats that slide and flip, the braces, the ramp, the circle."

"Shadows and the pole, the stage grid, the pouring test," Wren adds. "What do you notice? Nothing wobbles."

Nova hovers at the rail, her light low. "Would you like a hint? Every piece out there is a measurement you checked."

Comet grins. "What can we make next?" Wren opens the clipboard to a clean page. "Our designer, review the course. Then run your own Shop Day."

The set, piece by piece

PieceWeekThe geometry that made it work
the chalk grid and the arcs1definitions and compass constructions
the flats that slide and flip2 and 3rigid motions and congruence
the parallelogram frame4proofs about lines, angles and parallelograms
the scale model and the shadows5 and 6dilations and similar triangles
the ramp and the rigging7right-triangle trigonometry
the turntable and the spotlight8circles: angles, arcs and sectors
the stage grid9 and 10coordinates, equations of circles and parabolas
the foam props and the paint11volume: where the formulas come from
the honeycomb panel and the seats12modeling, density and design

The week in five lines

  • A model is the simple shape closest to an object, with only the measures that matter.
  • Density is an amount divided by the space it fills, by area or by volume.
  • Multiply a density by a new space to predict; divide an amount by its space to check.
  • A regular hexagon tiles with no gaps because 3 × 120 = 360.
  • A design problem has constraints. Geometry turns each option into a number so the best one can be chosen.
OPENING NIGHT REVIEW
  • Read the question.
  • Tap your answer.
Which shape is the best model for the backdrop?
114 hexagon tiles cover the 3 square meter panel. What is the density in tiles per square meter?
What is each interior angle of a regular hexagon tile?
The stair unit is a box 120 by 50 by 20 cm. What is its volume in cubic centimeters?
THE COURSE IN FOUR QUESTIONS
  • Read the question.
  • Tap your answer.
A circle on a grid with center (3, 2) and radius 5The turntable has center (3, 2) and radius 5 on the stage grid. Which equation describes it?
A cylinder with radius 20 cm and height 90 cmThe column: radius 20 cm, height 90 cm. What is its volume in cubic centimeters? Use 3.14 for π.
A flat has area 6 square meters. Every length is tripled for a bigger stage. What is the new area in square meters?
Walking around a hexagon tile, how many degrees is each turn at a corner?
Course reviewTrue or false?
A chipped column can still be modeled as a cylinder.?
Seats per square meter is a density by volume.?
Three regular pentagons meet at a corner with no gap.?
Doubling every length of a backdrop multiplies its area by 4.?
A cone holds one third of the cylinder with the same base and height.?
The equation (x - 3)² + (y - 2)² = 25 has radius 25.?
WHY THIS EXERCISESix checks from the last three weeks, the geometry that finished the set.
What word names a limit a design must respect, like the aisle on the floor plan? Type the word.
WHY THIS EXERCISENaming the constraint first is how every design problem starts.
Draw the finished set under the lights. Label three pieces with the geometry that made each one work.

The curtain is up, designer. Tomorrow is your Shop Day: a model, a plan and a volume check, run at home.

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