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

Shop Day

Shop Day: your own set
// Every prop a shape, every plan a number
⏱ about 20 min

Shop Day: Your Own Set

Comet clears the kitchen table and sets out cardboard, a ruler and the measuring jug. "Your turn to run the shop."

"Three parts," Wren says. "A model at a scale you choose, a plan with a density, and a volume check."

"What do you notice about the order?" Comet asks. "Model first, so the plan has numbers to use."

Nova projects a small checklist. "Would you like a hint? Write every measurement before you compute anything."

"And explain each step to your family as you go," Wren says. "If they can follow it, the geometry is right."

"Our designer," Comet says, "this is the whole course in one afternoon. Run it."

  1. A model is the simple shape closest to the object, with only the measures that matter.
  2. Density is an amount divided by the space it fills: sheets, cups, tiles or seats per unit.
  3. Regular hexagons tile a panel with no gaps because three 120 degree angles make 360.
  4. A design problem has constraints, and geometry picks the least material or the most that fits.
◇ RUN A SHOP DAY FOR YOUR FAMILY
The model: pick one wall or one piece of furniture. Build a cardboard model of it at 1 cm for every 20 cm.
The plan: measure the room's floor as a rectangle. Choose a chair size and an aisle. Compute how many chairs fit.
The volume check: model a container as a cylinder or a box, compute its volume, then count cups into it.
Present all three to your family. Explain the shape you chose, the constraint you set and what the cups showed.
For a grown-up
Cardboard is cut with scissors, sitting down. You cut anything thick. Water stays over a tray.
Ask the student to name the model shape, the density and the constraint out loud before showing numbers.
A model that is a little off is fine. Ask what they would measure again, and why.
SHOP DAY CHECK
  • Read the question.
  • Tap your answer.
Your model uses 1 cm for every 20 cm. A bookshelf is 15 cm tall on the model. How tall is the real one in centimeters?
24 chairs fit on a 12 square meter room floor. What is the density in chairs per square meter?
A storage box is 30 by 20 by 15 cm. What is its volume in cubic centimeters?
Your model uses 1 cm for every 20 cm. A table is 4 cm tall on the model. How tall is the real table in centimeters? Type the number.
WHY THIS EXERCISEEvery model length times the scale is the real length, which is how the plan gets its numbers.
Draw your model, your floor plan with chairs and aisle, and your container with its measurements.

Shop Day complete, designer. Twelve weeks, one set, and a Shop Book full of checked measurements. Well built.

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