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Geometry and Measurement 6-8 / Week 05 / Thursday
4/6
Week 05 · Scale Drawings

Thursday

The garage plan
// The whole garage on one page
⏱ about 20 min

Thursday: The Garage Plan

Raven lays the finished garage plan on the Blueprint Table. "Every wall, the door, the window, the table. All at 1 cm to 50 cm."

"The drawing is 8 by 6," Rocket says. "So the floor area is 48. Easy."

"48 what?" Raven asks. "What do you notice about the units?"

"Square centimeters on paper," Rocket says slowly. "But the real floor is 400 by 300."

Nova hovers over the plan, her light filling the rectangle square by square. "Each paper square is 50 by 50 real centimeters," she says.

"So 2,500 real square centimeters per paper square," Rocket says. "Times 48. That is a lot."

Raven multiplies. "One hundred twenty thousand. The floor plan says so, and the tape measure agrees."

Nova hums. "Lengths scale once. Areas scale twice."

Raven's garage plan

The crew's own tape measure numbers, drawn at 1 cm to 50 cm. Each drawn length is the real length divided by 50.

PartReal length (cm)Drawn length (cm)
Long wall4008
Short wall3006
Garage door2404.8
Window1002
Blueprint Table1503
Model spot751.5

The garage door is 240 cm, so 240 ÷ 50 = 4.8 cm on the plan. Drawn lengths can be decimals.

The model spot, where the cardboard clubhouse will stand, is 75 cm. On paper that is 1.5 cm.

Areas scale twice

A rectangle 8 cm long and 6 cm wide, the garage floor on the plan

The drawn floor is 8 cm by 6 cm, so its area is 8 × 6 = 48 square centimeters.

The real floor is 400 cm by 300 cm, so its area is 120,000 square centimeters.

Divide: 120,000 ÷ 48 = 2,500. That is 50 × 50, the scale factor used twice.

Every length grew by 50, and area is length times length. So the area grew by 50 × 50 = 2,500.

READ THE GARAGE PLAN
  • Read the question.
  • Tap your answer.
The garage door is 240 cm wide. At 1 cm to 50 cm, how wide is it on the plan, in cm?
The model spot is 1.5 cm on the plan. At 1 cm to 50 cm, how long is the real spot, in cm?
A rectangle 8 cm long and 6 cm wideThe drawn floor is 8 cm by 6 cm. What is its area on the plan, in square centimeters?
AREAS SCALE TWICE
  • Read the question.
  • Tap your answer.
A shape has area 48 square centimeters. Every length is multiplied by 50. What is the new area in square centimeters?
A shape has area 12 square centimeters. Every length is multiplied by 3. What is the new area in square centimeters?
A shape has area 5 square centimeters. Every length is multiplied by 4. What is the new area in square centimeters?
A shape has area 10 square centimeters. Every length is multiplied by 10. What is the new area in square centimeters?
How long is the garage door on the plan, in cm? Type the number.
The window is 2 cm on the plan. How wide is the real window, in cm? Type the number.
From the garage planTrue or false?
240 ÷ 50 = 4.8?
50 × 50 = 2500?
At 1 cm to 50 cm, a real area is 50 times the drawn area.?
At 1 cm to 50 cm, a real area is 2,500 times the drawn area.?
WHY THIS EXERCISETwo lengths each grew by 50, so the area grew by 50 × 50 = 2,500.
Try it
On paper, draw a 2 cm by 3 cm rectangle. Then draw it with every side doubled.
Count the squares in each. Write how many times bigger the area got.
Safety first
Work at the table with the paper taped down. Keep pencils out of pockets when you move around.
Draw the garage plan: the 8 by 6 floor, a 4.8 cm door and a 2 cm window on different walls.

The plan is complete. Tomorrow you redraw it at a new scale and review the week.

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