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

Tuesday

Choosing a scale
// The whole garage on one page
⏱ about 20 min

Tuesday: Choosing a Scale

"I want the garage bigger," Rocket says, holding up a huge sheet of poster paper. "This is 60 centimeters wide."

"Then pick a smaller scale number," Raven says. "What do you notice when 1 cm stands for 20 cm instead of 50?"

Rocket works it out. "400 divided by 20. Twenty centimeters. The drawing grows."

"And for the tiny notebook page?" Raven asks.

"1 cm to 100 cm," Rocket says. "Four centimeters. It shrinks."

Nova hovers over the three sheets, her light measuring each one. "The scale fits the paper," she says. "Not the other way."

Raven writes three columns in the Blueprint Book, one for each scale. "Same garage, three sizes."

Nova hums. "Same shape every time."

One wall, three scales

Scale1 cm stands forLong wall, 400 cm, on paper
1 cm to 20 cm20 cm20 cm
1 cm to 50 cm50 cm8 cm
1 cm to 100 cm100 cm4 cm

A smaller scale number makes a bigger drawing: at 1 cm to 20 cm the wall is 20 cm long on paper.

A bigger scale number makes a smaller drawing: at 1 cm to 100 cm the same wall is 4 cm.

Choose the scale so the biggest real length fits the paper with room for labels.

Finding a scale from the drawing

If a 3 cm line stands for the 150 cm table, the scale is 150 ÷ 3 = 50. So 1 cm to 50 cm.

Divide a real length by its drawn length to find what 1 cm stands for. Any matching pair works.

A table of drawing and real centimeters at 1 cm to 20 cm, from 1 and 20 up to 10 and 200
  1. Measure the longest real length.
  2. Measure the paper.
  3. Divide the real length by the paper width. Round up to a handy scale number: 10, 20, 25, 50 or 100.
  4. Check: real length divided by the scale number must fit the paper.
OTHER SCALES
  • Read the question.
  • Tap your answer.
The drawing uses 1 cm for every 20 cm. A wall is 5 cm on the drawing. How long is the real wall in centimeters?
The drawing uses 1 cm for every 100 cm. The real table is 300 cm long. How long is it on the drawing in centimeters?
The drawing uses 1 cm for every 20 cm. A wall is 2.5 cm on the drawing. How long is the real wall in centimeters?
The drawing uses 1 cm for every 20 cm. The real table is 90 cm long. How long is it on the drawing in centimeters?
WHICH SCALE FITS?
  • Read the question.
  • Tap your answer.
A wall is 400 cm long. The paper is 20 cm wide. Which scale gives the biggest drawing that still fits?
A wall is 300 cm long. The paper is 10 cm wide. Which scale gives the biggest drawing that still fits?
A wall is 600 cm long. The paper is 25 cm wide. Which scale gives the biggest drawing that still fits?
FIND THE SCALE
  • Read the question.
  • Tap your answer.
A 3 cm line on the drawing stands for 150 cm on the floor. The scale is 1 cm to how many cm?
A 4 cm line on the drawing stands for 400 cm on the floor. The scale is 1 cm to how many cm?
A 5 cm line on the drawing stands for 100 cm on the floor. The scale is 1 cm to how many cm?
A 2 cm line on the drawing stands for 50 cm on the floor. The scale is 1 cm to how many cm?
PICK A SCALE FOR A DRAWING
  • ?Measure the paper you will draw on.
  • ?Divide every real length by the scale number and draw.
  • ?Divide the real length by the paper width and round up to a handy scale number.
  • ?Measure the longest real length with the tape measure.
WHY THIS EXERCISEThe scale is chosen to fit the paper. Every length then uses the same number.
Draw the long wall three times: at 1 cm to 20, 1 cm to 50 and 1 cm to 100. Label each.

Three scales, one garage. Tomorrow is Build Lab: measure, choose a scale and draw for real.

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