← Back to course
Geometry and Measurement 6-8 / Week 05 / Monday
1/6
Week 05 · Scale Drawings

Monday

One centimeter stands for fifty
// The whole garage on one page
⏱ about 20 min

Monday: One Centimeter Stands for Fifty

Rocket drags the tape measure across the garage floor. "Four hundred centimeters! The paper is twenty centimeters wide."

"So the garage will not fit," Raven says, "unless we shrink it. What do you notice about a map?"

"Everything is tiny," Rocket says, "but the shapes are right."

Nova hovers over the Blueprint Book, her light drawing a short line. "Let one centimeter on paper stand for many centimeters on the floor."

"Fifty," Raven decides. "One centimeter for every fifty. Then 400 centimeters is 8 centimeters."

Rocket measures the other wall. "Three hundred. So that is 6 centimeters on paper."

He draws a rectangle 8 by 6. "The garage. On one page."

Nova hums. "Now every wall has two lengths: one on the floor, one on the page."

Rocket stretches a tape measure across the garage while Raven draws a scale map and Nova hovers above.

What a scale means

A scale drawing keeps the shape of the real thing and shrinks every length by the same amount.

The crew's scale is 1 cm to 50 cm: every centimeter on the page stands for 50 centimeters on the floor.

The long wall is 400 cm. On the page it is 400 ÷ 50 = 8 cm.

The short wall is 300 cm, so 300 ÷ 50 = 6 cm on the page.

A rectangle 8 cm long and 6 cm wide, the garage drawn at 1 cm to 50 cm

Two directions

Real to drawing: divide by the scale number. 150 cm of table becomes 150 ÷ 50 = 3 cm on paper.

Drawing to real: multiply by the scale number. A 2 cm window on paper is 2 × 50 = 100 cm on the wall.

The scale number is the scale factor from the page to the floor. Going back to the page, you divide by it.

A double number line: drawing centimeters 0 to 4 over real centimeters 0 to 200
DRAWING TO REAL
  • Read the question.
  • Tap your answer.
The drawing uses 1 cm for every 50 cm. A wall is 8 cm on the drawing. How long is the real wall in centimeters?
The drawing uses 1 cm for every 50 cm. A wall is 6 cm on the drawing. How long is the real wall in centimeters?
The drawing uses 1 cm for every 50 cm. A wall is 3 cm on the drawing. How long is the real wall in centimeters?
The drawing uses 1 cm for every 50 cm. A wall is 4.8 cm on the drawing. How long is the real wall in centimeters?
REAL TO DRAWING
  • Read the question.
  • Tap your answer.
The drawing uses 1 cm for every 50 cm. The real table is 400 cm long. How long is it on the drawing in centimeters?
The drawing uses 1 cm for every 50 cm. The real table is 150 cm long. How long is it on the drawing in centimeters?
The drawing uses 1 cm for every 50 cm. The real table is 240 cm long. How long is it on the drawing in centimeters?
The drawing uses 1 cm for every 50 cm. The real table is 100 cm long. How long is it on the drawing in centimeters?
StatementTrue or false?
400 ÷ 50 = 8?
6 × 50 = 300?
A scale drawing changes the shape of the real thing.?
At 1 cm to 50 cm, you divide a real length by 50 to draw it.?
WHY THIS EXERCISEThe same factor on every length keeps the shape. Dividing shrinks, multiplying restores.
The long wall is 8 cm on the drawing at 1 cm to 50 cm. How long is the real wall in cm? Type the number.
WHY THIS EXERCISE8 × 50 = 400 centimeters, the length Rocket measured on the floor.
Try it
Measure a table top with a tape measure. Draw it at 1 cm to 10 cm on grid paper.
Write the real lengths and the drawn lengths side by side in your Blueprint Book.
Safety first
Hold the end of the tape measure and let it slide back slowly. Never let it snap shut.
Measure things you can reach from the floor. Shoes on in the garage.
Draw the garage at 1 cm to 50 cm: a rectangle 8 cm by 6 cm. Label both real lengths.

The garage fits on a page. Tomorrow you pick scales for different sheets of paper.