Same place. New plan.

SparkClass

Read a scale in both directions, then reproduce the same actual space at a different scale.

CCSS 7.G.A.1
Reproduce · Original → New
New drawing Original scale
Dimensioned classroom scale drawing A 4 centimeter by 3 centimeter classroom plan at a scale of 1 centimeter to 2 meters represents an actual room 8 meters by 6 meters.
01

Same scale, same drawing. Move to 1 cm : 1 m and the same 8 m × 6 m classroom becomes an 8 cm × 6 cm drawing.

Actual Size · Does Not Change8 m × 6 m
Drawing Size · Centimeters4 cm × 3 cm
Drawing : Actual · Same Units1 : 200
Two-Way Length CheckLength ↔ Length

drawing length = actual length × drawing cm per actual m

Forward
4 cm = 8 m × 0.5 cm/mActual object → drawing. Multiply by the unit rate.
Reverse
8 m = 4 cm ÷ 0.5 cm/mDrawing → actual object. Divide by the same unit rate.

Width check: 3 cm = 6 m × 0.5 cm/m, and 6 m = 3 cm ÷ 0.5 cm/m.

Area Uses The Squarek → k²
Actual Area48 m²
↔1 cm² represents 4 m²
Drawing Area12 cm²
Forward
12 cm² = 48 m² × (0.5 cm/m)²Square the length unit rate to convert areas.
Reverse
48 m² = 12 cm² ÷ (0.5 cm/m)²Recover actual area from drawing area with the squared rate.
Same-units length ratio → area ratio1 : 200 → 1 : 40,000

Do not reuse the length factor for area. At this scale, every 1 cm² on paper represents 2² = 4 m² in the real classroom.

Teacher notes · Scale Drawing Studio

Keep the two directions visible: actual → drawing uses multiplication by drawing cm per actual m; drawing → actual uses division by that same rate. The actual object never changes when a new scale is chosen.

1

Read before revealing

Use the default classroom: 1 cm : 2 m and a 4 cm × 3 cm drawing. Cover the lower panels and ask for the actual length, width, and area. Then check with both reverse equations: 8 m = 4 cm ÷ 0.5 cm/m and 48 m² = 12 cm² ÷ (0.5 cm/m)².

2

Reproduce without changing the object

In Reproduce mode, move from 1 cm : 2 m to 1 cm : 1 m. The actual room remains 8 m × 6 m, while the drawing doubles in each length from 4 cm × 3 cm to 8 cm × 6 cm. Try 1 cm : 4 m as the shrinking boundary case.

3

Make the area square explicit

Compare 1 cm : 2 m with 1 cm : 1 m. Drawing lengths double, but drawing area quadruples from 12 cm² to 48 cm². In same units, a length ratio of 1 : 200 becomes an area ratio of 1² : 200² = 1 : 40,000.

4

Challenge the “ordinary multiplier” misconception

In “1 cm : 2 m,” 2 is not a unitless scale factor. It tells how many actual meters each drawing centimeter represents. Convert first: 1 cm : 200 cm = 1 : 200. Then drawing/actual = 1/200 for lengths and 1/40,000 for areas when both use the same units.

CCSS 7.G.A.1 alignment: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. The screen drawing preserves relative dimensions, but displayed “centimeters” are not calibrated to a physical screen or printer.