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Solve Problems Involving Scale Drawings

Students use scale drawings to find actual distances and dimensions. They identify the scale factor, set up proportions, and compute actual measurements. They also reproduce scale drawings at a different scale and apply these skills to maps and blueprints.

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Solve Problems Involving Scale Drawings

Grade 7 · Geometry · question 1 of 3

0 of 20

20 rungs. A star at the top.

2 : = 8 : 12

How it is taught

0:00 of 4:25

A scale drawing multiplies map length by the scale factor.

Remaining distance is actual length minus distance already flown.

Read it: Scale drawings

A map's scale is 1 cm : 6 km, and a road on it is 7 cm long. 7 cm is 7 groups of 1 cm, and each group stands for 6 km, so the real road is 7 × 6 = 42 km.

  1. Read the scale: the real distance that 1 unit on the drawing stands for.
  2. Count the groups of 1 unit in the drawing's length.
  3. Multiply the groups by the real distance each one stands for.

Every 1 cm on the map stands for the same 6 km, so equal groups multiply.

7 groups of 6 km is 7 × 6 = 42 km.

Going back, a real length divided by the scale's distance gives the drawing's length: 42 ÷ 6 = 7.

Real length = the drawing's length × the distance 1 unit stands for.

Adding the numbers: 7 + 6 = 13.

Each of the 7 groups of 1 cm is 6 km: 7 × 6 = 42.

A drawing uses a scale of 1 cm : 9 m. A line on it is 7 cm. How long is it really, in meters? — 63. 7 groups of 1 cm, each 9 m: 7 × 9 = 63.

Map scale 1 cm : 20 km — find real distance for 4 cm on map

Two cities show up just four centimeters apart on a map. How far apart are they really?

The map's scale tells us: one centimeter on the map stands for twenty real kilometers.

Let's set up a proportion. On the left, the scale itself: one centimeter over twenty kilometers.

On the right, the cities: four centimeters over x — the real distance we want to find.

Cross-multiply: one times x equals twenty times four.

Cities are 4 cm apart on a mapCity ACity B4 cmScale: 1 cm = 20 km120cm / km=4x480cm / km1 · x = 20 · 4x = 80ANSWER80 kmreal distance
Grade 7 · From map distance to real distance using a proportion

Twenty times four is eighty, so x equals eighty.

The cities are eighty kilometers apart in real life. Scale drawings unlocked!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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