Scale drawings — Mathematics, 11–13 years
Use a fixed relationship between a drawing and the real object to read maps, plans and models without losing the real distances.
What a scale drawing is
A scale drawing is a smaller or larger copy in which every length changes by the same factor. A map may say 1 cm represents 5 km, so the drawing and the landscape keep the same shape and proportions. The scale is a translation rule between a measured length on paper and the real length.
Why scales are needed
A real building, road system or country is usually too large to draw at its actual size. A scale makes it fit on paper while preserving useful information about distance and shape. The same idea also works in the other direction: engineers can enlarge a tiny part in a detailed drawing while keeping its proportions.
Reading a map scale
A map uses the scale 1 cm : 4 km. The route between two villages measures 3.5 cm on the map. Multiply the map distance by 4: 3.5 × 4 = 14. The real route is 14 km, assuming the map’s scale applies to that route and the measurement follows the road accurately.
Do not mix the units
A common mistake is using 3.5 metres directly with a scale written in centimetres, or multiplying when the question asks for the drawing length. This is reasonable because the numbers and the rule look familiar. First convert to matching units, then decide the direction: drawing to real means multiply by the scale factor; real to drawing means divide.
Scales beyond school
Maps use scales for journeys, while architects use them for house plans and model makers use them for buildings, vehicles or landscapes. Sports diagrams and weather maps also shrink large spaces. A scale is useful only when it is stated clearly and used consistently; it cannot make a map perfectly accurate where roads curve or the ground is uneven.
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