mr barton maths

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Scale Drawings

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Foundational skills
Interpret scale notation 1:n
\[ 1:100 \rightarrow 1\text{ cm} = 100\text{ cm} \]
Understand what the ratio scale 1:n means.
Interpret scale with units
\[ 1\text{ cm} \rightarrow 2\text{ km} \]
Understand scales written with explicit units.
Convert between scale formats
\[ 1:50{,}000 = 1\text{ cm}:0.5\text{ km} \]
Convert from 1:n notation to 1 cm : x km format.
Compare scales
\[ 1:100 \text{ vs } 1:1000 \]
Understand that smaller scale numbers mean more zoomed in.
Scale to real (lengths)
Find real length from scale length
\[ 6\text{ cm} \times 50 = 300\text{ cm} \]
Calculate real-world length from a scale drawing measurement.
Find real length using unit scale
\[ 3\text{ cm} \times 5\text{ km} = 15\text{ km} \]
Calculate real-world distance using a scale with units.
Find real length with unit conversion
\[ 4.5\text{ cm} \rightarrow 9\text{ m} \]
Convert from drawing measurement to real-world measurement with unit change.
Real distance between map points
\[ 8\text{ cm on } 1:25{,}000 \rightarrow 2\text{ km} \]
Calculate real distance from map measurement.
Real to scale (lengths)
Find scale length from real length
\[ 8\text{ m} \div 100 = 8\text{ cm} \]
Calculate drawing length from real-world measurement.
Find scale length using unit scale
\[ 20\text{ km} \div 4 = 5\text{ cm} \]
Calculate map length from real-world distance.
Find scale length with unit conversion
\[ 35\text{ m} \rightarrow 7\text{ cm} \]
Convert real measurement to drawing measurement with unit change.
Map distance for given real distance
\[ 3\text{ km} \rightarrow 6\text{ cm} \]
Calculate map measurement for a given real-world distance.
Finding scales
Determine the scale from measurements
\[ 6\text{ m} \rightarrow 3\text{ cm} = 1:200 \]
Calculate the scale given both real and drawing measurements.
Determine the scale as a ratio
\[ 15\text{ km} : 6\text{ cm} = 1:250{,}000 \]
Express the scale as a ratio in standard form.
Complete a partially given scale
\[ 1:\square = 4\text{ cm} : 200\text{ m} \]
Find the missing value in a scale.
Scale and area
Find real area from scale area
\[ 3\text{ cm} \times 4\text{ cm} \rightarrow 3\text{ m}^2 \]
Apply scale factor squared for area calculations.
Find scale area from real area
\[ 5\text{ m} \times 8\text{ m} \rightarrow \text{cm} \]
Calculate drawing dimensions for an area problem.
Calculate area on a map
\[ 2\text{ cm} \times 3\text{ cm} \rightarrow \text{km}^2 \]
Calculate real-world area from map measurements.
Area scale factor
\[ 1:200 \rightarrow 1:40{,}000 \text{ (area)} \]
Calculate the area scale factor from a length scale.
Reading scale drawings
Read a measurement from a scale drawing
\[ 8 \times 50 = 400\text{ cm} = 4\text{ m} \]
Read and interpret measurements from a scale drawing.
Use a scale bar
\[ 2\text{ cm} = 5\text{ km} \rightarrow \text{find distance} \]
Use a graphical scale bar to find distances.
Calculate perimeter from scale drawing
\[ 4\text{ cm} \times 2.5\text{ cm} \rightarrow \text{perimeter} \]
Find real perimeter from scale drawing dimensions.
Creating scale drawings
Check if a scale fits
\[ 12\text{ m} \times 8\text{ m at } 1:100 \text{ fit?} \]
Verify whether a given scale produces a drawing that fits.
Calculate drawing dimensions
\[ 150\text{ m} \times 100\text{ m} \rightarrow \text{cm} \]
Calculate dimensions needed to create a scale drawing.
Map problems
Calculate walking time from map distance
\[ 12\text{ cm} \text{ at } 4\text{ km/h} \rightarrow \text{time} \]
Combine scale conversion with speed-distance-time.
Estimate distance using grid squares
\[ 2\text{ cm grid} \rightarrow \text{km}^2 \]
Calculate the real-world area represented by map grid squares.
Calculate real distance from map
\[ 6\text{ cm on } 1:50{,}000 = 3\text{ km} \]
Find real distance from map for navigation purposes.
Special cases
Scale 1:1
\[ 1:1 = \text{actual size} \]
Understand that 1:1 means actual size.
Enlarged scales
\[ 2:1 = \text{twice life size} \]
Understand scales where drawings are larger than reality.
Very small scales for maps
\[ 1:40{,}000{,}000 \rightarrow \text{km} \]
Work with very small scale maps.
Mixed unit scales
\[ 4\text{ cm} : 1\text{ km} = 1:? \]
Convert non-standard scale format to ratio form.
Estimate real objects from scale models
\[ 1:24 \text{ model} \rightarrow \text{real size} \]
Apply scale reasoning to 3D models.
Timer (Optional)
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