Last reviewed: 7 November 2026
Updated November 2026. These Grade 8 scale drawing notes explain how to change actual lengths to scale lengths and back, and how to write a scale in statement form and ratio form. A scale of 1 : 50,000 means 1 cm on the drawing stands for 50,000 cm, which is 0.5 km, on the ground.
All examples are original practice. For the other topics, see our Grade 8 mathematics revision guide and the Grade 8 notes hub.
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What the Grade 8 Curriculum Covers
Scale drawing is a sub-strand under Geometry in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. Learners represent lengths to a given scale, convert between actual and scale length, interpret and write linear scales in statement and ratio form, and make scale drawings. The design is listed on the KICD Grade Eight curriculum designs page. Metric unit conversions follow the SI, described by the BIPM SI units page.
Units You Need
1 m = 100 cm and 1 km = 1,000 m = 100,000 cm. Most scale questions are easiest when everything is in centimetres first.
Statement Form and Ratio Form
Statement form uses words and units: “1 cm represents 5 km”. Ratio form has no units: both sides are in the same unit.
To change “1 cm represents 5 km” to ratio form: 5 km = 500,000 cm, so the scale is 1 : 500,000.
To change 1 : 20,000 to statement form: 20,000 cm = 200 m, so “1 cm represents 200 m”.
Actual Length to Scale Length
Divide the actual length by the scale factor, after converting units. Example. A road is 3 km long. Scale 1 : 50,000. 3 km = 300,000 cm; scale length = 300,000 ÷ 50,000 = 6 cm.
Scale Length to Actual Length
Multiply the scale length by the scale factor. Example. On a map of scale 1 : 250,000, two towns are 4.8 cm apart. Actual distance = 4.8 × 250,000 = 1,200,000 cm = 12 km.
Making a Scale Drawing
- Choose a scale that makes the drawing fit the paper.
- Convert every actual length to a scale length.
- Draw with a sharp pencil and ruler; use a protractor for angles.
- Write the scale on the drawing.
Example. A classroom is 9 m by 7.5 m. With scale 1 cm represents 1.5 m, the drawing is 9 ÷ 1.5 = 6 cm by 7.5 ÷ 1.5 = 5 cm.
Original Practice Questions With Worked Answers
- Write “1 cm represents 2 km” in ratio form.
Answer: 2 km = 200,000 cm, so 1 : 200,000. - Write 1 : 500 in statement form using metres.
Answer: 500 cm = 5 m, so 1 cm represents 5 m. - A field is 120 m long. Find its length on a plan of scale 1 : 2,000.
Answer: 12,000 cm ÷ 2,000 = 6 cm. - On a map of scale 1 : 100,000, a river is 7.5 cm long. Find its actual length.
Answer: 750,000 cm = 7.5 km. - A plot 40 m by 25 m is drawn to scale 1 cm represents 5 m. Find the drawing size.
Answer: 8 cm by 5 cm.
Grade 9 uses scale drawing for bearings and heights in our Grade 9 bearings and angles of elevation notes.
For daily practice across subjects, a Day Pass (KSh 20) or Monthly Pass (KSh 500) opens the full question bank.
Frequently Asked Questions
What does a scale of 1 : 50,000 mean?
Every 1 cm on the drawing stands for 50,000 cm, or 500 m, on the ground.
Why does a ratio scale have no units?
Both sides are in the same unit, so the units cancel. The ratio works in any unit.
How do I find actual length from a map?
Multiply the map length by the scale number, then convert to metres or kilometres.
How do I choose a scale for a drawing?
Pick a scale that makes the longest length fit comfortably on your paper and gives easy numbers to measure.
Ten-minute check: try the free Grade 8 CBC Challenge. It has 10 questions, each marked on the spot with the working, and it shows which topics to practise next.