Maps and plans

Scale on maps and plans

A scale of 1:50 000 means 1 cm on the map is 50 000 cm on the ground. Convert to km.

CAPS

Grade 10 · Mathematical Literacy · Maps and plans

Mathematical Literacy uses a context, not a bare sum.

  • Two papers

    Paper 1 uses familiar contexts: pay slips, till slips, maps you have seen, and data in a table. Paper 2 uses less familiar contexts and expects you to decide which method fits. Both papers are 150 marks.

  • What to show

    Write the value with its unit or its rand sign. Say whether you multiply or divide, and round only at the end, in the way the question asked (nearest rand, one decimal place, a whole number of tiles).

  • The relation

    real distance = map distance × scale number. Scale factor

  • How a marker reads it

    Write the conversion line: 1 km = 100 000 cm. First-timers forget that step and leave the answer in cm.

A correct number with the wrong unit, or a VAT amount treated as the full price, loses the mark the context was testing.

ABN

Diagram

Scale on maps and plans

Worked example

A map is 1:50 000. Two towns are 4 cm apart on the map. How far apart on the ground, in km?

Before any working — hunt first

Given

Numbers and units already in the sentence: 1 · 50 · 000 · 4 cm. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: How far apart on the ground, in km. Circle that word — that is the missing variable.

Find

We are required to find: How far apart on the ground, in km. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write real distance = map distance × scale number with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives How far apart on the ground, in km.

Simplified approach

Multiply 4 cm by 50 000, then convert cm to km.

Culture note

A Limpopo road map from Thabazimbi to Lephalale is this question.

Formulas

real distance=map distance×scale number

Scale factor

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

  • If the price already includes VAT, divide by 1.15 — do not subtract 15%

    How:Total = price × 1.15 when VAT is still to be added. When the till already shows VAT, price excluding = total1.15. Subtracting 15% of the total is a different number and loses the mark.

    When to use it:Till slips, VAT, and SARS-style tax questions.

  • Fencing is perimeter. Grass, paint and tiles are area. Tanks are volume.

    How:Underline the object: wire, border, fence → add the sides. Floor, wall, field, paint → multiply length by width, then divide by coverage and round tins up. Water in a tank → m³ then × 1 000 for litres.

    When to use it:Measurement papers: school fields, paint, Jojo tanks.

Step 1 / 5

Map to ground in cm

4×50 000=200 000 cm.

Diagram
Worked example
4×50 000=200 000 cm

Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

4. Step-by-step working

  1. 01

    Map to ground in cm

    4×50 000=200 000 cm.

    4×50 000=200 000 cm
  2. 02

    Convert to km

    100 000 cm=1 km, so 200 000 cm=2 km.

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

A map has scale 1 : 50000. Two places are 2 cm apart on the map. Find the real distance in metres and in kilometres.

4. Step-by-step working

  1. 01

    Multiply

    Real centimetres=2×50000=100000 cm.

    100000 cm
  2. 02

    Divide

    Metres=100000100=1000 m.

    1000 m
  3. 03

    Divide

    Kilometres=10001000=1 km.

    1 km

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: A map has scale 1 : 50000. Two places are 2 cm apart on the map. Find the real distance in metres and in kilometres.

In other words — as if you have never seen this before

If you have never seen this before: 1 cm on the map is n cm in real life. Divide centimetres by 100 to get metres, then by 1000 to get kilometres. We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

Scale 1 : 50000. Map distance 2 cm.

3. Which method — and why this one?

1 cm on the map is n cm in real life. Divide centimetres by 100 to get metres, then by 1000 to get kilometres.

4. Step-by-step working

  1. 01 / 06

    Multiply

    Real centimetres=2×50000=100000 cm.

    100000 cm

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  2. 02 / 06

    Divide

    Metres=100000100=1000 m.

    1000 m

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  3. 03 / 06

    Divide

    Kilometres=10001000=1 km.

    1 km

    Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.

  4. 04 / 06

    Step G — Sense-check the size

    Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.

    Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.

  5. 05 / 06

    Step F — Box the answer with its unit

    1000 m, which is 1 km.

    Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.

  6. 06 / 06

    Step H — What the marker is looking for

    On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.

    Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

1000 m, which is 1 km.

Copy onto your answer sheet — in this order

Formula: 100000 cm

Answer: 1000 m, which is 1 km.

6. Check it like a marker

Treating the scale number as metres, instead of centimetres, makes the distance 100 times too small.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

Ntsako · fx-991ZA PLUS. Tap to calculate.