Maps and plans

Plans, elevations and assembly

Floor plans, north elevation, assemble a desk from a diagram. Scale on the plan.

CAPS

Grade 11 · 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 length = plan length × scale. Plan scale
How a marker reads it
Convert the plan unit first if needed. mm and cm mix-ups lose the mark.

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

Diagram

Worked example

A bedroom on a plan is 40 mm long. Scale 1:100. Real length in metres?

Before any working — hunt first

Given

Numbers and units already in the sentence: 40 mm · 1 · 100. 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: Real length in metres. Circle that word — that is the missing variable.

Find

We are required to find: Real length in metres. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write real length = plan length × scale with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Real length in metres.

Simplified approach

40 mm×100=4 000 mm=4 m.

Culture note

RDP house plans at the municipal office in Thabazimbi use 1:100.

Formulas

real length=plan length×scale

Plan scale

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.
Always substitute the usage into both tariff options — the cheaper one can swap after break-even
How:Write cost A and cost B as two lines. Set them equal if they ask where the deals match. Circle the smaller total at the given usage. A graph with two lines makes the swap obvious.
When to use it:Cellphone contracts, prepaid electricity, and cake-sale break-even.

Step 1 / 5

Apply the scale

1:100 means multiply the plan by 100.

Floor plan with dimensions, scale and area and paint calculations — Diagram

Floor plan, route map and assembly — Diagram

Multi-tier seating and parking layout — Diagram

40 mm×100=4 000 mm

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

01
Apply the scale
1:100 means multiply the plan by 100.
40 mm×100=4 000 mm
02
Convert to metres
1 000 mm=1 m, so 4 m.

More worked examples

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

Example 1 / 20

A plan uses the scale 1 : 100. A wall is 4 cm on the plan. How long is the real wall, in centimetres and in metres?

4. Step-by-step working

01
Multiply
Real length=4×100=400 cm.
400 cm
02
Divide
Metres=400100=4 m.
4 m

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 plan uses the scale 1 : 100. A wall is 4 cm on the plan. How long is the real wall, in centimetres and in metres?

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

If you have never seen this before: Multiply the plan length by the scale number to get real centimetres. Then divide by 100 for metres. 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?

1 cm on the plan stands for 100 cm in the room. Plan length 4 cm.

3. Which method — and why this one?

Multiply the plan length by the scale number to get real centimetres. Then divide by 100 for metres.

4. Step-by-step working

01 / 05
Multiply
Real length=4×100=400 cm.
400 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.
02 / 05
Divide
Metres=400100=4 m.
4 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.
03 / 05
Sense-check
One centimetre on the plan is 1 m, so 4 cm is 4 times that.
4 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.
04 / 05
Step F — Box the answer with its unit
400 cm=4 m.
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.
05 / 05
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

400 cm=4 m.

Copy onto your answer sheet — in this order

Formula: 400 cm

Answer: 400 cm=4 m.

6. Check it like a marker

Dividing by the scale shrinks the wall. The plan is the small one.

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…”

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