Subtraction as the movement that gets you from start to target

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What to assume they know

Addition as movement: starting position plus movement gives target position: starting floor plus movement gives the target floor
Numbering the floors below the ground: why zero needs another side: signed floor numbers and Floor 0
Subtraction of whole numbers as taking away, and as finding what is missing
The habit, from earlier classes, of checking a subtraction by adding back

What they should be able to do

Recall both earlier meanings of subtraction and say which of the two the chapter keeps
Rewrite a subtraction as a missing-addend question and solve it that way
State the relation the chapter uses: target minus start gives the movement needed
Compute a difference of two signed numbers by locating both on a shaft and reading the arrow between them
Explain why swapping the two numbers flips the sign of the answer but not its size
Evaluate differences in which the second number is negative, and say what makes the answer come out larger than the first number
Apply the relation unchanged at metre scale and beyond any drawable scale
Recognise, from a worked case, that taking away a negative behaves like adding a positive — without yet claiming to have proved it

Where it usually goes wrong

"Subtraction means the answer gets smaller." (+ 4) – (– 3) is larger than + 4. Nothing has gone wrong: the target is above the start, so the movement points up.
"You always subtract the smaller number from the larger." In this chapter which number goes first is fixed by the question, not by their sizes. Reversing them answers a different question — it gives the journey home instead of the journey out.
"A subtraction with a negative answer is impossible." It is a journey downward. The book's own worked case has a negative answer on its second try.
"Target minus start is just a formula to memorise." It is derived on p.249 from the addition relation, in three lines. Show the derivation; a formula presented as a formula is exactly what this book is written against.
"– 2 – (– 2) must be – 4, because two minuses make more minus." The start and the target are the same floor, so no press is needed at all.
"Taking away a negative is a strange new rule." It falls straight out of the picture: to get from a floor below the entrance up to a floor above it, you press '+'. Do not state it as a rule here — The additive inverse, and how it turns every subtraction into an addition earns it.

Questions to check understanding

Given a start and a target, write the subtraction and state the movement
Evaluate a difference of two signed numbers
Rewrite a subtraction as a missing-addend question
Explain why reversing the two numbers changes the sign of the answer
Say what a subtraction with answer 0 tells you about the start and the target
Check a stated difference by adding the answer back to the start
The solutions block bound with this chapter file answers the p.248, p.249 and p.251 exercises on its footer pages 3–4

Examples worth working on the board

The books on the shelf (p.247). Ten books, four removed. This is the old meaning, stated so it can be retired. Keep it short.
The two purses (p.248). One person has ₹10, the other ₹6. The question is how much the second needs in order to match the first, and the book writes it both as a missing addend and as a subtraction. This is the meaning the rest of the chapter uses.
Three warm-ups (p.248). 15 – 5, 100 – 10, 74 – 34, each to be redone as a missing-addend question. All three are ordinary whole-number subtractions — that is the point: the new reading has to agree with the old one everywhere it already worked.
Art Centre to Sports Centre (p.248). Start + 2, target + 5. The book gives the press first and the expression second.
The three further cases (p.249). Target – 1 from start – 2; target – 1 from start + 3; target + 2 from start – 2. These three are the whole argument: one stays below the entrance, one crosses it going down, one crosses it going up.
Ten differences (p.249). (+ 1) – (+ 4); (0) – (+ 2); (+ 4) – (+ 1); (0) – (– 2); (+ 4) – (– 3); (– 4) – (– 3); (– 1) – (+ 2); (– 2) – (– 2); (– 1) – (+ 1); (+ 3) – (– 3). Note the deliberate pairs: the first and third differ only in order, and so do the second and fourth.
The mine, subtracting (p.250). (+ 40) – (– 50) and (– 90) – (+ 40), at the same mine whose labelled levels run from + 180 m down to – 175 m. Checked against p.250.
Three more at that scale (p.251). (– 200) – (– 40); (+ 200) – (+ 40); (– 200) – (+ 40). The first and third are the pair to dwell on.
The big one (p.251). Start – 200, target + 2000. The book walks the journey in two legs — up to the entrance, then onward — and then remarks that the answer matches a certain addition.

Figures to have open

A vertical shaft with a start marker, a target flag, and an arrow between them whose head is at the target. The arrowhead is the figure's whole job: it is what makes the answer signed.
The mine cutaway from Addition as movement: starting position plus movement gives target position, reused, with two labelled levels joined by an arrow.
A two-leg journey drawn on one long shaft, with the entrance marked as the break point. Reused in The additive inverse, and how it turns every subtraction into an addition.
No photograph or textbook data table is needed.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 10 "The Other Side of Zero", §10.1 "Bela's Building of Fun", p.247 — the named sub-heading on which button to press, and the shelf of books
§10.1, p.248 — the two purses, the three warm-ups, the boxed note to the teacher, the relation itself, and the Art Centre case
§10.1, p.249 — the book's own headed explanation, the three further cases, and the ten differences
§10.1, pp.250–251 — the same relation at the mine and at the infinite lift, including the two-leg journey from – 200 to + 2000
§10.1, p.252 — the remark this topic ends on, developed in The additive inverse, and how it turns every subtraction into an addition
Chapter Summary, p.269, for the general form of the relation
Solutions block bound with this chapter file, footer pages 3–4