Numbering the floors below the ground: why zero needs another side

What to assume they know

Counting numbers, and zero as the number that comes before 1
Every number sequence is a rule, not a list: a sequence is a rule, so "and so on downwards" is a legitimate thing to define
Line and ray: what changes when you refuse to stop: ray and line, since the chapter's opening question is put in exactly those words — the familiar picture is only a ray
Reading a simple scale where the marks are evenly spaced

What they should be able to do

State the chapter's opening question: whether anything lies to the left of 0
Explain why the picture learned in earlier classes is a ray rather than a full line
Write a run of lift presses as a single signed number
Number every floor of a building whose ground floor has been fixed as Floor 0
Distinguish a positive number from a negative number by the sign written in front of it
Explain why a floor number and a number of floors moved can be written with the same symbol
State that zero takes neither sign, and say why that is forced rather than chosen
Identify, in an everyday setting, what has been made the reference level and what would change if a different level were chosen

Where it usually goes wrong

"A minus sign means subtract." Here it does not. On Floor – 2 nothing has been subtracted from anything; the sign says below the entrance. Correct it by writing – 2 as a label on a door rather than in a sum.
"Negative numbers are numbers you cannot have." The Video Games shop is a real shop with real customers standing in it. The number is negative; the shop is not.
"The floor below the ground should be Floor 1, then Floor 2 going down." This is the honest instinct and the chapter is built to defeat it: two different floors would then both be called 1, and pressing the lift button would become ambiguous. The sign is what keeps the naming one-to-one.
"Zero is positive" (or "zero is negative"). Zero is the level everything is measured from, so it cannot be on one side of itself. The book prints this.
"The ground floor is 0 because there is nothing there." The Welcome hall is the busiest floor in the building. It is 0 because it was picked as the level to measure from — the same reason sea level is 0 m in §10.3.
"– 3 is bigger than – 2, because 3 is bigger than 2." Do not settle this here; it is the argument of Laying the integers out in order, and why −8 is less than −2. Flag it and move on.

Questions to check understanding

Write a stated run of button presses as a single signed number
Given a labelled building, name the floor a stated shop is on
Given a floor number, say how many presses of which button reach it from the entrance
State which of two given numbers is positive, which is negative, and which is neither
Explain why the ground floor is numbered 0
Say what would change if a different floor had been chosen as Floor 0
The solutions block bound with this chapter file answers the p.243 and p.244 questions on its footer page 1

Examples worth working on the board

The chapter's opening picture (p.242). A horizontal scale marked 0 to 10 with an arrowhead on the right only. The whole opening argument turns on that single missing arrowhead. Checked against p.242.
The Building of Fun, as drawn (p.243, repeated smaller on p.244). Checked against the printed page; the floor names are lettering inside artwork and extract as nothing. Reading upward from the entrance: Welcome hall, Food Court, Art Centre, Books, Ice Cream, Sports, Space. Reading downward from the entrance: Toys, Video Games, Cinema, Ghost House, Dinosaur. A lift shaft runs up the right-hand side of the building with a two-button panel at its top.
The four floor numbers the book states outright (p.244). Food Court + 1, Art Centre + 2, Toy Store – 1, Video Games – 2, and the ground floor as Floor 0. The Book Store is named as + 3 further down the same page. Everything else is the reader's job.
Button-press notation (p.243). Three pushes of '+' written as + 3; four pushes of '–' written as – 4. Two questions follow it: what to press to rise four floors, and what to press to drop three.
The building's extent (stated on p.250). Six floors above the entrance and five below it — that is, – 5 up to + 6. Useful as the closing frame of this topic, because it makes the next question ("does it stop there?") askable.
Zero's status (p.244). The book says plainly that zero is on neither side and is written with no sign at all. Treat this as a claim to be justified in section 11, not as a rule to be recited.

Figures to have open

A cutaway of a multi-storey building with floors above and below a ground line, each floor carrying a shop name. Redraw; do not reproduce the printed art. The mathematical content that must survive the redraw is the count — six named floors above the entrance, five below — and the fact that the lift shaft spans both.
The lift's two-button panel, large enough to read.
A number ray marked 0 to 10 with a single arrowhead, which the explanation later completes to a line. This figure recurs in Laying the integers out in order, and why −8 is less than −2 and should be drawn once and reused.
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", chapter opening pp.242–243 — the counting numbers, zero, fractions, the number ray, and the question the chapter is built to answer
§10.1 "Bela's Building of Fun", p.243 — the building, the lift, and button-press notation
§10.1, p.244 — the named sub-heading on numbering the floors, the four stated floor numbers, the definitions of positive and negative number, and zero's status
§10.1, p.250 — the stated extent of the building, – 5 to + 6, used as this topic's closing frame
Chapter Summary, p.269, for the book's own restatement of positive, negative and zero
Solutions block bound with this chapter file, footer page 1