The same children, different numbers: a number depends on what is being counted

What to assume they know

Counting to small whole numbers, and comparing two quantities as taller / shorter
Mathematics is the search for patterns *and* for why they hold: mathematics looks for a pattern and for the reason it holds — the same demand is made here
The idea of an ordered line: first position, last position, "next to"
Reading a picture as data rather than as decoration

What they should be able to do

State, in your own words, what each child in the picture is counting
Given a line of children of known heights, produce the row of numbers they would say
Explain why the numbers change when the same children change places
Explain why a child at either end can never say 2
Decide whether a proposed row of numbers is possible, and justify the decision
Show that at least one child must always say 0, whatever the heights are
Construct an arrangement of five children realising a stated row, or argue that none exists
Find the largest number of children who can say 2 at once in a line of five, and say why no more is possible
Recognise that a number reported without its context cannot be interpreted

Where it usually goes wrong

"The number belongs to the child." It belongs to the child in that position in that line. The two drawings on pp.55–56 are the same eight children with different numbers, which is the flat contradiction of this belief. Show them together, not one after the other.
"Saying 0 means you are short." It means nobody beside you is taller — which is what the tallest child in the whole line always experiences. In the first picture three children say 0, and they are not the three shortest.
"Saying 2 means you are the shortest." It means both your neighbours beat you, which only makes you a local dip, not the smallest overall. Heights 3, 1, 4, 2, 5 give two children saying 2, and only the child of height 1 is the shortest of all; the child of height 2 is a dip and nothing more.
"Any row of 0s, 1s and 2s could happen." Most cannot. The row of five 1s is impossible for any heights whatever, because the tallest child in the line has no taller neighbour and must say 0.
"A child at the end could say 2 if they were short enough." An end child has one neighbour, so their count can never exceed 1. This is about position, not height, and students consistently answer it from height.
"Equal heights count as taller." They do not. The rule turns on taller, strictly. This is exactly what makes "everybody says 0" possible when all the children are the same height — and impossible when their heights all differ.

Questions to check understanding

Given a line of children with stated heights, write down what each one says
Given a row of numbers, decide whether it is possible and justify the answer
Explain in one sentence why an end position can never report 2
"Can they all say 0?" — with the follow-up "and what must be true of the heights?"
Arrange a given set of children to maximise (or minimise) the count of a chosen number
Explain why the same children can give two different rows
Short-answer items of the form "what does the 2 tell you about the children on either side?"
Reasoning items asking why a stated row is impossible — the chapter's own question 5 is the model

Examples worth working on the board

The first line-up (§3.1, p.55). Eight children drawn side by side, each with a speech bubble. Read left to right the bubbles say 0, 2, 1, 1, 0, 2, 1, 0. These digits are drawn inside the artwork and do not appear in the extracted text; they were read off the printed page. Note: this row already contains two neighbours saying the same number (the two 1s in the middle), which settles question 3 on the next page by inspection.
The second line-up (§3.1, p.56). The same eight children, reordered. Their bubbles now read 1, 0, 2, 0, 1, 2, 1, 0. Also drawn artwork, also read off the printed page. Put the two rows one above the other — that pairing is the whole argument of the topic.
The rule (§3.1, p.56). A child reports how many of the people immediately beside them are taller: 0, 1 or 2. Nothing else about the child enters.
Heights that produce a given row. Useful inputs, each checked against the rule:
- five children of heights 1, 2, 3, 4, 5 in that order give the row 1, 1, 1, 1, 0
- five children of heights 5, 4, 1, 2, 3 give the row 0, 1, 2, 1, 0
- five children of heights 3, 1, 4, 2, 5 give the row 0, 2, 0, 2, 0.
The seven Math Talk questions (§3.1, p.56). Ends saying 2; everyone saying 0; two neighbours saying the same number; four 1s and a 0 among five children of different heights; the row of five 1s; the row 0, 1, 2, 1, 0; and the largest possible number of 2s. These are the spine of sections 6–11.
The chapter opening (§3.1, p.55). Before the picture, the book asks the class for five everyday settings where a number does a job. That list is the cheapest way into the thesis: a number means nothing until you know what it counts.

Figures to have open

The two line-ups from §3.1, pp.55–56, with all sixteen spoken numbers legible. These are the topic; without both, section 5 has nothing to compare. The printed art is a coloured illustration — redraw as eight labelled bars of clearly different heights with the numbers above them, so the heights are visible rather than guessed. The printed drawing deliberately does not make the heights easy to rank, which is part of its charm and of no use here.
A five-slot strip that can be re-filled repeatedly with different heights and recomputed. Needed for sections 10 and 11. Standard schematic.
No table, dataset or photograph from the textbook is required.

Where this sits in the book

NCERT Class 6 Mathematics (Ganita Prakash), Chapter 3 "Number Play": §3.1 Numbers can Tell us Things, pp.55–56
The named sub-heading inside §3.1 — What are these numbers telling us?, p.55 — is printed without a number, so it is cited by page
Chapter opening paragraphs and the first Math Talk prompt, p.55
The rule statement, the hint about heights, and questions 1–7, p.56
Forward link: §3.2 Supercells, pp.57–59, which re-runs the same idea on a grid (Supercells: a number's status comes from its neighbours)
Summary, p.73, for the chapter-level claim that numbers convey information