Negative numbers on the number line, and adding and subtracting them

What to assume they know

Class 6: negative numbers exist, are read off a number line to the left of zero, and are added and subtracted using green and red tokens
Class 6: a green and a red token together are worth nothing — the zero pair
Whole-number addition and subtraction, and the idea that they undo each other
Writing a situation as an expression before computing it: writing a situation down as an expression before evaluating it
Reading a position on a number line, and the convention that right is the direction of increase

What they should be able to do

Recover two integers from their sum and their difference by systematic trial, and say why the search always closes
Explain why a movement with a direction is naturally modelled by a signed number rather than by a pair (size, direction)
State the final-position formula for two carrom strikes and apply it when either or both strikes go leftward
Read an arrow diagram on a number line and infer the signs of the two movements and which has the larger magnitude
Separate the magnitude of an integer from its direction, and use the word correctly
Carry out a subtraction that "runs out" of tokens by inserting zero pairs, and justify why inserting them changes nothing
Rewrite any subtraction as an addition of an additive inverse, and read the notation −(−18) correctly

Where it usually goes wrong

"A difference cannot be negative." Rakesh's first trial row, (10, 15), produces −5 on the very first line of the chapter, and the second puzzle asks for −11 outright. The chapter's fixed order — first minus second — is what makes this coherent. Checked against p.24.
"The minus sign means the number is small." The sign says which way; the magnitude says how far. Picture 1 on p.27 has the negative movement as the larger of the two. Make magnitude and direction two separate readings of one symbol.
"Four direction cases means four rules to remember." The section sets the four cases up on p.26 precisely so it can throw them away. If the explanation lists the four cases and then teaches four rules, it has taught the opposite of the page.
"Adding zero pairs is cheating — you are changing the number." A green and a red together are worth nothing, so the bag's value is untouched; only its contents change. Show the count of positives rising from 7 to 18 while the value stays 7.
"7 − 18 cannot be done." It cannot be done by removal alone from seven tokens, which is exactly the difficulty the page stages. It can always be done once inverses are allowed. Nothing about integers is "impossible to subtract".
"−(−18) is some new operation." It is the inverse of the inverse, and it lands back where it started. Tie it to the picture: turn round twice and you face the way you began.
"The carrom coin's position is a distance, so it cannot be negative." The section's P is a position measured from 0, not a length. Its sign records which side of 0 the coin stopped on.

Questions to check understanding

Given a sum and a difference, find the two integers (the chapter's own "Figure it Out" task, six items, p.25)
Given one movement and the final position, find the other movement
Given a list of signed movements, find the final position
Read an arrow diagram and state the sign of each movement and which magnitude is larger
Perform a subtraction with tokens where zero pairs must be inserted, and say how many are needed
Rewrite a subtraction as an addition of an additive inverse, and evaluate
Simplify a repeated minus sign such as −(−a)
State the magnitude and the direction encoded by a given signed movement
Competency items at this stage usually dress the number line as a lift, a temperature scale, a bank balance or a game score; the phrasing is normally "represent the situation using integers and find …"

Examples worth working on the board

Rakesh's first puzzle (Part II, §2.1, p.24). Inputs: sum 25, difference 11. The printed trial table has four rows, in this order — (10, 15), (20, 5), (19, 6), (18, 7) — with the sum column reading 25 every time and the difference column reading −5, 15, 13, 11. Checked against p.24.
Rakesh's second puzzle (Part II, §2.1, pp.24–25). Inputs: sum 25, difference −11. The section's own answer is that the previous pair swaps over.
Six more sum-and-difference pairs (Part II, §2.1, p.25). Sums and differences, in the printed order: (27, 9), (4, 12), (0, 10), (0, −10), (−7, −1), (−7, −13). Checked against p.25. Two have a zero sum, two have a negative sum, and three have a negative difference. Those three counts are easy to conflate, and the last one is the only three: an explanation that says three of the sums are negative will contradict the cards.
Why the search always closes. In every printed pair the sum and the difference are both even or both odd. That is not an accident and it is not stated in the book — half of (sum + difference) has to be a whole number for the two numbers to be integers at all. Flag clearly that this is an added observation, not the chapter's, and use it only as the reason the guessing terminates.
The one-way carrom line (Part II, p.25). Checked against the printed page. A red line with dots marked 0 to 12 and a yellow coin sitting near 4, with a single rightward arrow above it. Inputs: first strike 4 units, second strike 3 units.
The two-way carrom line (Part II, p.26). Checked against the printed page. The same red line, now with arrowheads at both ends, labelled −ve at the left and +ve at the right, ticks running from about −5 to 6 with ellipses beyond. Inputs: first movement 5, second movement −7.
The two carrom questions (Part II, pp.26–27). (i) First movement −4, final position 5 — find the second movement. (ii) Movements taken in the order 1, −2, 3, −4, …, −10 — find the final position.
The three "Try This" arrow pictures (Part II, p.27). Checked against the printed page. Each shows a number line with 0 marked, a dashed coin at the halfway position and a solid coin at P, with two labelled arcs a then b. Picture 1: a goes right, b comes back further left, P lands left of 0. Picture 2: a goes right, b comes back a shorter way, P lands right of 0. Picture 3: a goes left and b returns exactly as far right, so P sits on 0. The task is to read magnitudes and directions off the picture, not to compute.
(+7) − (+18) with tokens (Part II, p.28). Checked against the printed page. The page shows seven green tokens, then a row of eighteen green above a row of eleven red after eleven zero pairs are inserted, then the same rows with the eighteen greens struck through. Inputs: start with 7, remove 18, and the fact that 11 zero pairs are exactly enough.
The inverse notation (Part II, p.29). Printed: the inverse of an integer a is written −a; −(18) is −18 and −(−18) is 18. This is the notational point the section closes on and it is needed in every later topic of the chapter.

Figures to have open

A number line that can be relabelled between the one-way version (0 to 12, ticks and dots) and the two-way version (arrowheads both ends, −ve and +ve labels, ticks about −5 to 6). Standard schematic; redraw rather than lift.
A carrom-style coin that can sit on the line, plus a "ghost" outline for the intermediate position. The book uses a solid yellow disc for the final position and a dashed one for the intermediate — keeping that distinction is what makes the Try This pictures readable.
Two labelled arcs above a number line, drawable in either direction, for the a-then-b diagrams.
Green and red circular tokens carrying + and −, in quantities up to eighteen in a row, with a strike-through state. Standard schematic.
No photograph or dataset from the textbook is needed.

Where this sits in the book

NCERT Class 7 Mathematics, Ganita Prakash Part II, printed Chapter 2 "Operations with Integers", §2.1 "A Quick Recap of Integers", pp.24–25; its unnumbered sub-headings "Figure it Out" (p.25) and "Carrom Coin Integers" (pp.25–29).
Forward pointers within the same chapter: §2.2 (Part II, pp.29 onward) builds multiplication on the token model recalled here.
Backward pointer: Part I, printed Chapter 2 "Arithmetic Expressions", for writing a situation as an expression.
Class 6 Ganita Prakash, for the token model and the zero pair, which this section explicitly treats as revision.