Zero pairs: why a positive and a negative token cancel

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What to assume they know

Numbering the floors below the ground: why zero needs another side: signed floor numbers, and '+' and '–' as buttons
Addition as movement: starting position plus movement gives target position: a sum of signed numbers read as position and movement
Counting two collections and comparing them
Matching objects one-to-one, from earlier classes

What they should be able to do

Lay out any given integer as a collection of tokens of a single colour
State what a green token and a red token together are worth
Name the pair, and say why the name is a description rather than a label
Add two integers by laying out tokens, removing every pair, and reading the surplus
Predict from the two counts alone which colour will be left over
Recover the lift attendant's floor from the contents of his pocket
Explain why the answer cannot depend on the order the tokens were collected
Give the addition statement that a drawn set of tokens represents

Where it usually goes wrong

"The tokens are a beginners' method you graduate out of." They are the chapter's argument that the answer is independent of order, and they are what §10.5 says the Chinese Nine Chapters was doing with red and black rods two thousand years ago.
"A green and a red make nothing, so they disappear from the world." They stop contributing to the total. The presses still happened; the lift really did go up and come back. What is zero is their net effect.
"You have to remove the pairs in the right order." Any pairing works and any order works, and that is the point of section 10 — the surplus is the same whichever greens you match with whichever reds.
"If there are more reds, the answer is red, so it must be bigger." The answer is negative, which on the line means lower, not bigger. Carry the ordering argument from Laying the integers out in order, and why −8 is less than −2 across.
"(– 3) + (– 2) has nothing to cancel, so the tokens do not work there." They work perfectly: there are no pairs, so nothing is discarded and the whole pile is the answer. The empty case is a case.
"A drawn set of tokens shows the answer." It shows the question. The answer is what is left after the pairs go.

Questions to check understanding

Add two integers using tokens and state the result
Given a drawn set of tokens, write the addition statement it represents
Given a drawn set, say which floor the attendant is on
Say how many zero pairs a stated layout contains
State the value of a set of tokens in which the two colours are equal in number
Explain why the pairs may be removed in any order
The solutions block bound with this chapter file answers the p.257 exercises on its footer pages 6–7

Examples worth working on the board

The bored lift attendant (p.256). He starts at the entrance with an empty pocket. Every time he pushes '+' he pockets a green token; every time he pushes '–' he pockets a red one. After an hour the pocket holds 5 green and 3 red.
The two routes (p.256). First route: turn the counts into a sum and evaluate it. Second route: pair off greens with reds, discard the pairs, count what is left. The chapter's argument is that these agree, so both must be shown.
The first drawn set (p.256). Checked against the printed page. Five green tokens in a row with three red tokens beneath the leftmost three, and each of those three vertical pairs struck through. Two green tokens stand unpaired at the right.
The second drawn set (p.256, resolved on p.257). Adding + 5 and – 8: five green above eight red, five vertical pairs struck through, three red left standing. Checked against both pages.
Four sums to run on tokens (p.257). (+ 6) + (+ 4); (– 3) + (– 2); (+ 5) + (– 7); (– 2) + (+ 6). The first two have nothing to cancel at all, which is worth remarking on rather than skipping.
Two drawn pockets to decode (p.257). Checked against the printed page. The first shows three green tokens above five red; the second shows six green above three red. For each, the task is to cancel the pairs, give the addition statement, and name the attendant's floor.
The chapter opener's frieze (p.242). Checked against the printed page. A decorative row of four token stacks along the top of the opening page, alternating green and red by layer and growing from three tokens to fifteen. It is ornament, not exercise, but it is the reader's first sight of the tokens and the explanation may use it as the visual bridge into §10.2.

Figures to have open

Token sets in two colours, laid out as an upper row and a lower row so that pairs are vertical. The vertical alignment is what makes cancelling visible and must be preserved in the redraw.
A strike-through that removes a pair without removing the memory of it — the book strikes tokens rather than deleting them.
An openable pocket that can hold a shuffled mixture, for sections 1 and 10.
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", §10.2 "The Token Model", p.256 — the named sub-heading on tokens for addition, the attendant, the definition of the zero pair, and the two worked layouts
§10.2, p.257 — the resolution of the second layout, the four sums, and the two drawn pockets to decode
§10.1, p.244, for the button convention the tokens stand in for
§10.5, p.266, for the historical counterpart in coloured rods — the forward pointer this topic should end on
Chapter opening, p.242, for the decorative token frieze
Solutions block bound with this chapter file, footer pages 6–7