Odd and even as "can this be arranged in pairs"

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What to assume they know

Even and odd numbers from earlier classes, at least as a familiar sorting
Skip counting in twos, and reading a picture of dots as a number
Adding several numbers, and the fact that order of addition does not matter
Consecutive whole numbers: what "one more than" means
Why whole units are not enough to measure with and the Class 6 work on multiples of 2
The idea, from The four angles at a crossing: vertically opposite and linear pairs, that an argument can settle a claim that no amount of measuring or checking would settle

What they should be able to do

Represent a given whole number as dots laid out in pairs, and read off from the picture whether it is even or odd
State what an odd number looks like in that picture: a full set of pairs with one dot over
Explain from the picture why any number of even numbers added together is even
Explain from the picture why two odd numbers added together are even, and why three added together are not
Predict the parity of a sum of odd numbers from how many of them there are
Use a parity argument to show that a stated total is unreachable, and set the argument out so that it applies to every attempt at once
Use the word parity correctly, and state what parity does and does not settle

Where it usually goes wrong

"Odd means it leaves remainder 1 when you divide by 2, and that is all there is to say." True but useless here. The chapter's picture is what lets you add five odd numbers without knowing a single one of them.
"I could not find five cards making 30, so probably there is a clever set I missed." The chapter's move is the opposite: stop looking. Five leftovers cannot pair up, so no choice of five odd cards reaches an even total — the argument covers every set at once, including the ones nobody tried.
"Adding odd numbers gives odd answers." Only when there is an odd number of them. Two odds give an even; four odds give an even. The count of the addends is what decides, not the addends.
"A picture is an illustration, not a proof." The chapter disagrees on p.130, and it is right to: the picture is drawn so that no particular size is used anywhere in it. A picture that only works for the numbers shown would not be a proof — this one never mentions them.
"Parity settles the question either way." It does not. Showing that a total has the wrong parity proves it unreachable; showing that it has the right parity proves nothing at all, because some other obstruction may still be in the way. This distinction is worth stating out loud in section 12 and is tested by the exercise about the loose encyclopaedia sheets on p.144 — see the sibling topic The parity of a sum or product is fixed before you compute it.
"Their ages might not be whole numbers." The chapter fixes a shared birthday precisely so the two ages are whole numbers one apart. Say that out loud, or a sharp student will produce 55.5 and 56.5 and be right.

Questions to check understanding

Find the parity of a sum described only by how many even and how many odd numbers it contains (the p.131 exercise set is exactly this)
Decide whether a claimed total is reachable from a described collection, and justify the answer without trying combinations
Given a stated total that is unreachable, identify what would have to change for it to become reachable
Complete a parity table for subtraction as well as addition
Explain in words why the sum of two consecutive whole numbers is always odd
Coin-and-total items — an odd number of one denomination, an even number of another, a stated total — are the standard exam dress for this argument; the p.131 piggy-bank question is the model
Say what has been proved and what has not, when a parity check comes out consistent

Examples worth working on the board

Kishor's puzzle (Part I, §6.2, p.129). Five empty boxes joined by plus signs, with 30 written after the equals sign. Beside them, seven loose heaps of number cards. Checked against the printed page: the heaps carry 13, 9, 1, 7, 11, 5 and 3 — seven values, all odd, several copies of each. The puzzle is set as something to solve; it is not solvable.
Even numbers as dots (Part I, §6.2, p.129). Checked against the printed page: three pictures, all in one colour, every dot in a pair — a block of six, a slanting chain of ten, and two rows of nine. Nothing is left over in any of them.
Odd numbers as dots (Part I, §6.2, p.129). Checked against the printed page: the same three pictures with one extra dot each, drawn in a darker second colour so the leftover is visible at a glance — seven, eleven and nineteen. That colour choice is the whole pedagogy of the figure; keep it in the redraw.
Two odds added (Part I, §6.2, p.130). Checked against the printed page: three stacks of paired dots, each stack two columns wide. In each stack one odd number is drawn green and the other purple, and there is exactly one mixed row — that row is the two leftovers pairing off. As drawn the three stacks are 3 + 3 = 6, 5 + 3 = 8 and 3 + 9 = 12. The totals are incidental, the mixed row is the argument.
The odd-count question (Part I, §6.2, p.130). Inputs: what happens with 3 odd numbers, then 4, then 5, then 6.
Martin and Maria (Part I, §6.2, pp.130–131). Two siblings born exactly a year apart, sharing a birthday, whose ages are claimed to total 112. The chapter offers 51 and 52 as a trial, totalling 103. Inputs: the claim, the trial, and the fact that consecutive whole numbers alternate in parity.
Whole-number alternation (Part I, §6.2, p.130). The counting numbers run even, odd, even, odd … so of any two neighbours exactly one is even. This is the fact that makes the sibling argument work and it is worth a beat of its own.

Figures to have open

Dot arrays that can be laid out in pairs and shown step by step: a single even array, a single odd array with a colour-contrasted leftover, and two odd arrays that can be pushed together. Standard schematic, but the second-colour leftover must be kept — it is the book's own device and it carries the argument.
Five boxes with plus signs and a total, plus a scatter of number cards whose values are visible. Redraw; the printed card art is the book's.
A number line or strip of the counting numbers tinted alternately, for the alternation fact in section 10.
No photograph, dataset or printed table from the textbook is required.

Where this sits in the book

NCERT Ganita Prakash, Class 7, Part I, printed Chapter 6 "Number Play", §6.2 "Picking Parity", pp.129–131 — the card puzzle and the two dot figures (p.129), the two-odds figure with the word proof, the resolution of Kishor's card puzzle and the posing of the sibling-ages question (p.130), and the last line of the sibling argument, the naming of parity and the Figure it Out set (p.131). The two resolutions are on different pages: Kishor's is settled in the body of p.130, and only Martin and Maria's carries over to the head of p.131
Same part, SUMMARY, p.145, second bullet, for the chapter's own statement of what parity is
Forward pointer: the parity of a sum, of a product and of an algebraic expression continues in the same section on pp.131–133 — The parity of a sum or product is fixed before you compute it
Solutions appendix bound after p.145 in the cached PDF (not part of the printed book), consulted only to confirm the intended verdicts on the p.131 exercises