Subtracting with tokens by first putting zero pairs in

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What to assume they know

Zero pairs: why a positive and a negative token cancel: tokens, the zero pair, and cancelling to a surplus
Subtraction as the movement that gets you from start to target: subtraction as the movement between start and target
The additive inverse, and how it turns every subtraction into an addition: the inverse, and converting a subtraction to an addition
Taking away objects from a collection, from earlier classes

What they should be able to do

Subtract by removing tokens, in the case where enough of them are present
Recognise the case in which the removal is blocked, and say precisely what is missing
State why adding a zero pair leaves the value of a set unchanged
Work out from a stated subtraction how many pairs must be added before the removal can proceed
Carry out the removal and read the answer off what remains
Explain why taking negatives out of a pile leaves a larger number behind
Check a token answer against the same subtraction done on the number line
Connect the token procedure to the conversion rule met earlier in the chapter

Where it usually goes wrong

"You cannot take away more than you have." With tokens you can, and the reason is not a rule but a picture: the pile you start with is only one of infinitely many piles worth the same amount.
"Adding zero pairs changes the answer." It changes the picture and not the value. Show the pairs going in and the running value staying put — a counter that does not move while tokens are added is worth a paragraph of words.
"Put in as many pairs as you like." You may; but putting in exactly the number needed is what makes the procedure finish in one step, and reading that number off the question is section 9's skill.
"Taking away a negative should make it more negative." It makes it less negative, and with tokens you watch it happen: reds leave the table and the greens that were paired with them are set free.
"Tokens and the number line will disagree somewhere." They do not, and section 10 exists to make the student check rather than trust. The book asks for the same check in its own words on p.258.
"The blocked case needs a different rule from the easy case." It is the same rule; the only extra step is manufacturing the tokens the rule wants.

Questions to check understanding

Subtract two integers using tokens and state the result
State how many zero pairs must be added before a stated subtraction can be done
Explain why adding zero pairs is allowed
Evaluate the same difference twice, once with tokens and once on the number line
Say what a set of tokens is worth after a stated removal
Rewrite a token subtraction as the corresponding addition
The solutions block bound with this chapter file answers the p.258 and p.259 exercises on its footer pages 7–8

Examples worth working on the board

The easy case (p.257). (+ 5) – (+ 4). Five green tokens are laid out and four of them are taken away. Checked against the printed page: the drawing shows five greens with the four leftmost struck through. Nothing has to be added because everything asked for is already present.
The second case (p.257). (– 7) – (– 5). Seven reds laid out, five struck through, two standing. The book then asks whether this is the same as adding + 5 to – 7 — a question it leaves for the reader, and the hinge between this topic and The additive inverse, and how it turns every subtraction into an addition.
The blocked case (pp.257–258). (+ 5) – (+ 6). Five greens are down and six greens are wanted. Exactly one green is missing, which is exactly how many pairs go in.
The free move (p.258). One green plus one red is added to the set. Checked against the printed page: the resolved picture shows six greens all struck through and one red standing. The argument to make is that the set's value did not change when the pair went in, so the answer read off the end is the answer to the original question.
Twelve differences (p.258). First six: (+ 10) – (+ 7); (– 8) – (– 4); (– 9) – (– 4); (+ 9) – (+ 12); (– 5) – (– 7); (– 2) – (– 6). Second six: (– 5) – (– 7); (+ 10) – (+ 13); (– 7) – (– 9); (+ 3) – (+ 8); (– 2) – (– 7); (+ 3) – (+ 15). Note the repeat: (– 5) – (– 7) appears in both lists, so the explanation can use it to show the two instructions ask for the same work.
The mixed case (p.258). + 4 – (– 6). Four greens are down and six reds are wanted, and there are no reds at all. Six pairs go in; the six reds are removed; ten greens remain. Checked against the two drawn stages.
Deciding the count (p.259). – 3 – (+ 5). Three reds are down and five greens are wanted. The book asks the student to say how many pairs are needed before it asks for the answer, which is the right order and should be kept.
Six more (p.259). (– 3) – (+ 10); (+ 8) – (– 7); (– 5) – (+ 9); (– 9) – (+ 10); (+ 6) – (– 4); (– 2) – (+ 7). Every one of these is a blocked case, which is why they come last.

Figures to have open

Token layouts in two colours with a strike-through for removal, matching the convention established in Zero pairs: why a positive and a negative token cancel so the two topics read as one model.
Dashed outlines for tokens that are wanted but absent. This is not in the printed art and it is the single addition worth making, because the shortfall is the quantity the whole procedure is driven by.
A running value counter beside the table, unchanged while pairs are added.
A number line for the side-by-side check in section 10, reused from Laying the integers out in order, and why −8 is less than −2.
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.257 — the named sub-heading on tokens for subtraction, the two straightforward cases, the question left open, and the start of the blocked case
§10.2, p.258 — the extra pair, the resolved blocked case, the twelve differences, and the mixed case with six pairs
§10.2, p.259 — the exercise that asks for the number of pairs before the answer, and the six blocked cases that close the section
§10.1, p.255, for the conversion rule this procedure enacts
Chapter Summary, p.270, for the book's statement that subtraction can always be turned into addition
Solutions block bound with this chapter file, footer pages 7–8