Removing a bracket after a minus sign flips every term inside

What to assume they know

• Every expression can be rewritten as a sum of terms — an expression re-set as a sum of terms
• Commutative and associative: why order and grouping are free — the terms of a sum may be reordered and regrouped
• Class 6 integers: the inverse of a number, and adding a negative
• Subtracting mentally in two stages (take off the tens, then the units)

What they should be able to do

• Rewrite an expression of the shape "a number minus a bracketed total" without its bracket, changing the sign of every term that comes out
• Explain that change from the meaning of subtraction rather than by quoting a rule
• Handle the case where a negative term inside the bracket emerges positive
• State that a bracket not preceded by a minus leaves its terms' signs alone, and say why
• Check a proposed bracket removal by evaluating both forms and comparing
• Predict how the value of an expression moves when one of its terms is nudged up or down, without recomputing
• Recognise that raising a term that is itself negative makes the total larger, not smaller

Where it usually goes wrong

• "Removing a bracket means rubbing it out." The expression that survives is a different string of symbols. 200 – (40 + 3) and 200 – 40 + 3 are not the same number, and the chapter makes that comparison explicitly on p.35.
• "Only the first term inside changes." Both 40 and 3 flip. This is the single most common slip, and it is why the chapter uses a two-term bracket first.
• "Everything inside becomes negative." No — every term reverses. A negative term inside emerges positive, which is precisely what happens to the −100 in Example 13. A student who converts rather than reverses will get 150 instead of 350 and will not know why.
• "A bracket after a plus needs the same treatment." Example 14 exists to say no, and to explain the difference rather than legislate it.
• "−15 must be less than −16, because 15 is less than 16." The chapter builds the whole first column of the tinker grid to catch this, then asks the question outright. Raising a negative term raises the total.
• "If a term goes up by one, the total goes up by one — always." True when the term goes up. But an exercise on p.38 changes the subtracted amount to keep a difference fixed, and there the two adjustments must move the same way, not opposite ways.
• "Two changes always cancel." Column three of the tinker grid contains a pair that cancels and a pair that does not, side by side, on purpose.

Questions to check understanding

• Remove the brackets and write an equivalent expression, with the signs varied across the set (Part I, p.37)
• Fill blanks and operation boxes so that two sides of an equality agree (Part I, p.37)
• Given a pair of expressions, guess before computing whether they are equal, then say under what conditions they would be (Part I, p.37)
• Insert brackets into an unbracketed expression so that it takes a stated value (Part I, p.38)
• Identify, without evaluating, which members of a list are equal to a given expression (Part I, p.38 and p.44)
• Judge whether a described mental shortcut always works, and justify the verdict (Part I, p.38)

Examples worth working on the board

Every one of them has a wrong candidate printed alongside the right one, and the wrong candidate is what makes the section teach.

• The opening case (Part I, §2.2, p.35): 200 – (40 + 3). Route one settles the bracket at 43 and subtracts. Route two subtracts 40 from 200 to reach 160, then subtracts 3. The chapter prints both and then draws attention to what it did not do — the version with a plus in front of the 3.
• Example 12 — Irfan again (p.35). Biscuits ₹15, toor dal ₹56, a ₹100 note. The change is worked once as 100 – (15 + 56) and once as two deductions: ₹100 less ₹15 leaves ₹85, and ₹85 less ₹56 is the change. The chapter's gloss on the intermediate ₹85 is worth keeping — it is what the shopkeeper would owe if only the biscuits had been bought.
• Example 13 — subtracting too much (p.36): 500 – (250 – 100). Settling the bracket gives 150 to take away, and the result 350. The chapter then argues that taking 250 straight off removes 100 more than was wanted, so 100 must be handed back — landing on 500 – 250 + 100. It closes by asking the student to check that 500 – 250 – 100 is a different number, which is the whole test.
• Example 14 — the harmless bracket (p.36). Hira keeps a rare coin collection in two bags, 28 in the first and 35 in the second, and gives away 10 out of the second bag. The expression is 28 + (35 – 10), which the chapter routes through 28 + (35 + (–10)) and the reordering freedom from the previous topic to reach 28 + 35 – 10, and states the value 53. Nothing inside the bracket changes sign, and the chapter says explicitly that this is because no minus stands in front of it.
• The boxed aside (p.36). A short piece of advice set in a tinted box with an owl beside it: reconstruct the sign behaviour from the meaning rather than memorising when to change and when not to. This is the chapter's own statement of the thesis and should be quoted in substance, in the wording used here.
• The three-column tinker grid (p.37). Column one is fully worked as the model: 53 + (–16) is 37, and 54 + (–16) is 38, with the reason printed underneath — 54 is one above 53, so the total is one above 37. It then leaves 53 + (–15) open, with a prompt asking whether −15 is above or below −16. Column two mirrors it downward, printing the reasoning for 52 + (–16) but leaving the total blank, and leaving 53 + (–17) open too. Column three is entirely blank: –87 + (–16), –88 + (–15), –86 + (–18), –97 + (–26). Checks available to the explanation, which should be derived rather than announced: the first two entries of column three land on the same total, because one term drops by one while the other rises by one; the third moves one further down; the fourth further still.
• Jasoda's shortcut (p.38, exercise 8). To subtract 9 she subtracts 10 and adds 1 back, and the chapter prints one instance of this. Whether it always works is the question asked.
• Exercise pairs worth using live (pp.37–38): six bracket removals built on 14, 12 and 10 with the signs varied; three same-or-different pairs including one that turns a bracketed subtraction into a bracketed pair of negatives; and a pair differing only in whether the final 1 is added or subtracted.

Figures to have open

• The tinker grid (Part I, p.37). Three boxed columns of ringed two-term sums, the first two carrying printed reasoning underneath and the third entirely open. Redraw. Checked against p.37: the entries and the blanks are exactly as listed above, and the third column carries no worked anchor at all — its anchor is the pattern set by the other two.
• A two-stage subtraction strip for section 1 — a bar of 200 with 40 taken off and then 3, against the same bar with 43 taken off in one go. Not in the book; the textbook prints no such picture on p.35.
• The boxed-aside styling (Part I, p.36) — a tinted panel with an owl. Worth echoing as a visual convention for the chapter's meta-advice, redrawn.
• A number line for section 9, marked from about −20 to 0, so that "−15 sits to the right of −16" is seen rather than argued. Not in the book; the chapter prints no number line here, which was confirmed against renderings of pp.36–38.
• No figure is needed for Examples 12, 13 or 14 beyond the expressions themselves.

Where this sits in the book

• NCERT Ganita Prakash, Class 7, Part I, printed Chapter 2 "Arithmetic Expressions", §2.2 "Reading and Evaluating Complex Expressions". Two unnumbered subheadings carry this topic: "Removing Brackets — I", pp.35–36, and "Tinker the Terms I", pp.36–38. The opening case and Example 12 are on p.35; Examples 13 and 14 and the boxed aside are on p.36; the tinker grid is on p.37; the exercise set runs pp.37–38.
• Chapter SUMMARY, Part I, p.44 — the fifth bullet states the sign change for a bracket behind a minus.
• Forward pointer: The distributive property, and using it to compute faster, the companion subheading "Removing Brackets — II" (Part I, pp.38–40), which handles a bracket standing behind a multiplication rather than behind a minus.